ANALYSIS OF THE BIOLOGICAL IMPLICATIONS OF THE MECHANICAL ENVIRONMENT WITHIN THE GROWTH PLATE DURING DEVELOPMENT IN PHYSIOLOGICAL AND PATHOLOGICAL SCENARIOS.

Presented by: JOHANA MARÍA GUEVARA MORALES

A thesis submitted in conformity with the requirements to obtain the degree of: Ph.D in Biological Sciences

Director: Luis Alejandro Barrera Avellaneda. Ph.D. Facultad de Ciencias – Pontificia Universidad Javeriana

Co-Director:

Diego Alexander Garzón Alvarado. Ph.D. Facultad de Ingeniería – Universidad Nacional de Colombia

PONTIFICIA UNIVERSIDAD JAVERIANA FACULTAD DE CIENCIAS PROGRAMA DE DOCTORADO EN CIENCIAS BIOLÓGICAS BOGOTA – COLOMBIA 2016

ARTICULO 23 DE LA RESOLUCION No. 13 DE JULIO DE 1946

“La universidad no se hace responsable por los conceptos emitidos por sus alumnos en sus trabajos de tesis. Solo velará porque no se publique nada contrario al dogma y a la moral católica y porque la tesis no contenga ataques personales contra persona alguna, antes bien sea en ellas el anhelo de buscar la verdad y justicia”

ANALYSIS OF THE BIOLOGICAL IMPLICATIONS OF THE MECHANICAL ENVIRONMENT WITHIN THE GROWTH PLATE DURING BONE DEVELOPMENT IN PHYSIOLOGICAL AND PATHOLOGICAL SCENARIOS.

Johana María Guevara Morales

______DANIEL SUAREZ. PhD. Evaluator 4

ANALYSIS OF THE BIOLOGICAL IMPLICATIONS OF THE MECHANICAL ENVIRONMENT WITHIN THE GROWTH PLATE DURING BONE DEVELOPMENT IN PHYSIOLOGICAL AND PATHOLOGICAL SCENARIOS.

Johana María Guevara Morales

______SHUNJI TOMATSU. MD. PhD. Evaluator 5

ANALYSIS OF THE MECHANICAL ENVIRONMENT WITHIN THE GROWTH PLATE DURING BONE DEVELOPMENT: PHYSIOLOGICAL AND PATHOLOGICAL IMPLICATIONS

Johana María Guevara Morales

______

CONCEPCIÓN J. PUERTA B. PhD. ALBA ALICIA TRESPALACIOS R. PhD.

Decana Facultad de Ciencias Directora Programa Posgrado

Thesis done in

Institute for the Study of Inborn Errors of Metabolism

Pontificia Universidad Javeriana

Bogotá, Colombia

Biomimetics Lab and Group of Numerical Methods

Universidad Nacional de Colombia

Bogotá, Colombia

And

Schuchman’s Lab – Genetics and Genomics Deparment

Mount Sinai School of Medicine

New York, USA

To all those who made possible this work and contributed to make of this a very enriching episode of my personal and academic life.

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ACKNOWLEDGMENTS

I apologize but I was unable to do this in English.

Primero quisiera agradecer a Dios por esta enriquecedora experiencia, por todo lo que he aprendido como persona y como investigadora, por todas las oportunidades, las lecciones, pero sobre todo por todas esas maravillosas personas que puso en mi camino de quienes he recibido mucho apoyo, muchas lecciones y con quienes he pasado muchos momentos inolvidables.

Y a mi familia, porque sin su apoyo y voz de aliento este logro no habría sido posible. Por ayudarme a levantarme cuando caí, por celebrar conmigo cada logro, por su amor incondicional. Especialmente quiero dar gracias a mis papás, las personas más importantes en mi vida, por todos sus concejos y todo el cariño que me brindan a diario. A mi tía Eliza que siempre ha sido mi ángel de la guarda, no creo poder pagar todo lo que has hecho por mí.

Muchas gracias al Dr. Barrera por acompañarme en este proceso y darme su apoyo para emprender cada aventura académica. Muchas gracias por ser quien me dio la oportunidad de formar parte del maravilloso grupo de errores innatos y permitirme llegar a ser el profesional que soy hoy en día. Gracias por guiarme y darme su apoyo no solo en lo académico sino también en lo personal. Muchas gracias doc.

Al Ing. Diego Garzón por darme la oportunidad de trabajar con él y ser parte del grupo. Gracias por toda la paciencia, por todo el tiempo y la dedicación.

A OYEP porque siempre estuvo a mi lado dándome su consejo y su apoyo. Regañándome cuando era necesario y también escuchándome en esos momentos de estrés. Gracias por ser mi amiga y mi sensei.

A mi compañera de batalla, Jokito, porque ¿qué habría sido de este camino sin tu valiosa compañía?. Gracias por los consejos, los regaños, las risas, los momentos de charlas profundas y los perros monstruo de la 45.

A Juanito por ser mi compañero, mi compinche, mi amigo y hasta mi maestro en muchos aspectos. Muchas gracias por hacer de este doctorado una de las etapas más bonitas y memorables de mi vida. Gracias por enseñarme a pensar diferente y a ver la vida con otros ojos. Gracias por ayudarme a crecer como investigador y como persona. A Miguelito por aguantarme en las buenas y en las malas. Por hacer de este un viaje divertido y por ser siempre tan especial.

A Hector porque creo que no hubiera terminado sin tu ayuda. Gracias por que a pesar de todo siempre estás ahí. Por ser mi compinche, mi par académico, mi revisor de estilo, pero sobre todo por ser un amigo incondicional.

A mis compañeros y amigos del Instituto de Errores Innatos del Metabolismo por ser mi familia académica y estar siempre ahí cuando los necesite.

A todos mis compañeros y amigos del laboratorio de biomiméticos y el grupo de métodos numéricos. Muchas gracias por recibirme y acogerme, ha sido muy grato tener la oportunidad de estar en la universidad nacional de Colombia y compartir con todos ustedes.

Al Dr. Edward Schuchmann y la Dra. Calogera Simonaro por brindarme la oportunidad de trabajar con ellos y por todo su apoyo. A Mike por su ser mi guía y por toda su colaboración.

Creo que ningún espacio será suficiente para agradecerle a todas las personas que han hecho posible este logro. A todos los que con sus conocimientos, su talento, su trabajo, sus concejos, su sonrisa, su cariño, etc, etc, han hecho parte de esta aventura académica. Son muchas muchas personas y aunque tal los nombres no estén en estos párrafos si están escritos en mi mente y en mi corazón ….

Muchas gracias a todos.

ANALYSIS OF THE MECHANICAL ENVIRONMENT WITHIN THE GROWTH PLATE DURING BONE DEVELOPMENT: PHYSIOLOGICAL AND PATHOLOGICAL IMPLICATIONS CONTENT

ABSTRACT ______14 INTRODUCTORY REMARKS ______15 1.1 INTRODUCTION ______15 1.2 OBJECTIVES ______17 1.2.1 General Aim ______17 1.2.2 Specific Aims ______17 1.3 THESIS OUTLINE ______17 2 CONCEPTUAL FRAMEWORK ______19 2.1 SKELETAL SYSTEM ______19 2.2 ANATOMY AND DEVELOPMENT ______20 2.3 THE GROWTH PLATE ______22 2.3.1 Hyaline ______24 2.4 ENDOCHONDRAL ______33 2.4.1 Differentiation ______34 2.5 BIOCHEMICAL REGULATION OF LONG BONE GROWTH ______39 2.5.1 Local Factors ______39 2.5.2 Systemic Factors ______44 2.6 MECHANICAL INFLUENCES ON LONG BONE GROWTH AND GROWTH PLATE ______45 2.6.1 Mechanical Effects on Behavior ______46 2.6.2 Mechanotransduction ______49 2.7 IN SILICO APPROXIMATIONS TO BONE GROWTH AND MORPHOGENESIS. THE ROLE OF STRAINS AND PRESSURES. ______50 2.7.1 Computational Models ______50 2.8 ABNORMALITIES IN LONG BONE DEVELOPMENT ______52 2.8.1 Chondrodysplasias ______53

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3 GROWTH PLATE STRESS DISTRIBUTION DURING BONE DEVELOPMENT 56 3.1 INTRODUCTION ______56 3.2 MATERIALS AND METHODS ______58 3.2.1 Model ______58 3.2.2 Loading conditions and constrains ______61 3.2.3 Data Analysis ______62 3.3 RESULTS ______63 3.3.1 Stress distribution during development ______63 3.3.2 Growth plate effect on epiphyseal OI distribution ______66 3.3.3 SOC effect on epiphyseal stress distribution ______66 3.3.4 Growth plate OI distribution ______67 3.4 DISCUSSION AND CONCLUSIONS ______69 4 ANALYSIS OF THE ASSOCIATION BETWEEN MECHANICAL ENVIRONMENT AND GROWTH PLATE MORPHOLOGICAL EVOLUTION DURING PROXIMAL FEMUR DEVELOPMENT. ______73 4.1 INTRODUCTION ______73 4.2 MATERIALS AND METHODS ______75 4.2.1 Geometric Model ______75 4.2.2 Mechanical Stimuli ______76 4.2.3 Part 1: Influence of Growth Plate Shape on Stimuli Behavior ______77 4.2.4 Part 2: Influence of Stimuli Behavior on Growth Plate Shape ______80 4.3 RESULTS ______83 4.3.1 Influence of Growth Plate Shape on Stimuli Behavior ______83 4.3.2 Stimuli Behavior through bone development ______85 4.3.3 Influence of Stimuli Behavior on Growth Plate Shape ______87 4.4 DISCUSSION AND CONCLUSIONS ______90 5 CELLULAR SCALE MECHANOBIOLOGICAL MODEL OF GROWTH PLATE. AN IN SILICO MODEL OF CHONDROCYTE’S HYPERTROPHY. ______94 5.1 INTRODUCTION ______94 5.2 MATERIALS AND METHODS ______95 5.2.1 Mathematical Model ______96 5.3 RESULTS ______106 5.3.1 Physiological Cases ______106 5.3.2 Biochemical sensitivity analyses ______110 5.4 DISCUSSION AND CONCLUSIONS ______115

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6 STUDY OF GROWTH PLATE PATHOLOGY IN THE RAT MODEL OF MUCOPOLISACCHARIDOSIS TYPE VI. AN EXPERIMENTAL AND COMPUTATIONAL APPROACH. ______118 6.1 INTRODUCTION ______118 6.2 MATERIALS AND METHODS ______119 6.2.1 Animals ______119 6.2.2 Sample Collection ______119 6.2.3 Histological analysis ______120 6.2.4 Immonuhistochemistry ______120 6.2.5 Quantitative analysis of growth plates ______120 6.2.6 Mechanical testing ______122 6.2.7 Statistical analysis ______122 6.2.8 In silico analysis of epiphyseal stress distribution ______123 6.3 RESULTS ______124 6.3.1 Growth Plate Histological Characteristics ______124 6.3.2 Mechanical Testing ______129 6.3.3 In silico analyses ______130 6.4 DISCUSSION ______131 6.5 CONCLUSION ______136 7 FINAL CONCLUSIONS AND PERSPECTIVES ______138 APPENDIX A. Growth plate stress distribution implications during bone development: a simple framework computational approach. ______142 APPENDIX B. Supplementary Material Appendix A – Chapter 3 ______153 Supplementary 1. Analysis of the effect of material properties transition on epiphyseal stress distribution. ______153 Supplementary 2: Cartilaginous epiphyseal (Stage 1) osteogenic index (OI) distribution for all simulations performed. ______155 Supplementary 3: Osteogenic index (OI) distribution in an with SOC (stage 2) for all simulations performed. ______156 Supplementary 4: Mesh convergence analysis. ______157 Supplementary 5: Optimum k value estimation. ______158 Supplementary 6-7-8: Osteogenic index distribution for non-straight morphologies. ___ 159 APPENDIX C Supplementary results chapter 4 ______163 Morphologies used for analysis of stimuli behavior through normal human femur development ______163 Changes in stimuli mean values (퐃) and variations (퐂퐕) during growth ______163

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APPENDIX D. A quantitative and qualitative growth plate description: a simple framework for chondrocytes columnar arrangement evaluation ______165 APPENDIX E. LIST OF PUBLICATIONS ______181 REFERENCES ______183

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LIST OF FIGURES

FIGURE 2-1. SCHEMATIC REPRESENTATION OF LONG BONE FORMATION THROUGH ENDOCHONDRAL OSSIFICATION...... 21 FIGURE 2-2. HISTOLOGICAL CHARACTERISTICS OF THE GROWTH PLATE...... 23 FIGURE 2-3. SHEMATIC REPRESENTATION OF AGGRECAN STRUCTURE...... 29 FIGURE 2-4. TISSUE EFFECTS OF COMPRESSIVE LOADING...... 46 FIGURE 3-1. GENERIC BONE GEOMETRY...... 60 FIGURE 3-2. GROWTH PLATE CHARACTERISTICS...... 61 FIGURE 3-3. LOADING CONDITIONS, CONSTRAINS AND DATA ANALYSIS...... 62 FIGURE 3-4. CARTILAGINOUS EPIPHYSEAL STRESS DISTRIBUTION (STAGE 1)...... 64 FIGURE 3-5. STRESS DISTRIBUTION WITHIN THE EPIPHYSIS AND GROWTH PLATE...... 65 FIGURE 3-6. CARTILAGINOUS EPIPHYSIS OI DISTRIBUTION...... 66 FIGURE 3-7. OSTEOGENIC INDEX (OI) DISTRIBUTION IN AN EPIPHYSIS WITH SOC...... 67 FIGURE 3-8. GROWTH PLATE OSTEOGENIC INDEX (OI) DISTRIBUTION FOR ALL CONDITIONS SIMULATED...... 68 FIGURE 3-9. GROWTH PLATE HORIZONTAL OI VALUE DISTRIBUTION ACCORDING TO MORPHOLOGY...... 68 FIGURE 4-1. GEOMETRIC BONE GEOMETRY...... 76 FIGURE 4-2. GENERATION OF GROWTH PLATE MORPHOLOGIES FOR PART 1...... 78 FIGURE 4-3. GENERATION OF GROWTH PLATE FOR PART 2 SIMULATIONS...... 80 FIGURE 4-4. DISTRIBUTION OF THE MEAN STIMULI VALUES (D) AMONG THE MORPHOLOGIES ANALYZED...... 83 FIGURE 4-5. DISTRIBUTION OF GROWTH PLATE VARIATION OBSERVED FOR EACH STIMULUS (CV) AMONG THE MORPHOLOGIES ANALYZED...... 84 FIGURE 4-6. MORPHOLOGIES FOR WHICH MAXIMUM AND MINIMUM D AND CV WERE OBTAINED...... 85 FIGURE 4-7. COMPARISON AMONG MORPHOLOGIES USED FOR ANALYSIS OF STIMULI BEHAVIOR THROUGH NORMAL HUMAN FEMUR DEVELOPMENT...... 86 FIGURE 4-8. STIMULI TRENDS OBSERVED FOR EACH STIMULI IN THE CONTEXT OF NORMAL HUMAN FEMUR DEVELOPMENT...... 88 FIGURE 4-9. MORPHOLOGIES OBSERVED IN THE PREDICTIVE SIMULATION OF GROWTH PLATE GROWTH UNDER THE INFLUENCE OF S, SY, P AND OI INDEPENDENT STIMULATION...... 89 FIGURE 5-1. WORK DOMAIN GRAPHICAL DESCRIPTION...... 96 FIGURE 5-2: BOUNDARY AND LOAD SETTINGS APPLIED TO THE Ω DOMAIN...... 97 FIGURE 5-3: DIAGRAM REPRESENTING IHH-PTHRP REGULATORY LOOP...... 98 FIGURE 5-4. GRAPHIC REPRESENTATION OF BIOCHEMICAL BORDER CONDITIONS IN THE WORK DOMAIN...... 100 FIGURE 5-5. GRAPHICAL REPRESENTATION OF PTHRP CONCENTRATION 푆푃 AS FUNCTION OF IHH CONCENTRATION 푆퐼...... 100 FIGURE 5-6. GRAPHICAL REPRESENTATION OF HYPERTROPHY TIME (T), TIME FRAME OF IHH PRODUCTION 휏ℎ, AND SIMULATION TIME 푡푠...... 102 FIGURE 5-7. GRAPHICAL REPRESENTATION OF IHH CONCENTRATION 푆퐼 AS FUNCTION OF PTHRP CONCENTRATION푆푃...... 102 FIGURE 5-8. CELL GROWTH FUNCTION 훾푡. GRAPHICAL REPRESENTATION OF THE FUNCTION 훾푡 WHEN Β=8.5, Θ=1.4 AND K=1X105...... 105 FIGURE 5-9. DOMAIN GROWTH FOR UNLOADED CASE...... 107

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FIGURE 5-10. IHH AND PTHRP CONCENTRATION CHANGES OVER TIME FOR NORMAL CASES (UNLOADED, TENSION AND COMPRESSION)...... 108 FIGURE 5-11. MAXIMUM CELL HEIGHT ACHIEVED DURING SIMULATION TIME...... 109 FIGURE 5-12. FINAL COLUMN HEIGHT AT THE END OF SIMULATION TIME FOR ALL CASES...... 110 FIGURE 5-13. IHH AND PTHRP CONCENTRATION CHANGES OVER TIME WHEN IHH PRODUCTION IS SUPPRESSED (UNLOADED, TENSION AND COMPRESSION)...... 111 FIGURE 5-14. IHH AND PTHRP CONCENTRATION CHANGES OVER TIME WHEN PTHRP PRODUCTION IS ABOLISHED (UNLOADED, TENSION AND COMPRESSION)...... 112 FIGURE 5-15. IHH AND PTHRP CONCENTRATION CHANGES OVER TIME WHEN PTHRP PRODUCTION IS DECREASED...... 113 FIGURE 5-16. IHH AND PTHRP CONCENTRATION CHANGES OVER TIME WHEN IHH PRODUCTION IS DECREASED...... 114 FIGURE 6-1. IMAGE PROCESSING FOR QUANTITATIVE ANALYSIS OF GROWTH PLATE CHARACTERISTICS...... 121 FIGURE 6-2. GRAPHICAL REPRESENTATION OF THE CELL DISTRIBUTION DESCRIPTORS ALONG THE DIFFERENT PHYSEAL ZONES...... 122 FIGURE 6-3. WORK DOMAIN GRAPHICAL DESCRIPTION...... 124 FIGURE 6-4. HISTOLOGICAL CHARACTERISTICS OF GROWTH PLATES FROM 4-DAY-OLD WT AND MPS VI RATS...... 124 FIGURE 6-5. HISTOLOGICAL CHARACTERISTICS OF GROWTH PLATES FROM 1-MONTH-OLD WT AND MPS VI RATS...... 126 FIGURE 6-6. MICROSCOPIC IMAGES OF DISTAL FEMUR EPIPHYSES OF WT AND MPS VI ANIMALS...... 127 FIGURE 6-7. HISTOLOGICAL CHARACTERISTICS OF GROWTH PLATES FROM 3-MONTH-OLD WT AND MPS VI RATS...... 128 FIGURE 6-8. HISTOLOGY-BASED ANALYSIS OF EXTRACELLULAR MATRIX COMPOSITION IN WILD TYPE AND MPS VI RATS...... 129 FIGURE 6-9. CALCULATED YOUNG MODULUS (E) IN CHONDROEPIPHYSES OF 4-DAY-OLD WILD TYPE AND MPS VI RATS...... 129 FIGURE 6-10. OSTEOGENIC INDEX (OI) DISTRIBUTION CONSIDERING DIFFERENT YOUNG MODULUS (E) VALUES...... 130 FIGURE 6-11. PREDICTED STRESS DISTRIBUTION WITHIN WILD TYPE AND MPS VI GROWTH PLATES AT 1 MONTH OF AGE...... 131 FIGURE 6-12. IHH AND PTHRP CONCENTRATION CHANGES OVER TIME FOR A NORMAL AND AN INCLINED GROWTH PLATE COLUMN...... 133

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LIST OF TABLES

TABLE 2-1. SUMMARY OF TIMES FOR SECONDARY OSSIFICATION APPARITION (SOC) AND PHYSEAL CLOSURE IN SOME LONG AS DESCRIBED IN [11]...... 22 TABLE 2-2: GLYCOSAMINOGLYCANS (GAGS) STRUCTURAL CHARACTERISTICS [54, 55]...... 28 TABLE 2-3: PROTEOGLYCANS PRESENT IN CARTILAGE [41, 55]...... 30 TABLE 2-4. CLASSIFICATION OF THE MUCOPOLYSACCHARIDOSES (MPS) ...... 54 TABLE 3-1. TISSUE MATERIAL PROPERTIES. ELASTIC MODULUS AND POISSON’S RATIO FOR CARTILAGE, BONE, AND RANVIER’S GROOVES AS ESTABLISHED BY PISZCZATOWSKI [275]...... 59 TABLE 4-1. TISSUE MATERIAL PROPERTIES. ELASTIC MODULUS AND POISSON’S RATIO FOR CARTILAGE, BONE, AND RANVIER’S GROOVES AS ESTABLISHED BY PISZCZATOWSKI2011 [275]...... 76 TABLE 4-2. SPECIFIC FORMULATION USED FOR 푆(푥𝑖) IN EQUATION 6...... 82 TABLE 4-3. RANGE OF VALUES TO WHICH GROWTH PLATE IS RESPONSIVE TO MECHANICAL STIMULATION ...... 82 TABLE 5-1: MECHANICAL PROPERTIES FOR EACH TISSUE INCLUDED IN THE MODEL...... 97 TABLE 5-2. PARAMETERS USED IN THE MODEL...... 105 TABLE 6-1. HISTOMORPHOLOGICAL MEASUREMENTS OF WILD TYPE AND MPS VI GROWTH PLATES...... 125 TABLE 6-2. COLUMN ORIENTATION ANGLE AND COEFFICIENT OF VARIATION FOR WILD TYPE AND MPS VI GROWTH PLATES...... 126

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ABSTRACT

The growth plate is a cartilaginous tissue located in the of long bones that is responsible for their longitudinal growth. Such process is regulated in part by mechanical factors. In order to establish possible associations between specific mechanical stresses and biological responses in normal and pathological conditions, here it is presented a combined computational and experimental approach to this issues. Thus, initially we analyzed the mechanical environment within the growth plate at different developmental stages under physiological conditions, using finite element analysis. Then a mechanobiological model of cellular behavior within the growth plate was formulated, integrating biochemical, structural and mechanical factors. Finally, growth plate pathology was studied histologically in a genetic chondrodysplasia (MPS VI), and the potential effects of the observed abnormalities were explored using in silico modeling. Our results suggest that mechanical stimulation may play different roles during bone development. In addition, for the first time, it was described histologically the progression of the growth plate involvement in the rat model of MPSVI mainly characterized by loss of columnar arrangement. Moreover, it was evidenced that structural abnormalities observed in MPS VI growth plates rather than mechanical alterations may be an important factor contribution to skeletal pathology in this disease. This project is the first step towards the development of new methodological approaches involving combined experimental and computational approaches to study growth plate behavior in physiological and pathological scenarios. Furthermore, results derived from this work will help elucidate mechanical events taking place within the growth plate and epiphysis during long bone growth. Additionally, the information generated may be useful to formulate hypotheses regarding mechanical influences on biological events taking place in normal and MPS bone growth.

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INTRODUCTORY REMARKS

1.1 INTRODUCTION

During embryonic development, long bones are formed from a cartilaginous mold (anlagen) through a process of cartilage ossification, known as endochondral ossification. Throughout this process, chondrocytes within the tissue undergo a series of phenotypical changes towards a terminal hypertrophic state that promotes tissue calcification. This process is continued after birth, in a structure known as growth plate, which is responsible for long bone elongation.

Endochondral ossification is mainly regulated by genetic, biochemical and environmental factors. However, since mid 1800’s it was suggested, based on clinical observations, that mechanical factors may also be involved in such regulation. Currently, several in vivo studies have evidenced the influence of mechanical loading on early anlagen ossification, growth rates in long bones, growth plate cellular functions and formation. Furthermore, in vitro studies have supported such observations by demonstrating that mechanical stimulations of chondrocytes cell cultures induces changes in cell proliferation, synthesis of extracellular matrix molecules, morphogens, among other cellular responses. However, specific details regarding the characteristics of mechanical stimuli triggering biological responses are poorly understood, since it is difficult to perform experimental approaches to evaluate the mechanical environment in vivo. Thus, in order to better understand mechanical influences on bone development, computational studies have explored the characteristics of the mechanical stimuli experienced by bones during development and their potential biological implications.

Studies available in literature have mainly focused on early anlagen ossification, epiphyseal development and joint formation. These studies constitute important theoretical approximations that generate basic knowledge that will improve the understanding of growth plate mechanical regulation in normal conditions. Moreover, they constitute valuable theoretical scenarios to approach the potential role of mechanical stimuli in the development of bone pathologies associated to acquired or congenital alterations leading to abnormal loading patterns, as well as genetic diseases that alter tissue composition and therefore tissue

15 mechanical properties. In this context, generation of such knowledge is a key step towards the development of new therapies and improve decision making processes regarding available orthopedic treatments for acquired or genetic bone pathologies associated to abnormal mechanical environments.

Up to know, few studies have analyzed in detail the mechanical environment, specifically within the growth plate during normal bone development. Therefore, there is still limited knowledge regarding the role of specific mechanical stimulus in growth plate ossification and their potential role in physiological and pathological scenarios. Taking this into account, the aim of this thesis was to analyze the mechanical stress distribution within the growth plate and its potential implications in biological responses using a combined computational and experimental approach. Thus, relationships between mechanical environment and normal growth plate processes such as growth rates and morphological changes were addressed. Furthermore, pathological alterations were also explored using a specific genetic disorder as an example.

In this work, initially computational modeling was used to analyze normal growth plate mechanical and cellular behavior. In the first case, the method of finite element analysis was implemented on a bone scale in order to analyze the mechanical environment within the growth plate at different developmental stages under physiological conditions. In addition, a cellular scale mechanobiological model of growth plate chondrocyte behavior was developed in order to better understand potential interactions among mechanical, biochemical and structural factors in the normal process of chondrocyte hypertrophy. Finally, mechanical and structural alterations were evaluated experimentally in a pathological conditions. For such purposes, the mucopolysaccharidosis type VI (MPS VI) was used as a prototype of genetic disease, since this is characterized clinically by a severe skeletal malformations and alterations in the composition of the extracellular matrix of cartilage and therefore growth plate. Moreover, the computational models here developed were used to approach the potential consequences of the abnormalities observed on bone development.

Results of the in silico analysis of the mechanical environment within the growth plate during normal bone development show that stress distribution patterns coincide with growth plate histological arrangement, and it variates during bone development. Furthermore, the results of the detailed analysis of different stimuli suggest that mechanical stimulation may play diverse roles during bone development. Moreover, results derived from this thesis suggest that mechanical stimulation may also play a role in the progression of bone pathology in genetic bone diseases. Thus, mechanical properties of MPS VI bones were assessed for the first time at early developmental stages. In addition, by computational modeling, it was predicted that pathological changes in extracellular matrix properties generate alterations in

16 the stress distribution patterns that may be involved in the development of growth plate and epiphyseal ossification disturbances. Additionally, the development of a mechanobiological model allowed a further insight at cellular level effects of mechanical and structural disturbances identified in MPS VI growth plates.

This project constitutes the first step towards the development of new methodological approaches focused on understanding regulation of long bone development. The results derived from this work contribute to elucidate mechanical events taking place within the growth plate and epiphysis during long bone growth, allowing the formulation of hypotheses regarding mechanical-biological interactions in normal and pathological conditions, as a contribution for the development of novel therapeutic approaches for diseases affecting long bone development.

1.2 OBJECTIVES

1.2.1 General Aim

To study the potential biological implications of the mechanical environment in the physiology and pathology of the growth plate.

1.2.2 Specific Aims

1. To describe the mechanical environment within the growth plate during normal bone development. 2. To develop a cell scale mechanobiological model representing interactions among biochemical, structural and mechanical factor in cellular behavior within normal growth plates. 3. To analyze the mechanical environment in pathological growth plates using MPS VI as a study model.

1.3 THESIS OUTLINE

The work here presented was performed in collaboration with the group of numerical methods from Universidad Nacional de Colombia (GNUM) and Schuchman’s Lab in the genetics and genomics department from Mount Sinai School of Medicine. The thesis conceptual framework, methodological approach, results, discussion and conclusions

17 contained within this document are organized in 7 chapters. Chapter 1 corresponds to this introductory section. In Chapter 2 a conceptual framework that summarized anatomical aspects, structural details and regulatory mechanisms associated to bone development and growth plate physiology is presented. This chapter includes a brief description of the skeleton and its process of development in humans, focused specifically in long bone development. Additionally, there are descriptions regarding anatomical and structural aspects of cartilage and growth plate, the process of endochondral ossification, as well as biochemical and mechanical regulation that influence the latter. To close this chapter it is included a brief description of some pathologies associated to altered endochondral ossification.

Chapters 3 and 4, include the approximations used to achieve the first objective of this thesis. Therefore, Chapter 3 contains a description of the mechanical environment within the growth plate at four different developmental stages under physiological conditions, using finite element analysis. Besides, in Chapter 4, the mechanical environment after epiphyseal ossification is further analyzed using the proximal femur as model of study. Thus, the computational model developed explored the relationship of mechanical stimuli and the growth plate morphological changes observed in that period of time.

Once explored the mechanical environment and its potential relationships to bone ossification patterns in the context of the normal bone development at a bone scale, a mechanobiological model of growth plate chondrocytes behavior was developed. Thus, in Chapter 5 it is described the development of a cellular scale mechanobiological model that integrates structural, mechanical and biological factors, as a platform to study interactions among those factors in normal and pathological conditions.

To end the analysis proposed, in Chapter 6 the characteristics of growth plate pathology in a genetic bone disease are analyzed. For such purposes, here we used a genetic disease that affects the degradation of an extracellular matrix component as study model: the muchopolysaccharidosis type VI (MPS VI). This disease was selected considering that stress distribution in the tissue is largely regulated by the composition of the ECM; thus we hypothesized that long bone alterations in MPS VI are related to an abnormal mechanical response due to ECM biochemical modifications. Therefore, this chapter summarizes the experimental methodology used for characterizing structurally and mechanically the growth plate pathology observed in the rat model of MPS VI at different stages of development, as well as the details of the computational modelling used to analyze the growth plate pathology observed in this disease.

Lastly, the main conclusions derived from this work are presented in Chapter 7, altogether with some limitations, perspectives and recommendations for future works.

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2

CONCEPTUAL FRAMEWORK

2.1 SKELETAL SYSTEM

The skeleton constitutes the body’s protection and support system. It is composed by the set of hard mineralized tissue elements (Bone) and the soft tissue present at the inter-element interface (Cartilage) [1-3].

The functions of skeletal system include:

 Protection. Bones cover most of soft tissues within the body.  Support. Skeleton acts as the body shape framework and it holds body posture.  Movement. Body movement results from orchestrated interactions between muscles and bone elements.  Blood cell production. Haematopoiesis occurs within the in long bones.  Storage. Bones matrix acts as reservoir for phosphate and calcium ions.  Endocrine regulation. Bone cells produce osteocalcin, a protein involved in calcium homeostasis, as well as glucose and lipid metabolism.

The human skeleton is formed by about 200 elements that can be classified taking into account different characteristics including: shape, location, and origin. According to their shape they can be: flat (e.g. skull, ribs, scapula), long (e.g. femur, humerus, phalanges), short (e.g. carpals and tarsals), and irregular (e.g. vertebral bodies). Regarding the location within the human body, skeletal elements are referred as axial or appendicular. The first group includes the bones located in the central region of the body (skull, vertebral column, sternum and ribs); in contrast, the appendicular skeleton includes the bones of the upper and lower extremities including the shoulder and pelvic girdle (scapulae, clavicle and hip bones) [4, 5]. Finally, according to their origin, there are intramembranous and endochondral bones. Such classification is based on the fact that during embryonic development, bone tissue formation (osteogenesis) is attained through two different mechanisms. Intramembranous ossification, occurring mainly in flat bones (including skull, clavicles and mandible), implies bone generation directly from mesenchymal cells. On the other hand, during endochondral

19 ossification, mesenchymal tissue first differentiates into a cartilage mold that is gradually replaced by bone. Endochondral ossification gives rise to limb bones and the vertebral column [1, 2, 6].

2.2 LONG BONE ANATOMY AND DEVELOPMENT

The term long bone refers to the skeletal element characterized for their elongated shape. Thus, long bones are larger than they are wide and comprise the bones of the upper and lower limbs: humerus, radius, ulna, femur, tibia, fibula, metacarpals, and phalanges [4, 7].

Long bones are anatomically divided in three different segments known as epiphysis, metaphysis and . The epiphysis refers to the ends of the bone, which are termed proximal or distal according to their proximity to the central axis of the body. Epiphyses are formed by a thin layer of compact bone surrounding trabecular or spongy bone, filled with red bone marrow; furthermore, epiphyses are covered by a layer of cartilage in the areas involved in articulations (articular cartilage). Diaphysis is the central portion of the bone. It is formed of a cylinder of compact bone that encloses the medullar or marrow cavity that contains mainly adipose tissue (yellow marrow). Finally, the metaphysis is the funnel shaped region that connects diaphysis and epiphysis. During long bone growth, this region contains the growth cartilage or growth plate, structure responsible for longitudinal growth (see next section) [4, 8, 9].

Long bone development starts from very early during embryonic development. Long bones are derived from the lateral plate mesoderm, where mesenchymal condensation of cells surrounded by ectoderm protrude from the ventrolateral zone of the body () around the first month of prenatal life in humans [2, 10, 11]. Embryological development of both limbs is similar, however, the timing differs such that lower is delayed by around 2 days [11]. Between week 5 and 8, and in a time lapse of approximately 1 month, the limb bud fully develops. During this time limb bud flattens and initiates distal elongation; along this process, mesenchymal condensation eventually will undergo segmentation forming three sections: stylopodium, zeugopodium and autopodium. In these sections, mesenchymal cells will differentiate into chondrocytes to form cartilage molds (anlagen) for future bones of the upper arm, forearm and hand respectively [12]. This differentiation initiates in the proximal elements and finishes at the most distal ones [12, 13].

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Figure 2-1. Schematic representation of long bone formation through endochondral ossification. A. Anlagen B. Initiation of endochondral ossification. Figure represents the hypertrophic differentiation of chondrocytes in the central region. C. Vascular invasion of the central hypertrophic region. D. Calcification of the matrix within hypertrophic region and posterior osteoblastic differentiation leading to the formation of the primary ossification center (POC). At this stage chondrocytes surrounding POC acquire columnar organization. E. Formation of the secondary ossification center in the epiphyses. F. Bone conformation after epiphyseal ossification is completed. At this stage two cartilage regions are evident within the bone: articular cartilage and growth plate. G. Final adult bone conformation after growth plate closure.

Between 7th and 12th gestational week, anlagen start undergoing ossification in the central portion of the cartilaginous elements forming the primary ossification center (POC) by a process known as endochondral ossification. Within POC starts matrix mineralization as well as vascular invasion of the tissue forming the so called primary spongosium (Figure 2-1A- D). POC will grow from the center to the bone ends such that by birth the diaphysis will be completely ossified and the epiphysis completely cartilaginous. As POC expands, the proliferating chondrocytes acquire a flattened shape and those near the ossification front organize in columns parallel to the bone growth axis, forming the growth plate (Figure 2-1D) [1, 9, 14-18].

Next stage in bone development implies ossification of epiphysis, which occurs in a process analogous to the POC and starts by the onset of the so called Secondary Ossification Center (SOC) in the central area of epiphyses (Figure 2-1E). Ossification of the SOC will extend radially until complete ossified epiphysis is attained. These events occur over a long period of time between neonatal period to puberty and vary according to the bone (Table 2-1).

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Table 2-1. Summary of times for secondary ossification apparition (SOC) and physeal closure in some long bones as described in [11].

Bone SOC apparition Physeal closure Proximal Humerus Birth – 6 months 13 - 20 years Distal Humerus 2-10 years 13 - 20 years Proximal Radius 5 years 12 - 17 years Distal Radius 1 -2 years 14 - 20 years Femoral head 6 months – 1 year 12 - 19 years Distal femur 3-6 years 14 - 20 years

All through bone ossification, even after epiphyseal ossification is completed, a region of cartilage is preserved, where continuous endochondral ossification takes place and drives bone elongation. Such structure is known as growth plate and it is active in humans until the end of adolescence when it is completely ossified and the bone acquires its final adult structure (Table 2-1; Figure 2-1 E and F). At the same time, and even after elongation has stopped, bones also increase in diameter by a process called appositional growth. This process implies subperiosteal deposition of bone derived from present in the and resorption of bone at the medullar side by [8].

2.3 THE GROWTH PLATE

The growth plate, physis or is a specialized type of , present in the metaphysis of long bones [9, 19, 20]. It is responsible for longitudinal growth of such bones by endochondral ossification in a process analogous to the development of the primary ossification center [14].

Histologically, growth plate is organized in four zones that illustrate different stages of chondrocytes terminal differentiation process characteristic of endochondral ossification. These zones are organized from the epiphyseal to the diaphyseal side in resting, proliferative, hypertrophic and calcification zones (Figure 2-2). Size of each zones within growth plate, in humans, similar to other big mammals, reserve zone constitutes most of the growth plate, while in rodents it does not exceed 10% [21, 22].

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Figure 2-2. Histological characteristics of the growth plate. A. Image corresponding to a longitudinal section of the distal femoral epiphysis of a 4-day-old rat (H&E, 20X magnification). B. Scheme representing histological organization of the growth plate.

The first one is called resting zone and it is structurally similar to hyaline cartilage. It contains progenitor cells and chondrocytes with rounded morphology. Cells in this zone are characterized by low proliferation rates and they are spread in the tissue with high amounts of ECM among them [1, 14, 23, 24]. It has been proposed that this zone plays an important role in determining growth orientation [25].

Towards the diaphysis, the second zone is called proliferative, there chondrocytes acquire flattened shape and they are characterized by their high proliferative rate. Additionally, within this zone chondrocytes get organized in columns oriented parallel to the growth axis [1, 14]. Columnar arrangement is conserved in the following growth plate zones, providing growth orientation. In fact, loss of columnar arrangement is observed in several skeletal dysplasias [26-28].

The third zone is formed by chondrocytes that have initiated their terminal differentiation to hypertrophic chondrocytes. Such cells are no longer proliferating and increase their cellular volume by five to ten times compared to reserve zone depending on species, specific bones and age [14, 29-32]. Such increase in volume is considered to be the main contributor to long bone longitudinal growth, accounting for around 50% of long bone growth [21, 32].

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Furthermore, hypertrophic chondrocytes are responsible for initiating ECM changes that will favor its calcification [14, 16].

Finally, there is a fourth zone formed by calcified cartilage that is in direct contact with diaphyseal bone. In this zone hypertrophic chondrocytes have undergone programmed cell death and ECM is calcified. In this region it can be observed active invasion by cells of osteogenic linage including osteoblasts and osteoclasts, as well as vascular invasion[1].

Continued proliferation and hypertrophy within growth plate allow longitudinal bone growth. As time goes by, growth plate experiences a senescence process, characterized by decrease in chondrocytes number in all three zones, as well as their proliferative rate, leading to a gradual growth plate thinning. In some species, this process is followed by a complete ossification of the growth plate, connecting the epiphysis and metaphysis, in a process known as epiphyseal fusion [23, 24, 32-35]. This process varies among species and even among bones, in humans it is completed following puberty [1, 11, 32]. During growth plate senescence, summed to the quantitative changes above mentioned, it has been observed a decrease in terminal hypertrophic chondrocytes size, particularly in rodents, and loss of columnar arrangement [24, 33, 36]. Up to now, the mechanisms regulating such process are not well understood; however, it has been proposed that it is the result of an intrinsic cell- cycle counting mechanism of reserve zone precursors instead of an age driven systemic changes. Such theories are derived from in vivo transplantation studies where growth rate of the transplanted growth plate depends on donor rather than recipient age, indicating that growth plate chondrocytes retain their previous growth history [24, 33, 34]. Furthermore, effects of estrogens on growth plate senescence have shown to be mediated by alterations in chondrocyte proliferation [34, 37].

2.3.1 Hyaline Cartilage

Hyaline cartilage is an avascular and hyperhydrated tissue, with water accounting for 60- 90% depending on anatomical localization [20, 38]. Structurally, the tissue is formed by only one type of cell population, the chondrocytes, that constitute less than 10% of the volume of the tissue [20, 38, 39]. These cells are in charge of synthetizing and maintaining high amounts of an intercellular matrix rich in collagens and proteoglycans [20, 38]. This matrix is organized such that two different areas can be distinguished based on localization and composition: a pericellular matrix (PCM) and the extracellular matrix (ECM) [40, 41].

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2.3.1.1 The Chondrocyte

Chondrocytes are a heterogeneous group of cells that display differences in shape, proliferative capacity and biosynthetic activity according to their localization [42]. Thus, within articular cartilage and growth plate, different chondrocyte population can be distinguished. As such, in articular cartilage chondrocytes on the surface are flattened and synthetize mainly collagen type II. In a medium-depth zone the cells are rounded with higher biosynthetic activity with high production of collagen type II and PG. Finally, in the deepest zone chondrocytes acquire a columnar organization and they synthetize mainly aggrecan. Likewise, in the growth plate three main chondrocyte populations can be distinguished: resting, proliferative and hypertrophic chondrocytes that will be further described in following sections [42, 43].

Chondrocytes are in charge of maintaining the ECM by synthetizing and degrading their components. Thus, they are characterized by actively synthesizing collagens type II, IX, XI and aggrecan mainly. Additionally, they express the enzymatic battery required for:

1) Glycosaminoglycans (GAGs) synthesis including several types of specific glycosyltranferases, epimerases and sulphatases [38, 44]. 2) ECM structure modification, including lysil-oxidases and lysil-hydrolases, in charge of posttranslational modification of collagen fibers, promoting their crosslinking which stabilize their structure allowing a better stretch endurance [38, 44]. 3) Modifications of GAGs sulphatation pattern, in charge of extracellular sulphatases, that regulate osmotic properties of the tissue [44]. 4) Degradation of ECM components. These include extracellular acting proteins such as several members of MMPs (metalloproteinase), and ADAMTs (Desintegrins and Metalloproteinase with Trombospondin Motifs) families, of which MMP-13 y ADAMTS 4,5 play a central role [44, 45]. It has been described the participation of other enzymes in ECM degradation, such as serine-proteases which act on collagen, proteoglycans (PG) and other glycoproteins [44, 45]. Degradation of ECM molecules fragments generated by extracellular enzymes is completed by a set of intracellular, lysosomal enzymes that include acid proteases, sulfatases and glycosidases that act on protein and GAGs fragments respectively. All these enzymes are involved in processes of tissue growth and remodeling, which are essential for endochondral ossification [38, 44, 46, 47].

Chondrocytes interact with their extracellular environment, sensing biochemical and physical stimuli through their membrane proteins that include growth factor receptors, ECM anchorage proteins and ion channels [48].

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As most eukaryotic cells, chondrocytes also present a primary cilium, an organelle consisting of a microtubule projection out of the cell that is recovered by a specialized cell-membrane, which is mainly associated to sensing and signaling functions. Such cilium is elongated from a centriole derived structure known as basal body. In chondrocytes such cilium is non motile and is formed by 9 microtubule doublets arranged in a cylindrical conformations. The cell membrane in the cilium is enriched with integrins, calcium channels, G proteins. The cilium in its base is tightly associated to Golgi apparatus and projects into the ECM interacting with collagens types IV and II. In chondrocytes, it has been implicated in mechanosensing, and some morphogen signaling as will be further described in following sections [49-51].

2.3.1.2 Extracellular Matrix (ECM)

Extracellular Matrix (ECM) constitutes the matrix present between cells providing structural and biochemical support to cells. Within cartilage, ECM characteristics make of hyaline cartilage a highly hydrated tissue with low permeability, and confers to cartilage its mechanical properties mainly high resistance to compression. In addition, ECM acts as an important regulator of chondrocytes behavior. Thus, ECM controls the diffusion of growth factors and hormones, as well as the osmotic and mechanical environment. ECM also regulates the kind of pressures to which chondrocytes are subjected, transducing in that way external stimuli [20, 38, 52].

As mentioned earlier, cartilage ECM is highly hydrated; in fact, solid phase only accounts for 10-20% of total weight. Such solid phase is composed mainly by collagens (60%), of which collagen type II is the most abundant (80% of collagens); Proteoglycans (25-35%); non-collagen proteins (15-20%) and GAGs, although water content and collagen/proteoglycans ratio within the tissue varies according to the anatomical localization [20, 38, 41, 52]. ECM is a dynamic environment that is in constant remodeling by equilibrium between synthesis and degradation [52].

2.3.1.2.1 Glycosaminoglycans (GAGs)

Glycosaminoglycans or mucopolysaccharides are complex carbohydrates consisting of lineal polysaccharides formed by repetitive disaccharides units containing uronic acid derivative (D-glucoronic acid or L-iduronic acid) and hexosamine or hexose, that in general are highly sulfated, and consequently negatively charged [53, 54]. GAGs are osmotically active molecules responsible for swelling pressure within the tissues, consequence of their capacity of retaining cations due to their charge. Furthermore, in aqueous solution they have the property of attracting water molecules; as a result GAGs occupy high volume relative to their mass acquiring their viscous and lubricating properties [41, 54]. Due to these properties their

26 main function is structural, acting as lubricators, shock absorbers and conferring compression resistance to tissues. GAGs have also been involved in several other roles, including cell signaling, morphogenesis, cell proliferation, and cell adhesion. These roles are related to the capacity of some GAGs to interact with growth factors, cytokines and morphogens [54-56].

Glycosaminoglycans present in human tissues include non-sulfated species represented mainly by hyaluronan, and sulfated molecules as heparan, keratan, dermatan, and chondroitin sulfates (Table 2-2). These GAGs types differ in the structure of their disaccharide units and the geometry of their glycosidic linkages (α or β). Sulfatation may occur either on hexosamine/hexose molecules and/or in the uronic acid and may involve carbons 2, 4 or 6 [54].

2.3.1.2.2 Proteoglycans (PGs)

Proteoglycans are the second most abundant component of the ECM, accounting for 5-10% of dry weight. They give hyaline cartilage its compression resistance and are responsible for retaining water within the tissue [20]. Additionally, it has been demonstrated that PG play an important role in regulating signaling within the tissue by interacting with growth factors and cytokines such as TGF-β and FGFs and modulating their diffusion and availability [41]. Structurally PGs are composed by a central core protein to which multiple GAGs units are covalently attached, whose physicochemical properties are main determinants of PG biological function[41]. Many types of PGs are present in ECM, which differ according to the identity of the core protein and the GAGs present in their structure [20, 38, 41, 54]. PG are classified according to their distribution, homology and function. Interstitial PGs include: small leucine-rich proteoglycans (SLRPs) and aggrecan families. The first one consists of at least 9 members carrying CS, DS or KS chains that present in their structure a central domain containing leucine-rich repeats flanked by cysteines. The second one is characterized by amino terminal HA binding domain, a CS central domain and a C-terminal C-type lectin domain. Aggrecan, versican, brevican and neurocan belong to this family [55].

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Table 2-2: Glycosaminoglycans (GAGs) structural characteristics [54, 55].

GAG Disaccharide Units MW Features Tissue (kDa) Distribution Hyaluronic D-GlcA-β(1→4)-D-GlcNAc-α(1→4) 4-8000 Non-sulfated Synovial fluid, Acid (HA) Non-covalently attached to proteins vitreous humor, Very large degree of polymerization ECM of loose (around 104 disaccharide units) connective tissue. Chondroitin D-GlcA-β(1→3)-D-GalNAcS- β (1→4) 5-50 Sulfatation on GalNAc may occur on Cartilage, ligament, sulfate carbon 4 or 6. tendon, aorta. (CS) Dermatan L-IdoA- α (1→3)-D-GalNAc4S- β (1→4) 15 – 40 Sulfatation on GalNAc may occurs on Skin, blood vessels, Sulfate (DS) carbon 4. heart valves Keratan D-Gal-β(1→4)-D-GalNAc6S- β (1→3) 4 – 19 Sulfatation can occur either on Gal or KSI in cornea sulfate I and GalNAc. KSII in cartilage II KSI and KSII differ in the way they attach (KSI – KSII) to proteins to form PG. Heparan D-GlcA-β(1→4)-D-GlcNAc- α (1→4) 10 – 70 Glc is present mostly in non-sulfated Ubiquitous Sulfate regions. It is substituted by IdoA in component of cell (HS) sulfated regions. surfaces Sulfatation may occur on carbon 2 of uronic acid derivatives or on hexosamine carbon 6. It is a highly heterogeneous molecule with variations in polysaccharide chain size, IdoA/GlcA ratio and amount and distribution of sulfate groups. MW: molecular weight; D-Glc: d-glucosamine; L-IdoA: L-iduronic acid; D-Gal: D-galactose; D-GAlNAc: N-acetylgalactosamine; D-GAlNAcS: N-acetylgalactosamine sulfate.

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Aggrecan is the most abundant PG in hyaline cartilage. It is formed by a core protein with the same name (approximately 200 KDa), to which molecules of KS and CS are attached (Figure 2). It is a high molecular weight PG with a molecular weight larger than 2 x 106 Da in the aggregate form [20, 38, 39, 41, 53]. Its structure is formed by 3 globular domains (G1, G2, G3), an interglobular and a GAG-attachment regions. Aggrecan interacts with hyaluronan forming aggregates that increase ECM viscosity, limit free diffusion of molecules through the tissue and confer the tissue with osmotic properties [20, 38, 39, 53]. Such aggregates are formed by up to 100 aggrecan molecules whose binding to HA is mediated by a link protein (Figure 2-3), that interacts with G1 domain of aggrecan core protein [38, 53]. Aggrecan is a molecule with negative net charge due to high sulfatation degree of the GAGs forming it. Such negative charges generate repulsive forces among them. This behavior contributes to compression resistance of the tissue, which is also favored by the high water content within the tissue. Cartilage is able to retain water up to 50 times its weigh. This property is the result of the capacity of aggrecan, due to its charge, to attract cations generating high osmotic pressure [20, 38, 41].

Figure 2-3. Shematic representation of aggrecan structure. The structure of the proteoglycan includes a core protein (blue) which has three globular domains (G1, G2, and G3). GAGs chainsare attached to the core protein between globular domains G2 and G3, including keratan (orange) and chondroitin (green) sulfates, whose molecular structure is detailed in the lower part in orange and green boxes respectively.

Summed to aggrecan, cartilage ECM contains other aggregation PG such as Versican which is present in lower concentrations. Four different forms of versican have been identified (V0,V1,V2, and V3), corresponding to alternative splicing variants. V1 is the major form

29 found in cartilage [38]. Other PG present in hyaline cartilage ECM include decorin, lumican and fibromodulin (Table 2-3) which interact with collagen type II fibers and are involved in regulating fibrilogenesis [38, 41, 57].

Table 2-3: Proteoglycans present in Cartilage [41, 55].

Proteoglycan Type Localization Core Glycosaminoglycans within Protein cartilage MW (kDa) Aggrecan Interstitial PG ECM 208 – 220 ̴ 100 CS chains And several chains of KS Syndecan Cell surface Chondrocyte 31 - 45 1 – 2 CS chains 1 – 3 HS chains Glypican Cell surface Chondrocyte ̴ 60 1 – 3 HS chains Decorin Small leucine- ECM 36 1 DS chain rich 1CS chain Byglican Small leucine- PCM 38 2 DS chains rich 1-2 CS chain Fibromodulin Small leucine- ECM 59 Several KS chains rich Perlecan PCM ̴400 1 - 3HS chains and CS Lumican Small leucine- ECM 37 1-4 KS chains rich Versican Interstitial PG ECM 265 12 -15 CS chains MW: Molecular weight; ECM: Extracellular matrix; PCM: Pericellular matrix.

2.3.1.2.3 Collagens

Collagens are major constituents of extracellular matrices. This is a family of proteins characterized by a molecular structure consisting of a triple helix of α-chains. These chains contain helical domains containing tandem repeats of Gly-X-Y amino acid motifs where X and Y can be any aminoacid, although usually there is high presence of proline and hydroxyproline. Additionally, α-chains present non-helical domains responsible for functional diversity of collagens [53, 58-60].

According to their molecular structure, localization and function collagens are divided in fibrillar, fibril associated, network forming, filamentous, short chain, long chain, collagens with globular domains, membrane collagens, and others. More than 30 types of collagen have been described differentially expressed among tissues and developmental stages [41, 53, 58, 60].

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The main collagen in the cartilage ECM is collagen type II (Col II), accounting for 50-90% of tissue dry weigh, depending on cartilage anatomical localization and developmental stage. Col II is a fibrillar collagen that arranges forming a scaffold for assembling of other ECM components and promotes chondrocytes organization [38, 41]. Studies in articular cartilage and growth plate have demonstrated that orientation and size of collagen fibers changes according to the localization within the tissue. In the superficial layer of the former, they are thin and are oriented obliquely to the surface; in the intermediate zone some fibers are arc- shaped. In the deepest zone collagen fibers are thick and are oriented perpendicular to the articular surface, assuring their anchorage to the underlying bone tissue. In a similar way, within the growth plate, Col II fibers are oriented mainly horizontally in resting zone and vertically in proliferative and hypertrophic zones [20, 61-63].

Collagen II fibers are formed by three identical α1 chains encoded by COL2A1 gene [64]. Within the ECM, Col II molecules associate among them via almidine-derived, pyridinoline or non-aldimidine derived crosslinks, forming stable fibrils and preventing thermal or mechanical dissociation. With age, crosslinks accumulate in the fibrils increasing their strength and resistance to proteolysis, in fact, matures collagen fibrils undergo little turn over under physiological conditions[38]. Col II fibrils are around 15 to 45 nm in diameter; their function is to provide tensile resistance to cartilage and preserve structural integrity of hyaline cartilage, by containing the expansion of the tissue due to swelling pressure [20, 41, 59, 62, 64].

In addition to Col II, the main forms of collagen found within hyaline cartilage are types XI and IX constituting 1-10% and 1% of the total collagen within such tissue respectively [38, 65]. Type XI collagen is a fibrillar collagen, formed by an heterotrimeric helix composed by α1(XI), α2(XI), and α1(II) chains encoded by COL11A1, COL11A2 and COL2A1 genes respectively [64]. This collagen is found in association with Col II and has been involved in regulation of collagen type II fibers diameter [38, 59, 64, 65]. On the other hand, collagen type IX is a member of the fibril-associated collagen with interrupted triple helix family (FACIT). It is a heterotrimer formed by α1(IX), α2(IX), and α3(IX) polypeptide chains encoded by COL9A1, COL9A2 and COL9A3 genes respectively [64]. It interacts with Coll II fibers and mediates its contact with other ECM components mainly PG [41, 64].

Other collagen types have also been found in cartilage ECM, although in smaller proportion and whose function is largely unknown. These include fibrillar collagens as collagen type III, and several types of fibril associated collagens have been detected such as types V, VII, VIII, XII, XIII, XIV, XVI, XXVII. Finally, the network forming collagen type X is also present in transient cartilage, but it will be further discussed in following sections [41, 52, 59, 65, 66].

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2.3.1.2.4 Non-collagen proteins

Although collagens form the main protein network, within cartilage ECM there are other proteins present which are believed to mediate matrix assembly. These proteins include COMP (Cartilage Oligomeric Protein), Matrilins (-1 and -3), link protein, chondrocalcin, junction proteins, cartilage derived C-type lectin (CLECSF1), PRELP, chondroadherin, and chondromodulin tenascin-C, where the first three are among the most abundant [38, 64, 67, 68].

COMP, also known as thrombospondin 5, is a homopentameric, multidomain calcium binding protein coded by the COMP gene with a molecular weight around 524 kDa. It interacts with several ECM components including type II, IX, and XII collagens, matrilin, fibronectin and aggrecan therefore playing an important role in matrix assembly and fibrillogenesis [64, 69]. Additionally there have been reports of interactions with growth factors, cell surface proteins, proteases among others [69].

Matrilins are a family of multidomain proteins composed by 4 members of which types 1 and 3 are mainly found in cartilage. Matrilin 1 also known as cartilage matrix protein (CMP) is a homotrimeric 148kDa protein. On the other side, Matrilin 3 is a 48.9KDa protein. These two proteins are found forming heterocomplexes in cartilage ECM, acting as adaptator proteins in ECM assembly, and mediating Col II - aggrecan interactions. Additionally, matrilins has been found in association with Col VI and COMP [64, 67, 68].

Finally, cartilage link protein 1 (Ctrl1), a member of the hyaluronan and proteoglycan- binding link protein family (HLPN), is a small 40-50 KDa glycoprotein that mediates aggrecan and hyaluronan interactions [68, 70].

2.3.1.3 Pericellular Matrix (PCM)

The pericellular matrix (PCM) is the thin layer of matrix that surrounds chondrocytes. Together PCM and chondrocytes are known as the chondron, which is considered the primary structural, functional and metabolic unit of hyaline cartilage [40, 71]. PCM provides chondrocytes mechanical strength and resistance to osmolarity changes. Additionally, it acts as a mediator that regulates the presentation of biochemical and biophysical stimuli to the cell [71-73].

PCM shares with ECM most of its components including proteoglycans and collagens. However, unlike ECM, PCM shows high keratan enriched PG content and fine collagen fiber arrangement, mainly composed of Collagen type VI [40, 71, 72, 74]. Thus, PCM main components include hyaluronan, aggrecan monomers, byglican, perlecan, link protein,

32 fibronectin, laminin, collagens type IX and VI [40, 71]. Other proteins identified within PCM include enzymes such as triosephosphate isomerase (TPI) and peroxiredoxin 4 (PRDX-4); TGFβ induced protein (TGFBIp); latent-TGFβ-binding protein 2 (LTBP-2; and neurexin-2- β [73].

Collagen type VI (Col VI) is a non fibrillar collagen found pericellularly forming filamentous networks [41]. It is an heterotrimer that arranges forming a central helical domain flanked by non-helical regions [38]. Several heterotrimeric monomers associate to form a beaded-like complex multimer [72]. Col VI interacts with several ECM components including biglycan, decorin, fibromodulin, hyaluronan, fibronectin, perlecan, and collagen II [72]. Although ColVI function is not well understood, it has been suggested to be involved in cell attachment and survival [73].

In addition to Col VI, PCM is also composed by different types of Proteoglycans including byglycan, decorin, and perlecan (Table 2). Byglycan and Decorin are small dermatan sulfate and chondroitin sulfate-containing PG that interact with Col VI and seems to play a role in its assembly [38, 40, 41]. Besides, Perlecan is a large PG containing heparin and chondroitins sulfate in its structure. It has been proposed to be the major PG contributing to PCM mechanical properties, and it has been involved in regulating cell proliferation through interaction of its HS chains with signaling molecules such as members of FGF family and platelet derived growth factor. It also interact with ECM and PCM components such as fibronectin, laminin, collagen VI as well as cell surface proteins such as growth factor receptors and integrins [41, 64, 71].

2.4 ENDOCHONDRAL OSSIFICATION

Endochondral ossification gives rise to most of human bones including the appendicular skeleton (except for the clavicles), vertebral bodies and jaws. This process implies bone formation through calcification of a previously formed cartilage mold known as anlagen. Thus, endochondral bone formation starts around the 6th gestational week with mesenchymal condensations that undergo differentiation to cartilage, process known as . Such differentiation implies changes in mesenchymal cells phenotype, from multipotent collagen type I producing cells to chondrocytes, the main cellular type within hyaline cartilage, characterized by producing collagen type II and aggrecan among others. The cartilage mold thus formed growths by continuous cell division and extracellular matrix synthesis.

Endochondral ossification starts in humans around the end of the first pregnancy trimester. It begins in the central region of the cartilaginous mold where chondrocytes start a process

33 of terminal differentiation to hypertrophic chondrocytes. The latter are responsible for promoting tissue calcification, vascular invasion and recruitment of osteoblasts, which colonize the tissue after chondrocytes apoptosis, forming the primary ossification center (POC) [1, 15-17].

2.4.1 Chondrocyte Differentiation

During this process, chondrocytes suffer a series of morphological and metabolic changes that include, first, entering in a highly proliferative state. After a while, chondrocytes experience cell cycle arrest followed by 5 to 10 fold increase in cell volume and changes in the synthetic profile [14, 23, 45]. Finally, chondrocytes undergo programmed cell death and and blood vessels invade the tissue completing the calcification process and forming the primary spongiosa [14-16, 23].

2.4.1.1 Chondrocyte Proliferation

The first step of chondrocytes differentiation implies the transition from resting to a highly proliferative state. This proliferative chondrocytes continue active production of cartilage ECM rich in Col II and PG [14, 19]. In addition, they acquire a flattened shape and display planar cell polarity (PCP); it implies alignment of the mitotic spindle in a plane orthogonal to longitudinal growth axis, resulting in oriented cell division in such plane [13, 26]. After cell division daughter cells, which also acquire a flattened shape, reorient and intercalate under the mother cell leading to the formation of columns oriented in the longitudinal growth direction of the bone, process known as convergent extension (CE) [13, 26, 75, 76]. Current evidence indicates that PCP and CE coordination involves cell-cell and cell-matrix interactions, Wnt/Frizzled signaling pathways, and regulation involving the primary cilium [13, 26, 75-78].

2.4.1.1.1 Cell-cell and cell/matrix interactions

Recent evidence points out that after the process of chondrocytes cell division, mother and daughter cells remain tightly in contact [76]. Such cell-cell interactions were shown to be required for chondrocytes rearrangement during column formation. Although such interactions are not yet well characterized, they seem to involve cadherins since inhibition on extracellular calcium binding to this proteins disrupts such cell-cell interactions [76].

Cell-matrix interaction implication in columnar organization has been suggested based on the findings of altered columnar structure in the growth plates of mice that display mutations in some ECM components including ColII, ColIX, ColXXVII, COMP, and Perlecan [64, 75, 79-85]. Additionally, a similar phenotype has been observed after disruption of the

34 expression of molecules involved in cell adhesion and chondrocyte-collagen interactions, like integrins and Gpi-anchored proteins[75, 86, 87]. In fact, cell-matrix interactions trigger intracellular signaling pathways leading to cytoskeleton rearrangement. Thus, defects in downstream effectors of cell-matrix interaction proteins have also shown failure of chondrocyte convergent extension and subsequently column formation [88, 89].

2.4.1.1.2 Wnt/Frizzled signaling pathways

Wnt is a highly conserved family of secreted cysteine-rich glycoproteins between 38-42 kDa. Up to date, 19 Wnt proteins have been identified in humans [90, 91]. These proteins are well recognized as morphogens involved in several developmental processes including body axis patterning, as well as cell differentiation, proliferation and migration [90-96].

As morphogens, Wnts can act in short and long range since, although highly hydrophobic, they can be transported through the extracellular medium by mechanisms involving postraslational modifications or interaction with heparan sulfate proteoglycans (HSPGs) and lipoprotein particles [90, 92, 97]. Physiological response to Wnt is concentration-dependent, and relies on the interaction of Wnt proteins with their specific receptor present in cell membranes belonging to the Frizzled receptor family (Fz), atypical G-protein-coupled receptors [90, 97]. However, it has also been reported a Wnt response triggered by Wnt interaction with non-Fz receptors, including Ror-2 (Receptor Tyrosine Kinase-Like 2), and RYK (Receptor Tyrosine Kinase) [77, 90].

Signaling mechanisms triggered by Wnt occur through two different pathways, the first one mediated by intracellular increase in β-Catenin is called the canonical Wnt Pathway; meanwhile the non-canonical pathway implies β-Catenin independent signaling leading ultimately to activation of ROCK(Rho-associated coiled-coil containing protein kinase), PKC and JNK in a process mediated by small GTPases RhoA (Ras homolog gene family member A) and Rac1as primary targets [90, 91, 96, 97]. This molecules have been associated mainly with regulation of adhesion, migration and polarization of cells. In fact, non-canonical Wnt-Fz signaling is recognized as the main regulator of planar cell polarity processes in different species and tissues, including the growth plate [26, 90, 98].

In general, non-canonical Wnt signaling involves recruitment of several membrane proteins by de Fz-Wnt complex, including the trimeric G protein Go, Dishevelled (Dsh), Strabismus (Stbm), Van Gogh like (Vangl), cadherins and Falmingo (Fmi). This generates an asymmetric distribution of such proteins in the cell membrane, leading to activation of several intracellular proteins associated mainly to cytoskeletal remodeling (e.g. RhoA, ROCK) [90, 96, 98]. Up to this moment the main non-canonical Wnt associated to chondrocyte columnar arrangement is Wnt5a, which has also been associated with regulation of PCP and CE in

35 other tissues [13, 26, 77, 95, 96, 98]. In fact, studies showing cartilage selective suppression of Wnt5a as well as disruption of frizzled signaling show that proliferative chondrocytes fail to acquire flattened shape and columnar organization[13, 26].

2.4.1.1.3 Primary cilium

Primary cilium (PC) is a cell structure that has been associated to sensory processes, cell signal transduction and cell-matrix interactions [99]. In fact, it has been associated to Wnt canonical and non-canonical signaling response as well as interaction with collagen fibers, processes that, as stated above, are relevant in proliferative chondrocytes columnar arrangement. Wnt-PC relation is not well understood, such association is based on demonstration of abnormal Wnt response in cell that display abnormal ciliogenesis [78, 100, 101]. Additionally, various proteins involved in Wnt signaling have been localized in the basal body including Dvl, Inversin (Inv) and some downstream effector GTPases; some of them have been involved also in ciliogenesis (e.g. Dvl, Vangl2) [78, 100]. Furthermore, mutations in proteins associated to cilium assembly have proven to disturb PCP in several tissues and animal models [78, 100].

Specifically within growth plate, proliferative chondrocytes present a primary cilium oriented parallel to the growth axis [102-104]. As evidenced in vivo studies, primary cilium seems to be involved in chondrocytes convergent extension, since disruption in cilium assembly or orientation has proven to disrupt columnar organization [49, 102, 105, 106].

2.4.1.2 Chondrocyte Hypertrophy

This process involves a combination of dry mass production, resulting in increased volume of intracellular constituents (cell organelles), and a process of swallowing implying an increase in cell fluid uptake consequence of changes in cell membrane transporters activity [14, 19, 29]. Hypertrophic chondrocytes are important regulators of endochondral ossification since they are responsible for changing the ECM composition, synthesis of morphogens, initiation of the matrix mineralization, and promotion of tissue vascularization [14, 23, 45, 46].

2.4.1.2.1 Changes in extracellular matrix composition and synthesis of morphogens

One of the first events during hypertrophy is the downregulation of Col II expression. At this stage, Col II is substituted by an increase in the production of Collagen X (Col X) [14-16, 23, 45, 46]. Col X is a homotrimeric protein belonging to non-fibrillar type collagens, coded by the COL10A1 gene. It is found in hexagonal arrays forming aggregates in the PCM [38, 58, 64]. Although the role of Col X in endochondral ossification has not been elucidated,

36 several hypotheses have been suggested. In fact, given its association with the chondrocyte terminal differentiation, it was initially suggested that it played a role in matrix calcification, which was discharged as no association has been observed between Col X and mineralization center or vesicles[107]. Collagen X is mainly associated to vascular invasion and has proven to influence the distribution of other extracellular matrix constituents such as GAG and PG. Additionally, a role of Col X in setting the marrow microenvironment required for hematopoiesis has been suggested [107-109].

Additional to Col X expression, changes in ECM composition are achieved by an active matrix degradation. This process facilitates chondrocytes cell volume increase, as well as vascularization and colonization of the tissue by cells of osteogenic linage [23]. Matrix resorption is achieved by extracellular matrix degrading enzymes produced by hypertrophic chondrocytes including: matrix metalloprotease 13 (MMP-13), a zinc dependent protease mainly responsible for collagen degradation although it could act also on aggrecan; ADAMTS-1, ADAMTS-4 and ADAMTS-5 aggrecanases, which are members of the ADAMTS (a desintegrin and metalloprotease with trombospondin motifs) family [45, 46, 110].

Changes in the protein expression pattern of hypertrophic chondrocytes also include the synthesis of morphogens involved in regulating the process of chondrocyte differentiation and chondrocytes organization within the growth plate including Bone Morphogenic Protein 6 (BMP-6) and Indian Hedgehog [45, 111].

2.4.1.2.2 Matrix Mineralization

Matrix mineralization is initiated by hypertrophic chondrocytes, which promote hydroxyapatite crystal formation in the ECM. This process starts inside the so called Matrix Vesicles (MV), extracellular membrane-invested particles released by the lateral surfaces of hypertrophic chondrocytes [46, 112-114]. HA crystal formation within MVs is favored by accumulation of calcium ions (Ca) and inorganic phosphate (Pi), that will lead to calcium phosphate accumulation [112]. Intravesicular calcium increase is mediated by membrane calcium-binding phospholipids, mainly phosphatidylserine (PS); and calcium-binding proteins that act as calcium channels including annexin II, V and VI [112, 114]. At the same time, increasing of the intravesicular Pi concentration is achieved by a combination between intravesicular Pi production and influx of extravesicular Pi. The first one results from the activity of a battery of phosphohydrolases present in MVs membrane and lumen, that include adenosine monophosphate phosphodiesterase, adenosine triphosphatase, nucleoside triphosphate pyrophosphohydrolase-1 (NPP1) and the phosphoetanolamine/phosphocholine phosphatase 1 (PHOSPHO1) [112, 113]. On the other hand, extracellular Pi, is mainly produced by the ATPase activity of the tissue-nonspecific alkaline phosphatase (TNAP).

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Intravesicular HA crystals increase in size and are then released to the extracellular medium where they continue their progression in association with collagen fibers in a process mediated mainly by TNAP activity [112, 113].

2.4.1.2.3 Vascularization

In addition to bone matrix mineralization, angiogenesis is another important event during cartilage to bone transition. Such process is triggered by hypertrophic chondrocytes synthesis of soluble factors, including Basic Fibroblast Growth Factor (bFGF), Nerve Growth Factor (NGF), Osteopontin (OPN), Bone Sialoproteina (BSP), Metalloproteinase-2 (MMP2) and Vascular endothelial Growth Factor (VEGF) [115, 116]. The latter has been recognized as the main molecule regulating vascularization [14, 23, 45].

VEGF is a family of small homodimeric proteins (32 – 42kDa) that act as pro-angiogenic factors that are synthetized in different tissues [116]. Human hypertrophic chondrocytes express mainly three isoforms of VGFA-A: 121, 165 y 189 (120, 164, 188 in mouse) [111, 116, 117]. VGFA acts mainly on vascular endothelial cells promoting blood vessel invasion. However, VEGF has also been associated to influence endochondral ossification by stimulating chondrocyte cell death, osteoblast differentiation, and chondroclast function [23, 116, 118].

2.4.1.2.4 Chondrocyte Apoptosis

Hypertrophic chondrocytes located immediately above the ossification front undergo programmed cell death [46]. Up to now, the mechanisms responsible for chondrocytes cell death are not clear [119, 120]. For many years, apoptosis was accepted as the mechanism of cell death in hypertrophic chondrocytes, based on electron microscopy observations describing characteristic apoptotic morphology that includes mainly cromatin condensation and presence of apoptotic bodies [14, 46, 120]. However, such morphology is not observed uniformly though all chondrocytes in chondro-osseus junction. In fact, atypical hypertrophic chondrocytes has been described, which have been referred as “dark” or “paralysis” chondrocytes. These are characterized by enlarged endoplasmic reticulum and Golgi apparatus, accompanied by numerous cytoplasmic vacuoles and vesicles budding in the cell surface [14, 120, 121]. Such findings were compatible with a process of autophagy, also recognized as programmed cell death type II [14, 120].

Currently, many authors suggest that hypertrophic chondrocyte cell death is a combined apoptosis-autophagy mechanism, considering the morphological heterogeneity observed and that expression of molecular markers of both processes in in vitro analysis [119, 120, 122].

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Furthermore, it has been suggested that chondrocytes represent the evidence for a new different type of programmed cell death [119, 123].

2.5 BIOCHEMICAL REGULATION OF LONG BONE GROWTH

2.5.1 Local Factors

Several paracrine signals have been associated with controlling endochondral ossification, including gradients of Insulin Growth Factors (IGFs), Bone Morphogenic Proteins (BMPs), Fibroblast Growth Factors (FGFs), regulatory loop formed by Parathyroid hormone related protein (PTHrP) and Indian Hedgehog (Ihh) and differential expression of FGFs receptors (FGFR)[15, 45, 111].

2.5.1.1 Insulin like Growth Factors (IGF)

In bone and growth plate IGF-1 act as local mediator of growth hormone, although in these tissues their synthesis can also be stimulated by parathyroid hormone and sex steroids. Expression of IGF-1 mature peptide, IGF-1Ec and IGF-2 has been demonstrated within the growth plate. In fact, IGF-1 increases proliferation rates in culture chondrocytes. Furthermore, mutation in IGFs or their receptors lead to long bone growth deficit in animal models due to reduced proliferation of growth plate chondrocytes [45, 124-127].

2.5.1.2 Fibroblast Growth Factors (FGF)

Expression of several FGFs and their receptor (FGFRs) has been demonstrated at different stages of bone formation and they show different spatial and temporal distribution patterns. FGF-9 has been identified in mesenchymal condensation previous to anlagen formation while FGFs -2, -5, -6 and -7 are expressed in the surrounding mesenchyme; FGFs -2 and -3 appear in the skeletal mold after chondrocyte differentiation has occurred. Later on in long bone development, it has been identified expression of FGFs -1, -2, -5, -6, -7, -9, -10, -17, - 18, -21 and -22 in the . In addition, FGFs -1, -2, -3, -7, -18, -21 and -22 were identified in growth plate chondrocytes [127-131]. Expression of FGFs -1 and -2 was mainly detected in proliferative and hypertrophic zones; FGF-18 in resting and hypertrophic zones; and FGF-22 showed a decreasing gradient from resting towards hypertrophic zone. Furthermore, FGFRs -1, -2 and -3 have been localized in hypertrophic chondrocytes, perichondrium and resting-proliferative zones respectively. [45, 128-130]. Although most of them show mitogenic effect on chondrocytes, some like FGF-21, show an inhibitory effect on proliferation and differentiation [111, 131, 132]. Although the exact mechanisms mediating FGF effect on growth plate chondrocytes are not fully understood, it has been

39 proposed that FGF modulate indirectly other endochondral ossification regulator molecules such as Ihh and BMPs [127, 129, 132].

FGFs influence chondrocyte proliferation, differentiation and cartilage matrix mineralization. Although they are recognized as pro-proliferative molecules in most tissues, in the growth plate, FGFs and their receptors act as negative regulators of endochondral ossification by inhibiting chondrocytes proliferation [16, 128, 129, 132]. The importance of FGF signaling in skeletal development have been pointed out by in vivo studies where ablation or overexpression of specific FGFs, as well as alteration of their receptors, have shown abnormalities in skeletogenesis [129, 130, 133]. As such, FGFs -2, -18 and -23 mutants are the only ones displaying alterations in long bone development. Additionally, mutation in FGFs receptors have been associated to several skeletal diseases. FGFR1 and 2 have been implicated in dysplasyas that display mainly craniofacial defects, and hands/feet abnormalities such as Osteoglophonic dysplasia, Pfeiffer syndrome, Jackson-Weiss syndrome, Crouzon syndrome, Apert syndrome, Saethre-Chotzen syndrome, among others. On the other hand FGFR3 loss-of function mutations cause CATSHL syndrome (campodactily, tall stature and hearing-loss syndrome) while gain-of function mutations are involved in dysplasias compromising normal long bone growth such as achondroplasia, the most common type of dwarfism, lethal tanatophoric dysplasia, hypochondroplasia. FGFR3 mutations have also been found in patients with Crouzon syndrome, and Saethre-Chotzen syndrome [129, 133, 134].

FGFR3 activation leads to negative regulation of chondrocytes proliferation and terminal differentiation. In vivo this receptor seems to interact with different FGFs including FGF -1, -2, -17, -18 and possibly -9 [16, 17, 111, 127, 133, 135].

FGF2 is one of the main identified ligand for FGFR3. The regulatory function of FGF2 in vivo is not fully understood, and in vivo and in vitro studies show some discrepancies. In one side, FGF-2 deficient mice don’t display any gross abnormalities in bone shape or size, although they showed abnormal trabecular structure and reduced bone mass [136, 137]. However, the phenotype observed in mice overexpressing FGF-2 suggests that it may act by inhibiting either proliferation or hypertrophy, since those animals show enlargement of resting-proliferative zones and reduced hypertrophic zone[138]. It also has been suggested that it is involved in promoting vascularization and mineralization [128, 132]. Furthermore, FGF-2 exogenous application to organ cultures lead to delayed growth associated to decreased chondrocyte proliferation and hypertrophy [128, 130, 132]. On the other hand, in vitro FGF-2 has shown to act as mitogen for chondrocytes [128, 132].

FGF-18 mutants showed a phenotype resembling the observed in FGFR-3 mutants characterized by long bone growth arrest, delayed ossification in both endochondral and intramembranous bone elements. Based on such findings, FGF-18 has been suggested as the

40 preferred ligand for FGFR3 [111, 127, 130, 133, 139]. Furthermore, long bone abnormalities observed in FGF18 null mice were initially associated to increased proliferation and subsequently wider proliferative and hypertrophic zones in late stage embryos and neonates. However, analysis in earlier development stages showed decreased proliferation suggesting a potential switch in cellular response to FGF18/FGFR3 through development [139-141].

2.5.1.3 Ihh/PTHrP

Parathryroid related hormone (PTHrP) is one of the main regulators of chondrocytes differentiation during embryonic development and postnatally in the growth plate. Its expression has been identified at the perichondrium, resting, proliferative and prehypertrophic chondrocytes [142-148]. PTHrP synthesis is controlled by Indian Hedgehog (Ihh), which is synthetized by prehypertrophic and hypertrophic chondrocytes [144-149]. The feedback loop between these proteins is one of the major regulators of chondrocytes transition from proliferative to hypertrophic state, regulating column length [16, 142, 147, 150].

PTHrP maintains the pool of proliferative chondrocytes mainly by preventing chondrocytes to undergo hypertrophy. In fact, PTHrP null animal models display shorter proliferative zone and premature hypertrophy, while PTHrP overexpression results in marked delay in hypertrophy and subsequently cartilage ossification in the growth plate [17, 143, 147, 150- 152].

By delaying hypertrophy, PTHrP decrease the number of cells capable of producing Ihh, thus forming a negative feedback loop that regulates its own expression and chondrocyte proliferation. As a consequence proliferative zone extends from the site of PTHrP production to the point where cells are able to escape from PTHrP regulation and start Ihh expression which in turn will stimulate PTHrP production [45, 127, 135, 147, 152].

In order to trigger cellular effects, PTHrP interacts with the so called PTH/PTHrP receptor (PPR) expressed at low levels by proliferative chondrocytes although its expression is upregulated once they stop proliferating and become pre-hypertrophic [45, 127, 142, 144, 145, 149]. PPR is a G coupled protein, which triggers mainly by cAMP and protein kinase A signaling pathways, leading finally to activation of Sox-9 [17, 45, 127, 147]. Mouse models in which PPR expression is suppressed display similar phenotype to PTHrP mutants characterized by accelerated chondrocyte hypertrophy and increased apoptosis [153]. Furthermore, PPR mutations causing its inactivation have been associated to Blomstrand chondro-osteodystrophy, an embryonic lethal skeletal dysplasia in humans; while mutations causing its overactivity are found in patients with Jansen-type metaphyseal dysplasia characterized by short-limb dwarfism [17, 45, 127, 134, 135].

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On the other side, Indian Hedgehog (Ihh) is a morphogen of the hedgehog protein family whose members play important roles in embryonic patterning and development. As the other family members, Ihh binds to a membrane receptor named Patched (Ptc), thereby releasing smoothened (Smo), a membrane protein that is responsible for triggering intracellular response [127]. Ihh expression has been detected from early stages of embryonic limb development up to the postnatal growth plate in prehypertrophic and hypertrophic chondrocytes [144-147, 149].

Ihh is recognized as an upstream regulator of PTHrP signaling, based on the evidence of PTHrP ablation in Ihh mutants, as well as upregulation of PTHrP after Ihh overexpression. In fact, Ihh is considered to be necessary and sufficient for PTHrP expression. However Ihh effect on endochondral ossification is even broader and it seems to be involved in regulating endochondral ossification at different levels by affecting different steps of chondrocytes maturation process and ossification. In fact, Ihh mutants exhibit a dramatic reduction in proliferative zone due to decrease cell proliferation, delayed and ectopic hypertrophy and finally delayed ossification [17, 150, 152, 154, 155]. Presence of hypertrophic chondrocytes near the articular surface is a feature that resembles the histological characteristics of PTHrP mutants bones, although the latter lack other growth plate alterations shown by Ihh mutants. Furthermore, treatment with PTHrP and/or activation of PTHrPR to Ihh deficient animals can rescue the ectopic hypertrophy observed, however in both cases proliferation is still severely impaired. These findings strongly suggest that Ihh effects on hypertrophy are mainly mediated by the Ihh-dependent induction of PTHrP synthesis. However, PTHrP-independent pathways may be responsible for other Ihh effects including: stimulation of proliferative to hypertrophic chondrocyte differentiation, and differentiation of resting chondrocytes into proliferative-columnar chondrocytes [16, 45, 111, 127, 142, 147, 150, 152, 154-157]. Mutations in Ihh gene have been identified in patients with autosomal dominant form of brachydactyly type A-1 (BDA-1) and acrocapitofemoral dysplasia [17, 134, 135].

Studies show that FGF and BMP signaling interact with the PTHrP/Ihh regulatory loop, with the former exerting negative regulation on Ihh while the latter forms a positive regulation. However it is unclear the extent of inter-dependency between those regulatory mechanisms. It has been suggested that BMP could act downstream of Ihh to stimulate PTHrP. Additionally, Ihh acts by stimulation Wnt signaling on proliferative zone [17, 45, 111].

2.5.1.4 Bone Morphogenic Proteins (BMPs)

Bone morphogenic proteins are multifunctional morphogenetic proteins with autocrine and paracrine effects. These are named due to their ability to induce ectopic bone formation. Presently it is recognized their role as bone formation promoting molecules that stimulate

42 endochondral ossification. Thus, BMPs affect bone formation by promoting condensation and chondrogenesis of mesenchymal stem cells, chondrocytes proliferation and differentiation, angiogenesis and mineralization [16, 17, 111, 127, 158-161]. In addition to their role in cartilage and bone formation, BMPs have also been involved in neural induction, angiogenesis, myogenesis inhibition, heart and kidney formation during early embryonic development [159, 162].

During early embryological stages of bone development BMPS are involved in mesenchymal cells condensation and chondrogenesis. Later on, these molecules are expressed in the perichondrium and growth plate chondrocytes where, as suggested by in vivo and cell culture studies [45, 111, 135, 150, 163, 164]. During embryological period, BMP -2, -4 and -7 have been identified in the developing limb [111, 127]. Within the growth plate, BMP and their antagonist show a zone dependent expression. BMP-2 and -6, which stimulate chondrocyte differentiation, are expressed in hypertrophic zone, while in proliferative and resting zones there is mainly expression of negative regulators of differentiation including BMP members and BMP antagonists. Thus, in proliferative zone, expression of BMP-7 and BMP-3B (GDF- 10) was observed. In turn, in resting zone, expression of BMP-3 and two BMP antagonists (Gremlin and Chordin) has been detected. Additionally, BMP receptors were detected all over the plate [111, 165].

Although BMPs impact on endochondral ossification is not yet fully understood, studies using BMP-2 and BMP antagonists such as Noggin suggest that these molecules have influence over several steps of chondrocyte differentiation. Thus, it has been suggested that BMPs stimulate chondrocyte proliferation and inhibit last steps of hypertrophy [150].

2.5.1.5 WNTs

Experimental evidences point out the importance of Wnt signaling in long bone development [93, 95, 166]. For instance, it was initially suggested that canonical Wnt signaling acts at early stages by promoting chondrogenic differentiation of mesenchymal cells to form the anlagen. Later, during endochondral ossification, it acts as a stimulator of chondrocytes terminal differentiation to hypertrophic phenotype [111]. However, recent evidence points out that canonical Wnt signaling displays different roles in each zone of the growth plate. In immature chondrocytes suppress hypertrophy while in mature chondrocytes it stimulate terminal differentiation [16, 45].

Currently, it has been observed that canonical and non-canonical Wnts are expressed on the growth plate especially in proliferative and hypertrophic zones, including Wnt-2b, -4, 5a/b, -10, -11 [167]. They are involved in regulation of chondrocyte survival, proliferation and

43 hypertrophy; however it is still poorly understood which members of Wnt family are responsible for each [167].

2.5.2 Systemic Factors

Endocrine signals are known to influence bone growth by affecting the processes occurring at any of the histological zones. Among the hormones that have proven to influence such processes are growth hormone, thyroid hormones, androgens, vitamin D, glucocorticoids and estrogens [45, 135, 168].

Growth hormone (GH) stimulate longitudinal bone growth. Current evidence suggest that GH has a dual effect on growth plate. On one side, it exerts a direct effect on cells in resting zone and the groove of Ranvier, in which it promotes proliferation. On the other side, GH enhances local synthesis of IGF-1 that increase clonal expansion of proliferative zone chondrocytes [23, 45, 135, 168, 169].

Thyroid (TH) hormones also stimulate long bone growth. In fact, receptors for T3 (3,5,3′-L- triiodothyronine) have been demonstrated in resting, proliferative and pre-hypertrophic chondrocytes [170]. Similar to GH, it has been observed that T3 promotes proliferation in resting chondrocytes, however its main effect is on proliferative chondrocytes in which it stimulates hypertrophy [170, 171]. Such effect has been also observed in vitro, where T3 treatment stimulates hypertrophy markers expression such as Col X [23, 45, 135, 168, 171]. T3 has also been involved in growth plate ECM homeostasis by regulating the expression of PG , aggrecanases and metalloproteinases; in addition, there is evidence that T3 affects the expression of some local morphogens including BMP4, Wnt4 and FGFR3 [170]. In vivo, hypothyroidism causes growth arrest, in fact, hypothyroid animals display shorter proliferative and hypertrophic zones and loss of columnar arrangement [23, 45, 135, 168].

Other hormones may also stimulate longitudinal growth, such as the androgens, leptin and vitamin D. In fact, deficiency of the latter, causes defective growth associated to abnormal mineralization and widening of the growth plate, furthermore, it has been demonstrated direct effects of Vitamin D in alkaline phosphatase and MMP expression in hypertrophic zones. However some of the effects of Vitamin D deficiency in vivo may also be secondary to phosphate and calcium deficiencies developed in such conditions. In contrast, glucocorticoids have inhibitory effects on chondrocytes proliferation and therefore long bone growth. Finally, estrogens have been involved in promoting growth plate closure at the end of puberty in humans, and although the mechanism is not well understood, currently it is proposed that estrogens accelerate chondrocytes senescence within growth plate [23, 45, 135, 168].

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2.6 MECHANICAL INFLUENCES ON LONG BONE GROWTH AND GROWTH PLATE

The role of mechanical stimulation as a regulator of bone has been intuitively recognized for more than a century based on clinical observations. Thus, in 1823, Delpech recognized that compression induced by devices used for club foot treatment were associated to “retard development of the compressed parts” [172]. Later, in 1862, the Hueter-Volkmann law was formulated. This is an orthopedical principle that recognizes the mechanical modulation of long bone growth such that sustained compressive loading inhibits growth, while tension accelerates it [21, 173, 174]. Moreover, alterations of mechanical modulation have been associated to development of skeletal abnormalities, including the angular progression deformities in tibia (Blount disease), and the development of scoliosis [21, 174, 175]. Based on such clinical evidence, various orthopedic techniques have been developed to use mechanical modulation to correct angular bone deformities and lower limb discrepancies [172, 174]. Such approaches consider applying devices to transfer either tensile or compressive loads to the growth plate in vivo [176]. These techniques were initially described in the middle of the XIX century by Blount, who proposed to use staples (Blount Technique), however various modifications have been suggested generating new protocols as the suggested, for example, by Metaizeau and Stevens, that imply the usage of screws intraphyseal or extraperiostic respectively [176-178].

Besides the above mentioned clinical evidence, a plethora of in vivo and in vitro studies have been developed to support the proposed role of mechanical stimulation on bone development, suggesting that such regulation may be important since early embryological stages. In fact, during development, bone elements experience a complex mechanical environment that is influenced by compressive forces derived in early life from the independent growth of diaphysis and epiphysis of the bone and later on from the load resulting from supporting body weight; restrictions imposed by nearby structures such as the periosteum, perichondrium, Lacroix ring and adjacent bones; and tensile influences exerted by muscles [21, 174, 179- 184]. The importance of such mechanical environment in embryonic bone development was confirmed in studies performed in chick and mouse models where muscle function has been altered, either by genetic lesions or immobilization techniques. These animals display abnormalities in prenatal bone development including: reduced bone ossification and length, reduced cartilage formation and abnormalities in joint formation [181, 182, 185]. In addition, the effect of mechanical loading on postnatal bone growth has also been explored using rodents (rabbit, rat and mouse) and bigger mammals (calf, sheep, and lamb) that were subjected to localized compressive or tensile loading either in long bones or vertebrae to study effects on growth rates, and growth plate structure and composition. These studies have confirmed the effects described by Hueter-Volkmann law, demonstrating that compressive loading reduces bone growth while tensile loading may stimulate it [21, 172, 183, 186-190].

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Within the growth plate, most of the studies report decrease in growth plate thickness on animals subjected to compressive loading; at cellular level, studies using rodents have shown that mechanical loading induces histological changes within the growth plate, specifically in the width of the proliferative and hypertrophic zones as well as disruption of columnar arrangement [183, 187-191]. Additionally, it has been observed a decrease in collagen type II and aggrecan concentrations in growth plates subjected to long term static compressions [191, 192].

2.6.1 Mechanical Effects on Chondrocytes Behavior

The growth plate is a structure mainly subjected to compressive mechanical loading in vivo [21, 193, 194]. The effects of such loading within the tissue include cell deformations, changes in the interactions among collagens and proteoglycans present in the ECM and flux of water. The latter has been associated to the generation of other types of biophysical stimulation that include shear stress, hydrostatic pressure, osmotic pressure, nutrient and ion gradients and pH changes (Figure 2-4) [48].

Figure 2-4. Tissue effects of compressive loading. In the upper panel it is shown effect of compressive loading on cell shape. In the lower panel it is shown that compressive loading promotes water flow within the tissue, generating shear stress on the cells present within the tissue.

Several in vivo and in vitro studies have been performed in order to identify the effects of mechanical compression in cell dynamics (proliferation, hypertrophy and apoptosis) [21, 46, 174, 183, 187, 189, 190, 195, 196], cell height [183, 197, 198] and the biosynthetic behavior of chondrocytes, assessed mainly in terms of expression of molecules of the ECM (Collagen type II, X and aggrecan) and some enzymes (MMP 13 and ADAMTS-4/5) [191, 192]. In

46 addition, changes in the expression of metalloproteinase inhibitors (TIMP-1 and TIMP-2), growth factors (VEGF), and other molecules have been evidenced [196, 199-202].

2.6.1.1 In vitro studies: Tissue Cultures

As a model to study the influence of mechanical loading over the chondrocytes behavior in vitro, protocols applying compressive loads to articular cartilage and growth plate explants have been performed. For articular cartilage, the reported results of ECM molecules synthesis under dynamic loading are contradictory with some studies showing an increase while others indicate either a decrease or no changes after loading [196, 201, 203-208]. For growth plate, studies using tissue explants have shown differential morphological changes of chondrocytes in the different zones under compression [198]. Additionally, under short term compressive loads, a decrease in aggrecan, collagen type II and X has been reported. In contrast, under compressive dynamic loading, no changes in ECM composition although changes in cell organization were observed [191].

2.6.1.2 In vitro studies: Cell Cultures

Given the difficulties for analyzing the individual effects of mechanical stimuli to which cartilage is subjected in vivo, the response of chondrocytes to such stimuli has been evaluated in monolayer and tridimensional cultures [38, 199, 203, 206-209]. These analyzes not only provide information about the cellular responses and the regulatory mechanisms associated, but also they allow to evaluate the use of mechanical stimuli in tissue engineering approaches [199].

The effect of compressive loads on in vitro cultures of chondrocytes depends on load’s intensity and duration [210]. In this context, it has been observed that the application of static compressive loads increased the production of several types of MMPs, and also inhibited the synthesis of collagen type II and PG [210, 211]. In turn, the effects of dynamic compressive loading in cell proliferation and synthesis of PG, GAGs and collagen type II are contradictory [196, 201, 203-208, 210-228]. This behavior may be related to the wide variability of the methodology used for each group, which can be related to different sources of chondrocytes, age of the animal model, characteristics of 3D matrix used, chondrocyte seeding density, frequency of the stimulus, load cycles and initiation and duration of the stimulation [201, 206, 210, 212-217, 221, 225].

The chondrocytes response to tensile loading have also been addressed using in vitro monolayer cultures. Such cultures have been performed by seeding cells in membranes that are submitted to uniaxial or biaxial dynamic stretching. Most of the studies have evaluated chondrocyte dynamics in terms of cell proliferation and molecular synthesis of collagens and

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PG. Similar to the observed for compressive loading, the evidence available suggests that the response of chondrocytes to tensile loading also depends on the duration and intensity of the stimulation [229-232]. In fact, anabolic effects in chondrocytes are induced after short term simulation (less than 12 hours); while a decrease in the ECM molecules is only observed after a prolonged stimulation [229]. In addition, some studies have reported an increase of other molecules such as proteases and their inhibitors (e.g. TIMPs, MMPs), soluble factors (e.g. TGFβ, VEGF, PTHrP, Ihh) and pro-inflammatory factors (e.g. Nitric Oxide, Prostaglandin E, cyclooxygenase 2) after tensile loading stimulation [209, 229, 230, 232- 235]. However, it is difficult to extrapolate definitive conclusions regarding the stimulus characteristics and chondrocytes response considering that, similarly to compressive loading, there is a high variability in the stimulation protocol used among different studies in terms of strain magnitude, loading duration and frequency (reviewed in [229]).

Hydrostatic pressure (HP) has been extensively used as a stimuli to induce changes over hyaline cartilage such as protein expression and matrix production [236]. However, the mechanism by which HP produces those changes is not well understood. HP provides a robust method of chondrocyte stimulation since it can be applied over cells cultured in monolayer, three dimensional engineered constructs or cartilage explants [237]. Several studies have shown the relation between HP and biological response of hyaline cartilage mainly in terms of ECM molecules synthesis [238-241]. Furthermore, HP has demonstrated to trigger the expression of inflammatory mediators and the synthesis of morphogens like Ihh [242, 243].

Finally, some studies have indicated that chondrocytes are exposed to different levels of fluid flow within the tissue [244, 245], suggesting that mechanical shear stress has a pathophysiologic relevance in cartilage biology [246]. Within this context, several studies have analyzed the influence of such stimuli on chondrocyte behavior. Results indicated that this stimulation scheme increased the release of pro-inflammatory mediators and nitric oxide, and induced molecular changes associated with apoptosis [247, 248]. Additionally, it is known that hyaline cartilage tissue engineering constructs, are also affected by shear stress, revealing that this stimulus may alter the intercellular signaling pathways in chondrocytes [241, 249]. Some reports suggest that fluid shear stress reduces expression of aggrecan and collagen type II [250]. Other studies, demonstrate that an intermittent application of dynamic shearing forces during four weeks, improved the quality of the cartilaginous tissue formed in vitro [248, 251]. These data indicate that the nature and magnitude of shear stress may play a significant role in the homeostasis of the structure and function of hyaline cartilage [246].

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2.6.2 Mechanotransduction

Mechanotransduction is the process by which mechanical signals are sensed by cells modulating their biological activity [211]. In chondrocytes, extracellular stimuli are sensed mainly by membrane proteins involved in ECM-cell interactions and ionic channels [48, 52]. The main proteins associated to cell-matrix interactions are integrins. Integrins are a family of 24 heterodimeric proteins that result from combination of 18 α subunits and 8 β subunits. Such dimers bind to several ECM molecules with different affinities [52, 56, 252]. The main integrins expressed by chondrocytes are α1β1 , α3β1, α5β1, α10β1, αVβ3 and αVβ5 which act as receptors for Collagen types VI and II, matrilin-1, fibronectin, osteopontin, COMP, and vitronectin [52, 252-255]. Cytoplasmic domains of integrins are coupled to kinases (ILK) that have been implicated in signal transduction through Ras, Rho and Rac pathways [209, 211].

In addition to integrins, other membrane proteins like CD44 and annexin V (also known as anchorin CII) have also been implicated in cell-matrix interactions in chondrocytes. The first one is a 85 kDa transmembrane hyaluronan-binding glycoprotein that has been implicated not only anchoring but also sensing and signaling functions [255-257]. Annexin V is a 34kDa protein, member of a family of calcium and phospholipid binging proteins that binds mainly to collagens present in the PCM and ECM, mainly type II and with lesser affinity to types V, IX, X and XI [256, 258].

Additionally to cell-matrix interactions, it has been described that in chondrocytes, cell deformations caused either by changes in cell volume or due to mechanical loading, lead to activation of different kinds of ionic channels [48]. Although a plethora of ion channels have identified in chondrocytes membranes, calcium channels are the main type of ion channels associated to mechanotransduction processes including Voltage-gated sodium channels (VGSCs) and stretch activated ion channels (SAC), in addition various members of the TRPV (Transient Receptor Potential vanilloid) non-selective cationic channels family, specially TRPV4, have been associated to osmotic stress responses [48, 211, 259]. Supporting this association among calcium channels and mechanosensing, some studies have evidenced changes in intracellular calcium levels in chondrocytes after mechanical loading [211, 260- 262].

In addition to calcium and GTPases, some other signaling pathways have been involved in mechanotransduction including MAPKs cascades, however the mechanisms leading to their activation are not well understood [209, 211, 263].

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2.7 IN SILICO APPROXIMATIONS TO BONE GROWTH AND MORPHOGENESIS. THE ROLE OF STRAINS AND PRESSURES.

2.7.1 Computational Models

In order to better understand how the mechanical stimuli influence bone growth and ossification, it is necessary the integration of the current understanding of biological and mechanical factors involved in such process, as well as their interactions.

As mentioned in previous sections, characterization of biological factors and their changes induced by mechanical loading have been extensively studied using experimental approaches at in vivo and in vitro scales, relying on the use of available methodologies for qualitative and quantitative evaluations on cellular and animal models. In contrast, studying experimentally the mechanical factors in the context of biological tissues has been more challenging. Although different techniques are available for characterization of mechanical properties of biological tissues [264-266], it is not possible to measure stress distributions in vivo [267]. Taking this into account, mathematical modelling has become a useful tool, since it offers accepted theoretical methodologies to approach such problems. Therefore, the studies developed until now have been encompassed in the field of biomechanics, a discipline that applies the concepts of classical mechanics of rigid bodies, deformable bodies and fluid mechanics to the analysis of mechanical behavior of biological tissues.

Biomechanics studies forces and their effects on motion and deformation of biological tissues, which depends on a variety of factors including: the size and direction of forces, mechanical properties of the tissue, and shape of the tissue [268, 269]. Biomechanical approaches to bone development have focused on performing stress analysis of bone elements, which implies the determination of the distribution of stresses and strains generated within the tissue during development. However such analysis go beyond the simple description of such mechanical environment, thus biomechanics applied to bone development has been used as a tool to study the “rules that govern the effects of mechanical loading on tissue differentiation, growth adaptation and maintenance” [270]. Therefore, it has explored the biological implication of the mechanical stress distribution, based on the hypothesis that mechanical loading influences cellular behavior of the tissue in terms of biosynthetic or catabolic activity, proliferation, and/or differentiation, among others. This kind of approximations are encompassed as a different discipline known as mechanobiology, which integrates biological and mechanical components, using often computational modeling [270, 271].

Computational tools have been widely used in mechanobiology since they allow to integrate experimental evidence at different scales, either mechanical or biological, and reveal resultant emerging behaviors that help to understand biological processes [272]. Therefore,

50 models are generated taking into account well-defined and concrete physical and biological inputs and their relationships. These are expressed mathematically in terms of variables, parameters and quantitative relationships generating a system of differential equations. One of the most used methods in mechanobiology of bone development for solving such equations is called finite element analysis (FEA) [270]. The FEA allows the fractioning a complex work domain (biological structure under analysis), in discrete finite number of segments (elements) for which the behavior is known and may be represented in terms of a system of differential equations that can be solved computationally. Thus, such approach allows to perform calculation on each element and predict interactions among elements, to finally construct an approximation to the behavior of the whole domain [270, 273]. Therefore, FEA has been a useful tool for analyzing biological processes, since they represent complex work domains for which biochemical and or mechanical behavior of the whole structure not always can be described in terms of equations, although the evidence may provide information for small segments. In fact, during the las 30 years, the FEA method has been widely used for approaching the behavior in implant design in orthopedics and other medical areas, as well as in modeling processes in developmental biology [274].

As mentioned previously, the process of mathematical modelling in mechanobiology implies the establishment of quantitative relationships between biological and mechanical factors. Since in most of the cases the latter are not well understood, mechanobiology approaches are based on establishing hypothetic potential rules and determine if the outcome resembles realistic structures, morphologies or biological patterns by comparing to experimental evidence. Hence, computational mechanobiology is an iterative process of “trial and error” [270, 272]. Taking this into account, computational modelling provides insights into the biological-mechanical interaction and possible explanations to known biological processes, however they are affected by the assumptions used for constructing the model and require experimental validation. Despite such limitations, this kind of approaches have become powerful tools for generating novel theoretical hypothesis and predict the behavior of a biological systems that may be helpful for optimization and targeting of experimental approaches.

2.7.1.1 Mechanobiological models of bone development

Up to now, different types of theoretical approaches have been performed in order to understand mechanical regulation of different aspects of long bone development. First, there are descriptive studies focused on analyzing the mechanical environment within epiphysis and growth plate of bones at different developmental stages in order to propose possible associations between specific mechanical stimuli and biological responses [275-278]. For instance, using this type of analyses, Carter and coworkers suggested that shear stress may favor ossification while hydrostatic pressure may preserve cartilage tissue[277]. A second

51 type of studies imply integrative mechanobiological models that have been developed to simulate several aspects of skeleton development using a combination of biological and mechanical factors, obtaining patterns that highly resemble biological behavior. Most of these works take into account a generic basal biological contribution to bone growth to which mechanical contribution is added. The latter varies among studies in terms of the biological- mechanical relationship established in each study and the specific biological processes represented. Some of these approaches include the study of: bone growth due to growth plate ossification in response to the combined effect of shear stress and hydrostatic pressure [279- 282]; joint morphogenesis using a combination of shear stress and hydrostatic pressure as stimuli, with the first promoting ossification while the latter inhibits it [283, 284]; and cartilage growth during joint morphogenesis in response to static or dynamic hydrostatic pressure as the main mechanical regulator, where the static loads inhibited growth while dynamic loads promoted it [285]. A third type of models are biochemical models where the biological contribution to bone development within the models is considered in terms of specific morphogens. In general such models imply the establishment of reaction-diffusion patterns combined or not with a mechanical contribution. Among these approximation different aspects of bone development have been addressed including: long bone elongation, development of secondary ossification centers and epiphyseal cartilage canals [281, 286- 289]. Finally, some other authors have used combined experimental and computational approaches to predict bone growth in response to mechanical loading, providing evidence that proves the importance of such relationship for in vivo bone development [186, 278, 282, 290].

In addition to the models representing bone development, tissue specific models have also been developed, to analyze at lower scale (cellular – molecular) the mechanical behavior or mechanical-biological interactions involved in cartilage or bone physiology. For cartilage such approximations include models analyzing the role of ECM molecules quantity and quality on tissue mechanical behavior [291-296]; tissue growth [297]; tissue mechanical response to loading [298]; and in vitro cellular response to mechanical loading [299-305].

2.8 ABNORMALITIES IN LONG BONE DEVELOPMENT

Development of long bones is a long process that starts from early embryological development until the end of adolescence. During prenatal development alterations in bone development are consequence of either genetic disorders (involving bone, cartilage or endochondral ossification) or induced malformations during gestations due to crowding or position, and together may affect around 6% of newborns [306]. The first group is known as skeletal dysplasias, and comprehend more than 400 different diseases forming a clinically and genetic heterogeneous group of disorders characterized by short stature and deformation/malformation of bone and cartilage with a wide spectrum of severity. Although individually each disorder is rare, birth incidence of these disorders is almost 1/5000 [307,

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308]. Initially, skeletal dysplasias were divided based on clinical and radiologic criteria mainly into: osteodysplasias (defects in mineralization), osteochondrodysplasias or chondrodysplasias (defects affecting cartilage and bone development), dysostoses (malformations of one or certain group of bones), however with increasing knowledge and number of diseases identified, they have been reclassified in around 40 groups based on biochemical, molecular and/or radiographic criteria [306, 307, 309].

Skeletal abnormalities developed after birth correspond to alterations in growth plate function, leading to abnormal shape and length of one or various skeletal elements. Such alterations may be due skeletal dysplasias previously described or acquired conditions. These latter involve conditions that result in either premature closure of growth plate (epiphysiodesis) or overgrowth, including: that may be consequence of traumatisms (e.g. Salter-Harris fractures), tumors, infections (e.g. osteomyelitis), abnormal loading of specific , inflammatory processes, muscular disorders, ischemia and metabolic disorders occurring during the childhood or adolescence that may involve growth plate or alter systemic factors involved in bone growth regulation (e.g. endocrine disturbances, malnutrition, etc) [310].

2.8.1 Chondrodysplasias

Chondrodysplasias are a group of more than 400 diseases that alter either directly or indirectly the structure and/or composition of cartilage ECM. They are caused by mutations in genes that codify ECM structural proteins, transcription factors, morphogens, proteins involved in signaling pathways (receptors, ligands, channels, etc), enzymes, chaperons and genes with unknown function [3, 311].

Chondrodysplasias are diseases that present high clinical, biochemical and genetic heterogeneity. They affect mainly the appendicular skeleton, leading to progressive development of bone deformities caused by alterations in long bones size and/or shape. These diseases frequently present as short trunk dwarfism and usually are accompanied by joint articular dysfunction. Moreover, they display a wide spectrum of clinical severity ranging from neonatal lethal phenotypes to mild adult forms presenting solely as arthropathies [3]. In general these pathologies severely compromise the patient’s quality of life and although their low individual frequency, as a group, they affect around 1 per 5000 newborns [3].

2.8.1.1 Mucopolysaccharidoses (MPS)

Mucopolysaccharidoses (MPS) are genetic chondrodysplasias caused by alterations in the catabolism of mucopolysaccharides or glycosaminoglycans (GAGs), important structural

53 components of ECM of connective tissues, particularly cartilage, where they are responsible for compressive resistance and maintaining osmotic pressure [38].

MPS are caused by mutations that lead to deficiency of lysosomal enzymes involved in GAGs degradation, resulting in a deficient GAGs degradation. Therefore, in the MPS, GAGSs accumulate within the cells and the ECM of different tissues giving rise to visceral involvement, bone deformities and in some cases central nervous system involvement with a wide spectrum of severity [47, 312, 313]. Currently, seven MPS types have been identified caused by mutations in 11 different enzymes (Table 2-4).

Table 2-4. Classification of the Mucopolysaccharidoses (MPS) Number Eponym Enzyme deficiency GAG affected IH Hurler (severe) α-L-Iduronidase DS – HS IH/S Hurler-Scheie (Intermediate) IS Scheie (mild) II Hunter Iduronate-2-sulfate sulfatase DS – HS IIIA Sanfilippo A Heparan-N-sulfatase HS IIIB Sanfilippo B α-N-acetylglucosaminidase HS IIIC Sanfilippo C Acetyl-CoA:α-glucosaminide HS acetyltransferase IIID Sanfilippo D N-acetylglucosamine-6-sulfatase HS IVA Morquio A Galactose-6-sulfatase KS – C6S (N-acetylgalactosamine-6 sulfatase) IVB Morquio B β-galactosidase KS VI Maroteaux-Lamy N-acetylgalactosamine-4-sulfatase DS, C4S (Arylsulfatase B) VII Sly β-glucuronidase DS-HS- C4S, C6S IX ------Hyaluronidase Hyaluronan DS: Dermatan sulfate; HS: Heparan sulfate; C4S: Chondroitin-4-sulfate; C6S: chondroitin-6-sulfate; KS: Keratan sulfate.

One of the most prominent clinical characteristics of MPSs is the bone and connective tissue involvement. The skeletal involvement observed in MPSs is a generalized compromise known as dysostosis multiplex. It includes abnormalities such as: short stature, vertebrae malformations, kyphosis or scoliosis, genu valgum, among others. These features are present in most MPS to some extent, regardless of the specific enzyme involved or the GAG being accumulated and may become evident very early in life and impact greatly the patient’s quality of life [47, 314]. In fact, the only MPS subtype where skeletal involvement is minimal or even absent is MPS III [47].

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Histological studies in MPS bones have shown not bone structural abnormalities, however alterations in articular cartilage and growth plate have been evidenced, suggesting that the disease may impact mainly the processes of chondrogenesis and endochodral ossification [315, 316]. Furthermore, studies performed using animal models indicate that GAGs accumulation may be associated to increased inflammation leading to chondrocytes apoptosis. In addition, altered expression of enzymes involved in ECM degradation has been reported [317].

Up to now there are no effective therapeutic approaches that can reverse or improve such skeletal involvement once established. For these reason, it is important to understand better the physiopathology of these diseases. Little is known about cellular mechanisms involved in the progression of the disease, although GAG metabolism and the metabolic defects are well described, [3, 313, 317].

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3 GROWTH PLATE STRESS DISTRIBUTION DURING BONE DEVELOPMENT

3.1 INTRODUCTION

Long bone development is a complex process. It begins early during embryonic development with formation of a cartilaginous mold (anlagen) through the process of chondrogenesis. This mold is progressively ossified by endochondral ossification [14-16]. This cartilage to bone transition, is characterized by cellular and extracellular matrix (ECM) changes. Thus, chondrocytes undergo a differentiation process implying changes in cell morphology, proliferative status, and ECM synthesis profile leading ultimately to bone and vascular cell recruitment and tissue mineralization [14-16]. In humans, this process starts during the second trimester of gestation and lead to the establishment of the primary center of ossification (POC) in the anlagen’s central region. Then, the ossification is extended towards the periphery giving rise to the diaphysis, which is flanked at both extremes by a cartilaginous epiphysis.

By the end of gestation the epiphyses experience a process of ossification similar to the one described for diaphysis formation. This leads to the generation of the secondary ossification centers (SOC), which will enlarge until a complete epiphyseal ossification is achieved between five and six years of age. When such process is completed, the only cartilaginous regions preserved within the bone correspond to the articular surface and the growth plate [11]. Articular cartilage will remain throughout life acting as shock absorber and providing a low friction surface. In addition, this structure assures proper joint mobility and loading bearing capacity, as well as preserving subchondral bone integrity [19, 38]. Cartilaginous tissue is also retained between the epiphysis and diaphysis in a region known as growth plate. Histologically the growth plate is arranged in three zones: reserve, proliferative, and hypertrophic [1, 14, 16]. Other growth plate features, such as location within the bone, morphology, and width, change according to species, bone type and age [11]. The latter was illustrated in the work published by Kandzierski et al. evidencing that the growth plate morphology of the proximal femoral epiphysis in humans can resemble a concave meniscus at the age of four. Moreover, with increasing age, at seven the growth plate becomes straight, as a ridged non-uniform line. Lastly, the growth plate assumes the form of an arch at the beginning of puberty [1, 11, 318-321]. In addition, growth plate’s width also changes through life, with a wider growth plate during early stages and diminishing progressively until the

56 end of adolescence, when it is completely resorbed and the epiphysis is fused to the metaphysis [23, 319, 322, 323].

Within the growth plate, endochondral ossification continues until the end of adolescence assuring longitudinal growth after epiphyseal ossification is completed [14, 19]. Such is a complex and highly regulated process affected by biological and mechanical factors, which, together, will ultimately determine bone formation velocity and consequently growth rates [180]. According to this, biological factors influencing chondrocytes differentiation within the growth plate include several systemic and local soluble factors, as well as components from the ECM [45, 46, 135]. Systemically several hormones are involved, which vary according to age, gender and even nutritional status [135, 168]. Locally, chondrocytes at different stages synthesize a plethora of growth factors and morphogens, generating gradients responsible for stimulating specific cell programs [46, 111, 135]. In addition to biological factors, it has been widely recognized that bone growth is influenced by mechanical loading, as stated by the Hueter-Volkmann law [174, 324]. Such association was suggested initially based on observations made in a clinical environment regarding the shape of bone joints and their potential relationship with the their loading history [21, 174, 325].These observations were then confirmed by in vitro and in vivo studies evidencing that mechanical stimuli may trigger changes in chondrocyte proliferation rates, hypertrophic cell size, alterations in ECM components, with the expression and synthesis of regulatory molecules [21, 183, 231, 235, 243].

In order to further understand the role of mechanical stimuli over bone development, several theoretical approaches have been performed [181, 326, 327]. Initial computational analysis over mechanical environment during SOC development, performed by Carter and Wong, revealed associations between octahedral shear stress (S) and ossification zones; as well as hydrostatic pressure (P) within cartilaginous zones [277]. Derived from such studies they proposed a mathematical relation between S and P, called osteogenic index (OI).This index is an ossification pattern predictor that reflects mechanical stimuli over the ossification process [277]. Subsequent works have focused on characterizing epiphyseal mechanical environment and its relation to epiphyseal ossification [279, 280, 283, 284, 328], joint development [277] and initial bone formation [278, 329, 330]. In addition, some authors have performed more complex models that integrate biochemical and mechanical factors [287, 288, 331]. All of them have only considered events occurring in the epiphysis, not taking into account growth plate characteristics or behavior. In fact, mechanical stimuli within the growth plate and its implication on growth rates have been poorly explored. For instance, Piszczatowski analyzed the distribution within the growth plate of “growth index” as reported in previous works considering a simplified geometry consisting of a cartilage segment between two layers of bone [275, 276]. However, up to now stress distribution on the epiphysis and growth plate through different stages of bone development has not been studied.

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In order to provide novel information regarding mechanical environment within growth plate, the aim of this work is to describe the stress distribution within the growth plate during different stages of development to approach three main issues: first, looking for patterns that may correlate to the known biological behavior of growth plate; second, to explore if within growth plate, mechanical influence may play similar roles to the proposed for epiphyseal development; and finally analyze the effect of growth plate morphology on epiphyseal stress distribution and vice versa. Therefore, it was devised a bone with generic geometry to explore growth plate stress distribution during different stages of epiphyseal ossification, using an axisymmetric (3D) finite element analysis. The results obtained by such analyses were then contrasted to the physiological changes in growth rates observed during human bone development to analyze their biological implications. Information derived from this work will help elucidate mechanical events taking place within the growth plate and epiphysis during long bone growth. Additionally, the information generated may be useful to formulate hypotheses regarding mechanical influences on biological events taking place in normal and pathological bone growth scenarios.

3.2 MATERIALS AND METHODS

To understand long bone mechanical behavior at different growth stages it was performed a computational analysis using a linear elastic model solved by finite element analysis (FEA). Solving was performed by finite element analysis employing a user developed subroutine implemented in Fortran (Formula Translating System, New York, USA) programming language, and solved in ABAQUS v 6.1. Results were visualized in TECPLOT 360 (Tecplot Inc. Bellevue, WA USA).

3.2.1 Model

A 3D axisymmetric model of a generic bone was designed representing an extreme of a long bone. Taking into account that several human long bones epiphysis have a similar shape during early embryological stages such as the proximal femur head, a simplified morphology corresponding to a rounded joint surface was considered [318, 326]. Since such morphology displays symmetry in terms of geometry, loads, constrains and material properties, a model consisting of an axisymmetric geometry was used for analysis (Figure 1). Bone´s longitudinal length was 25 mm and epiphyseal radius was 10 mm based on the dimensions reported for prenatal human femur (Figure 1A) [283, 318]. For simplification of the model the same morphology was maintained for latter developmental stages.

The model included six regions: articular cartilage, diaphysis, growth plate, Ranvier’s groove, epiphysis and secondary ossification center (Figure 1). To perform mechanical analysis, a linear elastic model was used, considering that applied load was static and

58 constant, and contour fluid flow was not taken into account. In addition, linear elastic models have proven to be as reliable as poro-elastic constitutive models for cartilage stress distribution analysis in the context of bone development according to previous reports, thus here we used the former considering its simplicity for a first approximation to growth plate mechanical environment [326, 327].

Material properties for each zone are described in Table 3-1. For simulations elastic modulus and Poisson’s ratio in different tissues were as follows: diaphysis and secondary ossification center were designated as trabecular bone; Ranvier´s groove, a mechanical support structure, as fibrous tissue; and growth plate and articular cartilage as cartilage. In order to discard possible influences of material transition in stress distribution results considering the drastic change in material properties between growth plate region and diaphysis, an analyses was performed using a transition zone that presented a gradual change of material properties (Appendix A – Material and methods); results evidenced similar patterns with or without a transition zone (Appendix B – Figure B1).

Table 3-1. Tissue material properties. Elastic modulus and Poisson’s ratio for cartilage, bone, and Ranvier’s grooves as established by Piszczatowski [275]. Tissue Elastic Modulus Poisson Ratio Location within the (E) (ν) model* (MPa) Cartilage 6.0 0.495 Epiphysis (Stages 1-3) Growth Plate Articular Cartilage Trabecular Bone 345.0 0.300 Trabecular Bone SOC (Stage 2-3) Epiphysis (Stage 4) Fibrous tissue 10.0 0.300 Ranvier’s groove *See Figure 3-1. SOC: Secondary Ossification Center

Our model included events posterior to diaphyseal ossification. To study mechanical environment along bone development, we simulated four stages that recapitulate sequential events observed in normal human long bone development:

Stage 1: Completely cartilaginous epiphysis (Figure 3-1 A). This stage corresponds to embryological development, from blastema formation to birth.

Stage 2: Within the epiphysis a small area of trabecular bone was included, resembling initial stages of SOC formation (Figure 3-1B). This stage occurs from the perinatal period to the first year of life depending on the bone. For this stage, SOC size and shape were designed individually for all conditions tested based on high osteogenic index (OI) areas obtained in

59 stage 1 simulations as shown in Figure B2 in Appendix B (see Data Analysis for further information); thus SOC geometry varies in size and shape, including circles and differently oriented ellipses as shown in Figure B3 in Appendix B.

Stage 3: Within the epiphysis a medium size area of trabecular bone was included, resembling an intermediate phase of SOC growth (Figure 3-1C). Secondary center of ossification enlargement occurs through early infancy from two to five years of age for most bones.

Stage 4: Completely ossified epiphysis, where all tissue is considered trabecular bone except for the region corresponding to articular cartilage located at the upper limit (Figure 3-1D). For most bones this stage is achieved at middle childhood around 6 years of age.

Figure 3-1. Generic bone geometry. Geometries corresponding to stages 1 (A); Stage 2 (B); Stage 3 (C); and Stage 4 (D) as indicated within the text.

Different widths and location of the growth plate were simulated for each of the aforementioned stages trying to resemble the conditions of different bones as shown in Figure 3-2. Three growth plate width sizes were used (W1: thin, W2: medium, W3: thick, corresponding to 0.125, 0.25 and 0.5 mm respectively). Growth plate sizes were selected according to the width reported in 5 year-old humans and 30-days-old rats which was established as W2; W1 and W3 corresponded to half and double W2 size [332]. In addition, three locations within the epiphysis (L1: low, L2: middle, L3: high) were simulated for each morphology (Figure 3-2 B-D). To construct different locations, configuration L2 was used as reference and L1 and L3 were achieved by moving the growth plate to upper or lower L2 edge respectively. Lastly, four growth plate morphologies were considered: straight, concave, convex, and irregular, according to Kandzierski et al [319]. As a result, a total of 36 morphologies were used for simulations. For meshing, conventional cuadrilateral elements were used. Based on a convergence analysis performed using different element sizes for meshing (between 0.005 and 0.1 meshing length units), an element size of 0.01

60 meshing length units was chosen given the good results obtained for both epiphyseal and diaphyseal stress distribution at low computational cost (Figure B4 – Appendix B). The number of element varied among morphologies ranging from approximately 16.000 to 20.000.

Figure 3-2. Growth plate characteristics. Different growth plate widths (A-C), growth plate locations (D-F) and morphologies (G-I) were considered. A. Thin growth plate (W1). B. Growth plate with medium width (W2). C. Thick growth plate (W3). D. Growth plate located at low height (L1). E. Growth plate located at middle height (L2). F. High Growth plate location (L3). In figures A to F a representative images for straight morphology are presented. G) Concave morphology. H) Convex morphology. I). Irregular morphology. Representative images for the non-straight morphologies used correspond to W2-L2 configuration. Modified from [333].

3.2.2 Loading conditions and constrains

For the model, Y axis was taken as symmetry axis; additionally zero displacement constraints for Y axis at the lower edge of the geometry was established. No additional constrains were taken into account among layers within the model, since in vivo such structures are not expected to generate internal movement in physiological conditions. Loads were applied on the upper arch (longitude of arc = 8.4 mm)[284]. Due to limited knowledge regarding the

61 loading conditions in a prenatal bone, the load applied in the simulation corresponds to a pressure of 1 MPa (Figure 3-3A), based on previous computational approaches reported in literature, since this allows the observation of general stress patterns [283, 289].

Figure 3-3. Loading conditions, constrains and data analysis. A. Contour figure showing symmetry axis and constrains used. Load position is indicated with arrows. B. Growth plate sections used for stress distribution analysis. Paths used (L, H1, H2 and H3) are marked with discontinuous lines. Modified from [333].

3.2.3 Data Analysis

Initially, in order to analyze the changes in the mechanical environment through development, the distribution patterns of octahedral normal stress (P) and octahedral shear stress (S) were analyzed for all stages in the straight-W2-L2 configuration.

Distribution of such stresses was observed in the epiphysis and within the growth plate for all stages (Stages 1-4). To characterize the behavior of these stresses along the model, their distribution was measured in the central region of the model using a longitudinal path called Path L as indicated in Figure 3-3B. Afterwards, the effect of changes in growth plate morphology on epiphyseal and growth plate stress distribution patterns were analyzed. For such purposes, we analyzed the mechanical environment in terms of the OI proposed by Carter and Wong [277].

According to studies developed by Carter and Wong cartilage preservation resulted from octahedral normal stress (P), and bone was the result of octahedral shear stress (S) [277]. Based on such concepts, they defined a numerical relation for P and S, named osteogenic

62 index (OI) as an indicator of mechanical stimuli influence on the ossification process given by:

OI = S + kP 3.1

Where k is an empirical constant that was tested with values between 0.2 and 2 (Figure B5 - Appendix B). Since the values of k have important impact on OI distribution (Figure B5 - Appendix B), for all simulations k = 0.5 was used, since this value closely resembles a biological setting as described by Carter et al, where a region of low OI in the articular cartilage region is observed and high values of OI for the predicted area of secondary ossification center, which was clearly distinguished within the epiphyses [277].

Osteogenic index is a scalar parameter integrating the competing effects of octahedral normal stress (P) and octahedral shear stress (S). Thus, OI can be used to predict which regions of a cartilaginous skeletal element are likely to ossify first (high OI values) and which are likely to remain cartilaginous (low OI values) [277]. Thus, in order to describe the effect of growth plate width, location and morphology on the mechanical environment and thus analyze the potential effect on growth plate ossification, all the results are presented in terms of OI. In addition, OI distribution was analyzed only in cartilaginous structures within the model that include epiphysis (only for stages 1 and 2, results of stage 3 were omitted since they were similar to those observed for stage 2) and growth plate.

In order to characterize mechanical environment within the growth plate, for all conditions simulated, OI distribution was analyzed in a similar way indicated for P and S using a longitudinal path L (Figure 3-3B). In addition, analysis in the horizontal plane were performed using sections named Path H1, H2 and H3 (Figure 3-3B). These paths illustrate OI values across the growth plate, starting from the center to Ranvier’s groove for resting (H1), proliferating (H2), and hypertrophic (H3) zones.

3.3 RESULTS

3.3.1 Stress distribution during development

Epiphyseal stress distribution analysis during the earliest stages of bone development with a completely cartilaginous epiphysis (stage 1) demonstrated peak octahedral normal stress (P) beneath the loading area. Furthermore, highest values for octahedral shear stress (S) were observed in the central zone of the epiphysis. Likewise, highest OI values were also centrally located as observed for S (Figure 3-4).

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Figure 3-4. Cartilaginous epiphyseal stress distribution (stage 1). Representative sample for straight growth plate in the middle with medium width (L2,W2 stage 1). The load bearing area is indicated by the arrow. A. Octahedral normal stress (P). B. Octahedral shear stress (S). C. Osteogenic index (OI).

When S, P and OI were analyzed in different developmental stages (Stages 1-4) it was observed that P reached the highest values in the areas corresponding to articular cartilage and growth plate for all simulations performed. In the latter, P increased concomitantly with epiphyseal ossification progress (Figure 3-5). In contrast, for shear stress, highest values were reached surrounding SOC. A similar pattern was observed for the osteogenic index (OI) (Figure 3-4; Figure 3-5).

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Figure 3-5. Stress distribution within the epiphysis and growth plate. A. Octahedral normal stress (P). B. Octahedral shear stress (S). C. Osteogenic Index (OI). To the left side the results of the complete epiphyseal distribution obtained using Path L1 are represented. To the right, a magnification of the growth plate zone is presented. RZ: Reserve zone, PZ: Proliferative Zone, HZ: Hypertrophic zone. Red line correspond to 0 value for all stimuli.

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3.3.2 Growth plate effect on epiphyseal OI distribution

As described in the published manuscript [333], it was observed that OI distribution changes were mainly associated with growth plate localization (Figure 3-6, Appendix A, Figure B2 – Appendix B). A growth plate in the lower position (L1) presented the highest value for OI in the center with a vertical elongated distribution that flattened as growth plate location became closer to the loading area (L3) (Figure 3-6A). Maximum OI values within the epiphysis, showed a marked decreased value for a growth plate located at L3 compared to L2 and L1 (Figure 3-6B).

Figure 3-6. Cartilaginous epiphysis OI distribution. A. Representative sample of OI value distribution for simulations on straight growth plate in three different localizations and medium width (L1, L2, L3, W2 stage 1). B. Maximum OI values obtained in central region of epiphysis for all localizations, morphologies, and widths. Two way ANOVA was performed in order to establish the effect of all conditions tested, followed by Tukey’s post hoc test to determine statistical significance for specific conditions. Statistical significance was considered at p< 0.05. Figure taken from the published manuscript derived from this work [333].

3.3.3 SOC effect on epiphyseal stress distribution

When a bone structure within the epiphysis (SOC) was considered, changes in epiphyseal OI distribution were observed when compared to a completely cartilaginous epiphysis (stage 1) as shown in Figure 3-7. Results of this analyses are further discussed in Appendix A [333].

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Figure 3-7. Osteogenic Index (OI) distribution in an epiphysis with SOC. Representative sample of OI value distribution for simulations on straight growth plate in three different localizations and medium width (L1, L2, L3, W2 stage 2). Figure modified from the published manuscript derived from this work [333].

For stage 4, representing a completely ossified epiphysis, OI response to changes in growth plate width, location and morphology were not analyzed for the epiphysis since OI represents ossification stimulus on cartilaginous tissue. Therefore, for stage 4, OI values were only evaluated in the growth plate.

3.3.4 Growth plate OI distribution

Considering that the growth plate is the structure responsible for bone’s elongation, OI value distribution was specifically analyzed in this structure taking into account different growth plate characteristics (localization, morphology, and width) and developmental stages. In contrast to OI values for the epiphysis, OI values within the growth plate were affected by all variables studied: localization, morphology, and width, particularly in the central region (Figure 3-8; Figure 3-9).

Our results showed a heterogeneous OI value distribution, reaching peak values in the zone close to the epiphysis corresponding to the reserve zone for Stages 1 and 2 (Figure 3-8). However, such pattern was drastically changed when a completely ossified epiphysis was considered (stage 4) (Figure 3-8).

Further details regarding the osteogenic index distribution are provided in the published manuscript (Appendix A) [333].

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Figure 3-8. Growth plate osteogenic index (OI) distribution for all conditions simulated. Representative sample of simulations for straight growth plate. Figure taken from the published manuscript derived from this work [333].

Figure 3-9. Growth plate horizontal OI value distribution according to morphology. Representative sample of simulations for each growth plate morphology (L2,W2, case 1). Results obtained from Path H1. Figure taken from the published manuscript derived from this work [333].

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3.4 DISCUSSION AND CONCLUSIONS

This computational work presents a detailed stress distribution analyses over growth plate structure during different stages of bone development, which, to the best of our knowledge, has not been addressed previously in literature. As further discussed in Appendix A, computational analyses performed revealed a longitudinal stress distribution pattern that seems to correlate with the histological arrangement in zones characteristic of the growth plate. Such findings suggest that mechanical influence on cell behavior within specific zones (mainly resting zone) may be involved in stimulating longitudinal bone growth [333]. Additionally, it was observed that complete epiphyseal ossification has a drastic impact on growth plate stress distribution favoring its maintenance rather than ossification [333]. Furthermore, our results suggests that mechanical stimuli may play an important role on epiphyseal development as well as growth plate ossification, in particular during early stages of development, in agreement with the increasing in vivo and in vitro evidence regarding mechanical effect on long bone development [21, 191, 290].

In order to study events that take place during early stages of human long bone development, initial simulations were performed considering a completely cartilaginous epiphysis [11, 321, 334]. We simulated such events as stage 1 occurring during the second trimester of human development up to the first year of life. Our results agree with those presented by Carter et al. under similar loading conditions and constrains [277]. Epiphyseal areas with high OI values allow predicting SOC localization and morphology. Furthermore, according to our results, future SOC characteristics depend mainly on growth plate location (Figure 3-6), which may resemble the behavior observed during the development of some bone element in the human appendicular skeleton as further discussed in appendix A [333].

With SOC formation and during its expansion (stages 2 and 3), our results showed stress redistribution, especially in terms of octahedral shear stress, which highest values were found surrounding the SOC in areas corresponding to the ossification front (Figure 3-5). This result might be indicative of an association between high S values and triggering of specific cellular programs related to the differentiation process that include synthesis of soluble factors, such as growth factors, morphogens or inhibitors, in addition to promoting cell proliferation [48, 211, 231, 235, 243, 335, 336]. This assertion is supported by in vitro evidence that suggests chondrocyte’s capability of sensing changes in the ECM secondary to mechanical stress [337]. Reports indicate these changes occur mainly through membrane proteins that interact directly with the ECM and mechanosensitive ion channels, leading to changes in biological responses decreasing ECM synthesis and inducing molecular changes associated with apoptosis [337].

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The above mentioned behavior was also observed for OI, thus a non-uniform stress redistribution was observed, leading to higher OI values laterally rather than vertically, resulting in an ovoid growth trend (Figure 3-5; Figure 3-7). Such results seem to resemble SOC growth pattern for bones such as the distal femur [11, 320]. Additionally, as for stage 1, OI values and distribution seem to be affected mainly by growth plate localization (Appendix A; Figure B3 – Appendix B).

Within the growth plate, mechanical environment is also affected by SOC development (stages 2-3). The results show that P increased concomitantly with epiphyseal ossification progress (Figure 3-5). These results agree with the proposed role of P in cartilage conservation [277]. Such theoretical relationship has been evaluated by in vitro assays, where chondrocytes under cyclic hydrostatic pressure downregulated hypertrophic markers while increasing matrix synthesis, supporting the proposed chondro-protective role [249, 337, 338]. According to this, our results suggest that as epiphyseal ossification progresses, mechanical stimuli within growth plate gains a preserving role. As such at later stages, mechanical influence may be more related with maintenance of this cartilaginous structure rather than favoring growth. This correlates with the low values observed for S in stage 4 compared to the observed within the epiphysis for stages 1-3 (Figure 3-5).

Despite changes in magnitude, S values showed a consistent decreasing trend from the epiphyseal to the diaphyseal end of the growth plate throughout all developmental stages studied (1-4), with peak values localized in the reserve zone (Figure 3-5). Moreover, a similar pattern was obtained for OI during stages 1-3 (Figure 3-5; Figure 3-8), with OI values comparable to those observed in the epiphysis. Although such trend may seem contradictory to the observed in the epiphysis, it is important to consider that ossification within the latter occurs radially and there is no histological evidence of zonal organization which may imply a fast transition from resting to hypertrophic state of the chondrocytes there present, while in growth plate such process is delayed allowing development of a longitudinal zone arrangement [14, 23]. Thus, within growth plate the reserve zone is in charge of providing cells to the proliferative zone assuring growth process continuity [25]. Moreover, it has been proposed that resting chondrocytes may synthesize biochemical factors, responsible for growth orientation and inhibition of hypertrophy in the proliferative zone. These events favor growth plate histological organization in distinct zones [25, 111, 135, 165]. Therefore, based on the S and OI observed pattern, we suggest that high S and therefore OI values in the reserve zone may be stimulating cells to start to proliferate or synthesize biochemical factors or both, particularly in early stages of development (stages 1 and 2)[333]. As mentioned earlier, reports in the literature show an association between mechanical stimulus and differentiation process as well as synthesis of morphogens [191, 235, 243, 339, 340].

In sum, according to our results, within the growth plate OI presented a similar behavior prior and during establishment of SOC (stages 1-3). In such stages, OI values are close to 0, only

70 attaining slightly positive values in the area corresponding to the reserve zone (Figure 3-5; Figure 3-8). Moreover, values observed in resting zone were comparable among the three stages (Figure 3-5; appendix). Once epiphyseal ossification is completed, a drastic change in the pattern is observed with an important decrease in OI values (Figure 3-5; Figure 3-8). Based on such results, and only taking into account mechanical stimuli, comparable growth velocities may be expected in stages 1-3 while a delay in growth potential once epiphyseal ossification is completed. However, biological data indicate a high growth rate during embryological development, decreasing progressively during the first two years of life [34]. Later on, 2 – 10 years old, stabilization is achieved followed by a final increase in adolescence. After that, a continuous decrease is observed until growth plate closure is attained by 20 years of age (Fig. 6)[34]. Thus according to our data, a completely mechanical approximation to bone development highly resembled biological behavior during initial stages, although fail to do so once epiphyseal ossification is completed. Furthermore, growth rate changes occurring during life could not be predicted. Such behavior is consistent with the fact that growth rate is a result of mechanical and biological interactions that change according to age [135, 168].

In order to explore the usefulness of OI as an indicator of mechanical stimulation of ossification within the growth plate, in this study, OI distribution analysis was performed considering growth plate morphological characteristics that might be present in a wide range of long bones. However, the results obtained are highly influenced by the unique load scheme considered, thus it is important to consider that in vivo each bone has specific loading characteristics that are related to bone interactions with muscles, ligaments and other bones. Taking this into account, even though here it was observed a trend that correlate with some biological findings, to derive more accurate biological conclusions particularized simulations for specific bones should be performed.

The formulation of the computer model here presented includes several simplifications regarding epiphyseal geometry, loading conditions and the model used for mechanical behavior analysis. Despite such limitations, the model used revealed important information related to epiphyseal and growth plate stress distribution and the ossification process. Therefore, in order to obtain more accurate results our findings should be confirmed using bone specific models that take into account poroelasticity and interstitial fluid flow [182, 278].

In conclusion, this work pointed out the changes that the mechanical environment within growth plate experience through different developmental stages. Furthermore, the stress distribution pattern identified may have biological implications. Results from this study may be useful for understanding general mechanisms underlying mechanical influence on bone development, helping to direct future research on growth plate biomechanics and to formulate hypotheses regarding bone pathologies resulting from genetic or acquired conditions.

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Nonetheless, further work is needed to consider factors such as epiphyseal shape, loading conditions, and growth plate morphology in specific bones.

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4 ANALYSIS OF THE ASSOCIATION BETWEEN MECHANICAL ENVIRONMENT AND GROWTH PLATE MORPHOLOGICAL EVOLUTION DURING PROXIMAL FEMUR DEVELOPMENT.

4.1 INTRODUCTION

Longitudinal bone growth is regulated by the growth plate, a cartilaginous region located between diaphysis and epiphysis of long bones [14, 23]. Growth plate generates new bone tissue by endochondral ossification, a process in which cartilage is changed into bone by mineralization and subsequent remodeling of the calcified tissue. Such process is regulated by several factors among which genetic, hormonal and biochemical have been traditionally considered as the most important ones controlling proliferation and differentiation of chondrocytes within the growth plate [14, 23, 45, 168, 179, 180]. However, mechanical stimulation has been also proposed as a major role in the biology and development of the growth plate. This theory is based on the fact that, during development, bone elements experience a complex mechanical environment that is influenced by compressive forces derived from the independent growth of diaphysis and epiphysis of the bone; restrictions imposed by nearby structures such as the periosteum, perichondrium, Lacroix ring and adjacent bones; and influence exerted by muscles [21, 174, 179-184].

Confirmation of the importance of mechanical stimulation on growth plate biology has been accomplished by several experimental studies. For instance, in vivo studies have demonstrated that in prenatal stages, muscle contractions are required for normal bone ossification, and that axial loading affects bone growth rates and growth plate histological characteristics [181, 182, 187-190, 285]. Additionally, based on clinical observations and in vivo studies in rodents, it is recognized that overloading of bones is associated with growth restriction, while tension accelerates it; a phenomenon known as the Hueter-Volkmann law [21, 174].

From the computational point of view, some studies have been performed in order to analyze the mechanical environment within epiphysis and growth plate of bones at different

73 developmental stages in order to propose possible associations between specific mechanical stimuli and biological responses [275-278, 333]. For instance, using this type of analyses, Carter and coworkers suggested that shear stress may favor ossification while hydrostatic pressure may preserve cartilage tissue [277]. Studies derived from the latter have attempted to simulate several aspects of skeleton development using a combination of biological and mechanical factors, obtaining patterns that highly resemble biological behavior. Some of these works include the study of: bone growth due to growth plate ossification in response to shear stress [176, 279-282]; joint morphogenesis using a combination of shear stress and hydrostatic pressure as stimuli, with the first promoting ossification while the latter inhibits it [283, 284]; and cartilage growth during joint morphogenesis in response to static or dynamic hydrostatic pressure as the main mechanical regulator, where the static loads inhibited growth while dynamic loads promoted it [285]. Lastly, some other authors have used combined experimental and computational approaches to predict bone growth in response to mechanical loading, providing evidence that proves the importance of such relationship for in vivo bone development [186, 278, 290]. Nevertheless, there is still uncertainty about the role of mechanical loading in growth plate development since, during growth, this structure experiences several morphological changes comprising modifications in width, the location within the bone and the geometry of the structure [11, 35, 319, 320, 326, 341, 342]. In humans, it is observed that growth plate width diminishes progressively through life, and, in the proximal femur, for instance, its morphology exhibits changes acquiring straight, concave, convex and irregular shapes at different ages [11, 319, 320, 322, 323].

Based on the above, we hypothesize that growth plate morphological changes may respond to specific mechanical stimuli. Therefore, in this study we aim to analyze computationally the influence of mechanical stimuli in the growth plate morphological changes observed in vivo. For such purposes, here we analyzed mechanical stimuli previously reported to have a potential influence on growth plate ossification (hydrostatic pressure, shear stress, compression and osteogenic index) during bone development. Thus, we used a mechanical approximation to study a specific aspect of bone growth that has not been assessed previously from a computational point of view. In fact, as mentioned above, up to now, computational studies exploring mechanical influence on long bone development have mainly focused in exploratory analyses and theoretical predictions of epiphyseal ossification patterns and growth rates.

This study constitutes a first approximation to understand the relationship between mechanical stimuli and growth plate morphological evolution. This information will be important to better understand mechanical regulation of bone growth in order to favor future development or improvement of orthopedic therapies for pathologies that imply abnormal bone growth due to abnormal mechanical stimuli.

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4.2 MATERIALS AND METHODS

In order to establish the influence of growth plate shape on the behavior of selected mechanical stimuli, and the reciprocal influence of such stimuli on growth plate shape we performed a two part finite element analysis. For such purposes, the proximal femur was used as model for study considering the availability of literature reports regarding its morphological evolution through development and imaging corresponding to different ages. On the first part we hypothesize that, within each acquired growth plate shape during development, chondrocytes are inclined to minimize (or maximize) a given stimulus in an attempt to boost proliferation or hypertrophy. Therefore, we performed a descriptive approach in which the distribution of each stimulus was analyzed for different growth plate morphologies. This was performed in order to identify potential minimization or maximization trends of the stimuli studied during normal growth plate shape evolution.

On the second part, it was considered that changes in growth plate morphology are due to displacement of the cartilaginous tissue in the direction of growth. This is caused by an increased rate of either chondrocyte proliferation or hypertrophy which, in turn, is modified by an undetermined mechanical stimulus [183, 282, 290]. Based on this idea, we developed a predictive scenario in which we simulated the growth plate morphological evolution considering each separate mechanical cue as the sole mechanical contributor to bone growth. This in order to approach the potential contribution of each stimulus to the known biological behavior of the growth plate, specifically in terms of its morphology.

4.2.1 Geometric Model

For all analyses an axisymmetric model of the proximal portion of a developing femur was used according to the described in chapter 3 section 3.2.1 (Figure 4-1). The model included the femoral epiphysis, metaphysis and a portion of the diaphysis. It also encompassed three types of tissues: bone, growth plate cartilage and groove of Ranvier. For simplification purposes, and assuming that the events herein described present small deformations, as suggested by evidence of a controlled growth, all tissues were modeled as linear-elastic. Values of Young’s modulus and Poisson ratio are presented in Table 4-1. Meshing was done with 0.01 mm2 square elements, obtaining a total of 16197 elements and 16509 nodes.

For simplification, and considering that simulations aim to represent different stages of development that imply high variations on loading conditions, for simplification in this study a distributed unitary compressive load (1 MPa) was used in all cases, allowing the observation of general stress patterns [283]. Load was applied over the upper central zone of the femoral epiphysis (longitude of arc=8.4 mm), which corresponds to the area of contact with the coxofemoral joint where compressive forces are generated in vivo (Figure 4-1B)

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[193, 284]. Last, the metaphyseal end had partial movement restriction in the direction of femoral longitudinal axis as previously reported [284, 333].

Figure 4-1. Geometric Bone Geometry. A. Geometry description. In green are show the areas considered as bone, in blue is marked the growth plate and grey is the Ranvier’s groove. B. Constrains and Loading.

Table 4-1. Tissue material properties. Elastic modulus and Poisson’s ratio for cartilage, bone, and Ranvier’s grooves as established by Piszczatowski2011 [275]. Tissue Elastic Modulus (E) Poisson Ratio (ν) Location within the (MPa) model Cartilage 6.0 0.495 Growth Plate Trabecular Bone 345.0 0.300 Trabecular Bone Epiphysis Fibrous tissue 10.0 0.300 Groove of Ranvier

Formulation of both parts was performed using finite element analysis. Numerical implementation was carried out in a Fortran user developed subroutine, and solution was calculated using Abaqus solver.

4.2.2 Mechanical Stimuli

In order to explore the behavior of specific mechanical stimuli and their potential association with the morphological changes observed in vivo in the growth plate, here we analyzed four different stimuli that have been associated to modulation of bone growth process in literature [186, 277]. The stimuli considered in these study corresponded to the following equivalent

76 stresses: axial compressive loading (Sy), shear stress (S), hydrostatic pressure (P), osteogenic index (OI).

The role of axial loading on bone growth was initially suggested by the Hueter-Volkmann’s law which states that compressive loading inhibits growth while tensile loading stimulates it [174, 324]. Such principles have been supported by studies such as the one reported by Stokes and collaborators who described quantitatively the relationship between the magnitude of a sustained axial stress and growth rates of growth plates in different animal models. Furthermore, several other in vivo studies have reported decrease of growth rates and bone lengths after sustained compressive loading in different animal models [172, 186-189]. Based on such evidenced, some authors have proposed mathematical approximations to calculate mechanical stimulation for ossification within the growth plate using the axial loading as the main mechanical stimulus [186, 275, 276].

In addition, shear stress and hydrostatic pressure have been also associated to the regulation of specific biological responses of the tissues involved in skeleton development. Based on a descriptive computational analysis of stress distribution in developing bones using finite element analysis, Carter and coworkers proposed an association between specific mechanical stimuli and cartilage ossification suggesting that shear stress (S) may favor ossification while hydrostatic pressure (P) may preserve cartilage tissue. Furthermore, based on their findings, they proposed a mathematical relationship of S and P called osteogenic index (OI) as an indicator of mechanical stimuli influence on the ossification process [277]. Furthermore, Sundaramurthy et al. have provided some experimental evidence that correlated to mechanism for mechanical stimulation proposed by Carter and Wong [290]. In addition, a similar computational analysis was performed by Nowlan et al. in chick embryo bone rudiments that showed that areas of high octahedral shear stress correlated with regions where ossification will take place [278].

4.2.3 Part 1: Influence of Growth Plate Shape on Stimuli Behavior

During bone development, growth plate suffers several changes in its morphology that comprise the appearance of irregularities and changes in its curvature [11, 319, 320, 322, 323]. Such differences in shape can alter the mechanical environment to which growth plate is exposed and thus, they can also modify physeal ossification patterns. Based on this, we analyzed the behavior of each of the aforementioned mechanical stimuli on different growth plate morphologies.

For growth plate morphologies generation, an nxn array of equidistant points was established. In our case, we chose 6 points since it was a suitable number that allowed generation of all possible physiological morphologies with a low computational cost. The points array were

77 placed at the metaphyseal area of the geometry were the growth plate is located, with the first point of each row placed on the central side of the model, while the last one was placed on its lateral side (Figure 4-1A and Figure 4-2A). Within this array, a line was generated connecting 6 points such that the following rules were fulfilled:

1) X-coordinate of any point in the line must be greater than the corresponding coordinate of the previous point 2) In every combination, the first point must be in the central side of the model and the last one must be in the lateral side

Points within each combination were interpolated with a cubic spline. This gave as a result a line with the shape of the growth plate. This line represented the epiphyseal side of the tissue (Figure 4-2B). However, in order to generate the complete structure, another line with the same shape as the epiphyseal one was placed below it at a distance of 0.5 mm (diaphyseal side), as shown in figure 2C [332]. In addition, all elements of the underlying mesh that were located between the two lines were defined with growth plate tissue mechanical properties (Table 4-1).

In order to test as many morphologies as possible, different lines were generated by computing all the possible combinations of 6 points that fulfilled the criteria above described, giving a total number of 46656 different morphologies of the growth plate.

Figure 4-2. Generation of growth plate morphologies for part 1. A. spatial distribution of 6x6 array of points used for growth plate morphology generation. B. Epiphyseal line generation by cubic spline interpolation. C. Growth plate generation by projection of diaphyseal line.

Based on previous works that hypothesize that mechanical cues required to stimulate ossification are sensed on the epiphyseal side of growth plates [333], S, P, OI and Sy values were integrated along the epiphyseal line of each growth plate (solid line in Fig. 2B) using the midpoint rule. For this, we subdivided the intervals generated by the set of points obtained

78 previously to model growth plate morphologies in 10 further intervals. On these new subintervals, we calculated the values of each mentioned stimulus on the midpoint and approximated the integral as follows:

퐷𝑖 ≅ 퐷(푦̅푖)푑푙𝑖 4.1

Where 퐷𝑖 is the approximate value of the stimulus along the 𝑖-th subinterval, 푦̅푖 is the image of the 𝑖-th midpoint 푥̅푖 on the epiphyseal line, 퐷(푦̅푖) is the value of the stimulus on the midpoint and 푑푙𝑖 is the line differential of the 𝑖-th subinterval containing the midpoint 푥̅푖.

In order to analyze the results for all morphologies tested we further calculated the average value and coefficients of variation for each stimulus in the epiphyseal line for all 46656 morphologies. Average values were calculated with the following equation:

푛 ̅ ∑𝑖=1 퐷(푦̅푖)푑푙𝑖 퐷 = 푛 4.2 ∑𝑖=1 푑푙𝑖

Where 퐷̅ is the average stimulus value, n is the total number of subintervals, and 퐷(푦̅푖) and 푑푙𝑖 correspond to value of the stimulus on the midpoint and the line differential of the 𝑖-th subinterval containing the midpoint 푥̅푖 respectively. Likewise, coefficients of variation were calculated as follows:

푛 ̅ 2 √∑𝑖=1(퐷(푦̅푖)−퐷) 푑푙𝑖 퐶푉 = 푛 4.3 ∑𝑖=1 퐷(푦̅푖)푑푙𝑖

Where 퐶푉 represents coefficient of variation of the stimulus, n is the total number of subintervals, 퐷(푦̅푖) is the value of the stimulus on the midpoint, 퐷̅ represents average stimulus value and 푑푙𝑖 corresponds to the line differential of the 𝑖-th subinterval containing the midpoint 푥̅푖.

In addition, to make an approximation to the behavior of each mechanical stimulus during normal human proximal femur growth, the results obtained for 퐷̅ and 퐶푉 were analyzed on those morphologies that better resembled plate shape at each specific ages. Since there are limited reports regarding normal human growth plate morphologies and their inter-individual variations, here we selected the morphologies that better correspond to the images reported by Kandzierski et al.; Carter et al.; and other case reports published or available in web databases as detailed in Appendix C (Figure C1) [319, 326, 343-347].

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4.2.4 Part 2: Influence of Stimuli Behavior on Growth Plate Shape

Despite the evidence showing the relevance of mechanical cues on growth plate biology, there is still unawareness of which of these stimuli is most likely to have a predominant role in growth plate ossification. Thus, to study the influence of each stimulus independently and based on the specific effects described for each one in the literature, we simulated a developmental scenario where growth plate ossification was driven only by one stimulus at a time. This approach aimed to visualize the growth plate shape evolution as a consequence of different ossification velocities along the structure directly related to the distribution pattern of each stimulus.

For all stimuli, a fixed initial straight growth plate geometry was established, which corresponded to the physiological shape observed by 1 year of age in humans [326, 348]. For growth plate generation, a straight line (epiphyseal line) was overlapped to the geometry described previously. Such line was drawn by connecting a set of 12 equidistant points located at the metaphyseal area of the model, with the first point placed on the central side of the model, while the last one was placed on the upper internal limit of the groove of Ranvier as shown in Figure 4-3A. Similar to the described in part 1, for generating the complete structure another line with the same shape as the epiphyseal one was placed below it at a distance of 0.5 mm (diaphyseal side) as shown in Figure 4-3B [332]. All elements of the underlying mesh that were located between the two lines were defined with growth plate tissue mechanical properties, while elements outside were considered bone (Table 4-1).

Figure 4-3. Generation of growth plate for part 2 simulations. A. spatial distribution of the set of 12 points used for growth plate generation. B. Epiphyseal line generation by cubic spline interpolation. C. Growth plate change in shape resulting from mechanical stimulation.

To simulate the effect of each stimulus on growth plate shape, it was established that every point in the epiphyseal line of the growth plate could only have a vertical displacement in the

80 direction of growth. Furthermore, at a time t, the velocity of displacement is given by the following equation:

푑푦 𝑖 = 푓(푥 ) 4.4 푑푡 𝑖

Where 푦𝑖 represents the displacement of point 푥𝑖 in the epiphyseal line due to function f, which represents mechanical influence on growth. Therefore, after reorganization and integration of terms, the new position is given by:

푦푡+∆푡 = 푦푡 + 푓(푥𝑖)∆푡 4.5

Where 푦푡+∆푡 is the updated position of point 푥𝑖, 푦푡 is its current position, 푓(푥𝑖) is the function representing the mechanical influence on growth and ∆푡 is the time step. This assumption is based on the literature reports that suggest that mechanical stimuli affect the ossification process within the growth plate [183, 188, 189]. Since such ossification implies longitudinal apposition of bone tissue at the diaphyseal line, different ossification velocities along the structure are likely to be responsible for changes in shape of the growth plate [283]. Then, in the simulation, at each time step, new position of the points is calculated based in equation 4.5. Based on this, the epiphyseal line is redrawn using cubic spline interpolation and growth plate morphology is updated (Figure 4-3C).

Calculation of the mechanical influence on growth was based on the following equation:

푓(푥𝑖) = 훼(푆(푥𝑖)) 4.6

Where 푥𝑖 corresponds to the 𝑖-th interpolation point of the epiphyseal line, 푆(푥𝑖) is the value of the stimulus on point 푥𝑖, 푓(푥𝑖) is the image of point 푥𝑖 after stimulation, and 훼 is a constant used for numerical stabilization of the model.

Taking into account that, according to literature, the influence of each stimuli on ossification varies, the form of 푆(푥𝑖) depended on the specific stimulus as shown in Table 4-2. Thus, axial loading was considered to affect with an inverse proportionality since the reports show a linear relationship among stress values and growth rates [186]. S and OI were considered to be directly proportional, since the first one has been implicated in stimulation of ossification and the second one is a relationship that represent ossification stimulus [277]. Lastly, for P an inverse relationship was used since its proposed role is to prevent cartilage ossification [277].

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Table 4-2. Specific formulation used for 푆(푥𝑖) in equation 6.

Stimulus 푺(풙풊)

Axial loading (Sy) 1 + 푆푦(푥𝑖)

Octahedral shear stress (S) 푆(푥𝑖)

Hydrostatic pressure (P) 1 + 푃(푥𝑖)

Osteogenic index (OI) 푂퐼(푥𝑖)

Additionally, there is evidence that specific cellular responses to mechanical stimulation may occur under a certain range of intensity [48, 206, 215, 229, 249]. Thus, in order to include such scenario within the simulation, here we performed the analysis considering different ranges of sensibility of the growth plate to the mechanical stimulus, which implies that growth plate was responsive to mechanical stimulation only under certain range of values. Since there are no quantitative reports providing information regarding growth plate sensitivity, here we used 10 intervals for values of the stimulus to which growth plate was responsive. The values used for this approximation were derived from an analysis of the distribution of each stimulus within the growth plate at the initial stage (straight shape). Thus, the distribution of values observed in such analysis were grouped by quartiles (Q1, Q2 and Q3) that were used for stablishing the intervals as indicated in Table 4-3. Results obtained were contrasted with images available in the literature of growth plate shapes at different points of human bone development.

Table 4-3. Range of values to which growth plate is responsive to mechanical stimulation

Intervals Description 1 Minimum value of the stimulus to Q1 2 Minimum value of the stimulus to Q2 3 Minimum value of the stimulus to Q3 4 Values of the stimulus greater than Q1 and lower than Q2 5 Values of the stimulus greater than Q2 and lower than Q3 6 Values of the stimulus greater than Q1 and lower than Q3 7 Values of the stimulus greater than Q3 and lower than Maximum value. 8 Values of the stimulus greater than Q2 and lower than Maximum value. 9 Values of the stimulus greater than Q1 and lower than Maximum value. 10 All possible values of the stimulus.

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4.3 RESULTS

4.3.1 Influence of Growth Plate Shape on Stimuli Behavior

In order to analyze the effect of growth plate morphological changes on the mechanical environment within the growth plate, we performed a quantitative description of the distribution of the mean values (퐷̅) of each stimulus along the epiphyseal line obtained among all morphologies simulated. Thus, Figure 4-4 illustrates the distribution of the values obtained for each mechanical cue in all morphologies analyzed. Results show that, Sy and P values were highly dependent on growth plate morphology as evidenced by the high dispersion observed. On the contrary, S and OI values demonstrate to be less influenced by growth plate morphology. In fact, the results obtained among all morphologies were clustered around 0.17 and 0.04 MPa respectively (Figure 4-4).

Figure 4-4. Distribution of the mean stimuli values (D̅) among the morphologies analyzed. It is shown the dispersion of the mean value of S, Sy, P and OI obtained among the 46656 morphologies analyzed.

In addition to the mean values of each stimulus, variations, expressed in terms of the coefficient of variation (퐶푉), experienced along the epiphyseal side of the growth plate were also analyzed. Figure 4-5 summarizes the results obtained of such analysis for all the studied morphologies. Based on this figure, we observed that all stimuli presented a heterogeneous behavior along the growth plate with no apparent relationship with growth plate morphology. However, variation ranges differed among the four stimuli, with S showing the lowest variations (Figure 4-5C), while OI exhibited the highest (Figure 4-5D).

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Figure 4-5. Distribution of growth plate variation observed for each stimulus (CV) among the morphologies analyzed. It is shown the frequency distribution of the CV obtained for S, Sy, P and OI for each one of the 46656 morphologies analyzed.

In order to identify trends in stimuli values or variations along the structure during normal human femur development, we extracted the morphologies were maximum and minimum values of 퐷̅ and 퐶푉 were achieved (Figure 4-6). However, when we qualitatively compared the morphologies where maximum and minimum values of 퐷̅ and 퐶푉 (Figure 4-6A) were achieved to the ones acquired through development (Figure 4-6), we did not found any match among them.

When analyzing mean stimulus values (퐷̅), it was observed that the morphologies corresponding to the maximum and minimum values of S and OI mean values coincide. Hence, the shape that corresponded to the maximum mean value presented an elevation towards the central part but did not have a final concave geometry (Figure 4-6B). In turn, the morphology corresponding to the minimum mean value had an elevation towards its lateral side but, as in the previous case, did not have a final concave geometry (Figure 4-6B).

Similarly to the described for S and OI, the morphologies for Sy and P were similar. The shapes corresponding to maximum and minimum mean values exhibited large interdigitations towards the lateral side and a small arc, with low interdigitations, in the

84 central side a more irregular morphology with high interdigitation. For the former, interdigitation was present towards the center of the growth plate while in the latter it occurs laterally (Figure 4-6A). In contrast, the morphologies corresponding to the minimum P and Sy mean values, although not entirely equal, had interdigitations in the central side resembling an “M” letter (Figure 4-6A).

Regarding the shapes corresponding to the maximum and minimum variations of each stimulus, we could not identify any trend since the obtained morphologies were (Figure 4-6B).

Figure 4-6. Morphologies for which maximum and minimum D̅ and CV were obtained. A. Results for mean values of the stimulus D̅ B. Results corresponding to the variation along the growth plate

CV of each stimuli. The morphologies presented were obtained after comparing the results among all morphologies analyzed.

4.3.2 Stimuli Behavior through bone development

To better understand the behavior of mechanical cues during normal development, the results obtained in part 1 (see material and methods) were compared with literature imaging and histologies of human growth plates at different ages (Figure 4-8A). For comparisons at specific ages, the morphologies that better resembled growth plate shape at each specific age were selected (Figure 4-7).

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Figure 4-7. Comparison among morphologies used for analysis of stimuli behavior through normal human femur development. To the left are images corresponding to the morphologies observed in vivo as previously published [319, 326, 343-347]. In the center there are pictures that illustrate the morphologies selected among the 46656 used as corresponding to each age. The mean values and variations of S, P, Sy and OI were analyzed for each of the selected morphologies. Thus, in Figure 4-8B the averaged results for all morphologies selected per age are presented. For S, the mean values observed in the simulations showed a flat behavior through childhood and early adolescence (1-13 years), with an increase in value in those morphologies corresponding to the last stages of femur growth before growth plate closure. In contrast, Sy mean values showed an increasing trend during childhood (1 – 10 years) that stabilized at the beginning of the adolescence.

In addition, the results obtained for P and OI mean values show an increasing trend through development. The first one displayed a linear increase during childhood, except for a peak observed around 8-10 years, achieving maximum values between 4 and 12 years (Figure

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4-8A). In contrast, although OI mean values tended to increase from early infancy to the end of adolescence, its values and their variations display fluctuations through development.

4.3.3 Influence of Stimuli Behavior on Growth Plate Shape

Based on the discrepancies found in literature regarding the main mechanical stimulus involved in growth plate ossification and cartilage growth [186, 277, 285], we analyzed the influence of each separate stimulus on growth plate shape evolution starting from a straight growth plate shape (Part 2 materials and methods).

Results for OI showed that, in general, there were little changes on growth plate shape. In fact for most of the intervals the shape of the growth plate remained unaltered. However, when growth plate was considered to respond to the whole range of values (interval 10), the results obtained corresponded to a highly irregular shape. In addition, in those cases where maximum values were considered (intervals 7-9) distortion in the zone near Ranvier’s Groove was observed (Figure 4-9).

In turn, results for S showed heterogeneity in its behavior. In most of the intervals tested the growth plate acquired an irregular shape that tended to maintain a straight flat geometry (Figure 4-9).

In addition, P and Sy were the stimulus that, according to our results, affected the most growth plate shape. In most of the cases, there was preferential growth in specific regions of the growth plate depending on the range of values to which growth plate was considered responsive to. As such, when growth plate was responsive to values below Q3, its growth occurred mainly towards the center of the structure showing a final concave trend for Sy and an M shape for P (Figure 4-9). In contrast, when maximum values were included, growth was more evident towards the edges, resulting in a convex shape.

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Figure 4-8. Stimuli trends observed for each stimuli in the context of normal human femur development. A. Morphologies displayed by human proximal femur at different ages. Compilation generated based on images reported by [319, 326, 343-347]. B. Changes in stimuli during growth. The results presented correspond to the average values of each stimulus obtained in each of the growth plate morphologies shown in Figure 4-7 and Appendix C – Figure C1.

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Figure 4-9. Morphologies observed in the predictive simulation of growth plate growth under the influence of S, Sy, P and OI independent stimulation. Intervals 1 – 10 refer to those described in Table 4-3.

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4.4 DISCUSSION AND CONCLUSIONS

Growth plate is the structure responsible for longitudinal growth of long bones through endochondral ossification [14, 23]. It is a dynamic cartilaginous structure that experiences multiple morphological and functional changes through development, including changes in ossification velocity, width and shape [11, 35, 319, 320, 326, 341, 342]. Many factors have been associated to the regulation of such growth plate dynamics, including biochemical, genetic, hormonal and mechanical factors. In order to better understand the mechanical environment at specific bone development scenarios, several computational approximations have been performed [176, 275-285, 333]. Derived from such studies different types of mechanical stimuli have been proposed to influence growth plate ossification: shear stress (S), hydrostatic pressure (P) and axial stress (Sy), among others [181, 186, 277, 278]. However, up to now there is poor understanding of the role of such stimuli on the morphological changes experienced by growth plate during development. Thus, in this study we explored the behavior of four mechanical stimuli that have been involved in bone development: S, OI, P y Sy.

Initially, a descriptive analysis was performed considering different predetermined morphologies (Part I). Thus, it was first analyzed how did S, Sy, P, and OI mean values change as a consequence of growth plate shape. The obtained results show different sensibilities among these stimuli to growth plate shape. Thus, S, the main mechanical stimulus driving ossification and growth rate, was poorly affected by changes in growth plate morphology [277, 280, 283, 284]. A similar trend was observed for OI, which has a similar biological interpretation, at least in the context of epiphyseal ossification. Thus, OI values above 0 indicate stimulation of ossification while negative values suggest ossification inhibition [277]. In contrast, mean values of Sy (the main stimulus involved in Hueter – Volkmann’s law) and P (associated to cartilage preservation) changed greatly depending on the growth plate morphology [186, 277].

Despite the observed differences among stimulus, in general, all stimuli displayed high variations along the growth plate in all morphologies analyzed (Figure 4-4). Such behavior may be important when considering that in humans, after the onset of SOC, growth plate located at the proximal femur experiences several morphological changes through all childhood and adolescence (Figure 4-8A) [319, 326]. Based on the fact that the observed heterogeneity in stimuli values is evident even when the morphology is straight (data not shown), observed during early childhood (around 2 years old as depicted in Figure 4-8A), we suggest that such changes may be the cause rather than the effect of morphological changes. In addition, since different in vivo and in vitro studies have shown that mechanical stimulation affects endochondral ossification, we suggest that variations of stimuli values along the plate may be influence differentially the chondrocytes present within the tissue

90 causing different growth rates at specific locations [183, 191, 290]. Therefore, mechanical stimulation may play an active role on growth plate morphological evolution during normal bone development. Furthermore, based on their sensibility to growth plate shape Sy and P may be particularly important in such process.

To further analyze such hypothesis, we studied the behavior of each different stimuli within the growth plate to approach two main aspects: 1) is there any mechanical trend during normal growth plate morphological evolution?, and 2) how do stimuli change during normal development?.

To address the first question, we analyzed whether growth plate changes towards the acquisition of a morphology that maximizes or minimizes either the main value of a given stimulus or its variation along the structure during development. As depicted by Figure 4-6, the shapes corresponding to maximum and minimum (퐷̅) and (퐶푉) (Figure 4-6A and B respectively) did not corresponded exactly to any physiological morphology observed during normal human proximal femur development (Figure 4-8A). However, it was observed that the tendency to form downward concavity forms corresponding to maximum S and OI mean values and minimum Sy variation along the growth plate, may emulate the observed trend at the end of bone development (18 years in Figure 4-8A). Furthermore, the morphologies corresponding to minimum S and P mean values emulate some M shapes observed at different stages of development (Figure 4-8A). Taking this into account and in order to have a complete picture of mechanical changes during development, we then analyzed the mechanical environment in morphologies similar to those observed at different time points of human femur development (Figure 4-8A: Figure C1 – Appendix C). Such analyses revealed information consistent with the results previously mentioned. Along these lines, we observed high S and OI and low Sy mean values throughout all age-matched morphologies analyzed (Figure 4-8B).

When analyzing in detail each stimulus evaluated, we observed that S remains nearly constant (Figure 4-8B), which is in good agreement with initial results demonstrating that it was poorly affected by changes in growth plate morphology (Figure 4-4). In fact, such behavior seems to correlate with the current conception that S may be the main mechanical stimulus driving ossification and growth rate [277, 283, 284]. Thus, it might be expected to remain mostly unaffected despite the changes in morphology through all bone development, since despite the changes in growth plate morphology, the growth rate in bone suffers little changes after early childhood until adolescence despite physeal morphology [332, 349, 350]. Furthermore, the only change observed was an increase in S mean values in late adolescence, which matches with the growth spur characteristic of this period (Figure 4-8B) [23, 34]. A similar interpretation may be used for Sy, since it is the main stimulus involved in Hueter – Volkmann’s law [186]. Thus, although it seemed to be greatly affected by growth plate morphology, when analyzed in physiological growth plate morphologies, it showed a very

91 stable behavior, particularly after the age of 4 (Figure 4-8B). Such trend may be expected since in a biological setting, in normal conditions, growth plate is under the influence of physiological loading constantly, and growth plate response to such stimulation may be comparable at different developmental stages [21]. Furthermore, our results suggest that before closure, the growth plate tends to develop downwards concave form that may favor homogenization of these stimuli along the plate (Figure 4-6A), which in fact corresponds to the observed trend for Sy and S variations along the aged-matched growth plate morphologies analyzed (Figure C2 – Appendix C).

Lastly, P and OI presented a subtle increasing trend. Since P has been mainly associated with cartilage preservation, the fact that P diminishes in absolute magnitude, may correlate to the known growth plate thinning observed in vivo, favoring growth plate closure at the end of adolescence [23, 277]. Furthermore, the observed behavior in OI values suggest that for events taking place after epiphyseal ossification, OI rather than predicting growth rate, may be associated to intrinsic events in growth plate, reflecting mainly the effect of P, since S remains constant.

In sum, results of the first part of the study suggest that mechanical environment may play an important role in growth plate morphological evolution. Moreover, it seems that it is an event taking place independently of overall growth rate, and each stimulus may contribute different to such processes. However, this analyses require further validation considering that they were based on morphological data obtained from few individuals, using reported images that may not correspond to representative morphologies of each specific age. Besides, although the results here presented show biologically relevant patterns, it is important to take into account that the growth plate displays a complex tridimensional shape, making it difficult to extrapolate results obtained in a 2D environment to the whole structure. Therefore analysis considering a 3D environment, for both in vivo images and computational modelling, must be performed to confirm these results. Furthermore, age specific loading conditions must be taken into account in future studies in order to confirm the results presented here.

In addition, the results of the first part of this chaptercorrespond to static analysis at specific time points and no time evolution is taken into account. For this reason, such resultsrepresent, mainly, the effects on mechanical environment of growth plate changes in shape, making difficult to determine the specific contribution of each stimulus to this process. Therefore, as a first approximation to further analyze the possible influence of the mechanical stimulus studied and derive more information that may support the results discussed so far, a predictive model was used to test the impact of each stimulus on growth plate shape separately (Part II).

The results obtained for the predictive model showed changes in growth plate morphology when mostly all ranges of S values, and most negative P values were considered, which

92 correlates with the proposed roles as ossification stimulator and inhibitor, respectively. In addition, Sy affected mainly growth plate when medium ranges were used (intervals 2 – 6), which is in accordance to the proposed by Hueter-Volkmann’s law [174, 186].

The final growth plate morphologies obtained differ for each stimulus and resemble different stages of bone development (Figure 4-9). As such, under S stimulation, it was obtained irregular morphologies similar to the observed around 6 to 7 years in humans, although later on some irregularities are also present (Figure 4-8A; Figure 4-9). With P, it is possible to reproduce an m-shape growth plate that occurs at different time points (Figure 4-8A; Figure 4-9); finally, Sy is the stimulus that better resemble the acquisition of an arc-shape characteristic of the human proximal femur (Figure 4-8A; Figure 4-9). Contrasting with the results for S, P and Sy, the results obtained for OI did not corresponded to any of the biological observed morphologies (Figure 4-8A; Figure 4-9). Thus, according to our results OI fails to predict biological behavior of growth plate in the period considered (posterior to SOC consolidation). Such results agree with the results presented in chapter 3 that suggest that OI is unable to predict growth plate growth once epiphyseal ossification is completed [333].

The results obtained suggest that S, P and Sy may contribute to the morphological change of the growth plate, however, none of them is enough to completely predict the actual in vivo behavior. Based on such results we suggest that, from a mechanical point of view, the changes observed in vivo, may result from an interaction among them or even that each stimulus trigger specific cell responses in a time dependent way. The characteristics of such interactions must be the focus of future studies. Furthermore, it is important to consider that during bone development several biological factors that are also involved in growth regulations were not considered here [45]. Moreover interaction among mechanical and biological factors are still not well understood.

To the best of authors’ knowledge, this is the first attempt to analyze simultaneously the behavior of S, Sy, P and OI during femur development and their relationship with growth plate morphological changes. Thus, the results obtained shed light on the possible role of each stimulus on growth plate physiology. However, it is important to consider that here we considered a unique loading scheme, and due to the computational cost growth plate morphologies were simplified. Taking this into account, further works should aim to further understand the patterns here observed using dynamic loading schemes and analysis on an experimentally derived 3D morphologies. Despite such limitations, this work is an initial approximation to elucidate the role of specific mechanical stimuli on growth plate ossification and morphological changes. The results obtained suggest that mechanical stimulation may play different roles on growth plate function simultaneously. This results contribute to improve current knowledge of mechanical influence on long bone development and provides information useful to direct future studies in the field.

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5 CELLULAR SCALE MECHANOBIOLOGICAL MODEL OF GROWTH PLATE. AN IN SILICO MODEL OF CHONDROCYTE’S HYPERTROPHY.

5.1 INTRODUCTION

Growth plate is a cartilaginous structure, in which the main cellular type, the chondrocyte, is in charge of synthetizing an extracellular matrix that is enriched with proteoglycans and collagen type II. Such structure is responsible for long bones longitudinal growth through a process known as endochondral ossification [14, 23] During this process, cartilage is constantly replaced by bone starting with chondrocytes proliferation, followed by extracellular matrix synthesis, hypertrophy, and finally extracellular matrix mineralization, vascular invasion and chondrocyte apoptosis [15, 16]. Histologically, growth plate is arranged in three zones: resting, proliferative and hypertrophic. The first one is characterized by rounded chondrocytes with low proliferative rate and extensive extracellular matrix. Proliferative zone is formed by flattened, highly proliferative chondrocytes that are arranged in columns. Finally, in hypertrophic zone chondrocytes stop cell division and undergo terminal differentiation. Such process is characterized by cell volume increase up to 10 times, and synthesis of proteins that promote extracellular matrix calcification, and vascular and osteoblast invasion [14, 45, 46].

Hypertrophy plays a pivotal role in longitudinal bone growth, considering that it is responsible for 70% of total growth, while the remaining 30% is fulfilled by proliferation [21, 183]. Transition of chondrocytes from proliferative to hypertrophic zone is a highly regulated process involving biochemical (systemic and local) and mechanical factors. Among biochemical factors, one of the main regulators of chondrocytic differentiation is the regulatory loop formed by Indian Hedgehog (Ihh) and the Parathyroid hormone related peptide (PTHrP) [351]. Ihh is produced by prehypertrophic cells and is diffused towards resting zone where it triggers PTHrP synthesis. This, in turn, increases cell proliferation and inhibits hypertrophy [15, 16, 45, 46]. As to the mechanical factors, Hueter-Volkman law states that static compression is essential for bone development; however, excessive loading may disturb bone growth. This agrees with experimental data that points out that growth plate is sensitive to the mechanical environment, particularly in proliferative and hypertrophic zones. In fact, several studies show that height of these zones is affected by loading [21, 46, 183, 187, 188, 190]. Furthermore, in vitro analysis had shown that loading affects synthesis

94 of extracellular matrix proteins, morphogens and growth factors such as Ihh and collagen type II [48, 211, 231, 234, 235, 243, 335, 336, 340].

Poliferative-hypertrophy transitions have also been studied using in silico approaches through mathematical modelling. Such models describe endochondral ossification progress within growth plate, focusing on either ossification front advance as either a function of biochemical or mechanical parameters, or using a macroscopic point of view, that measure bone size as indicative of ossification process [280, 282, 284, 287, 352-354]. However, most of the published works do not specify the effect of such parameters on cellular processes such as chondrocyte proliferation, and hypertrophy, as well as mineralization within the growth plate, limiting their capacity to analyze growth plate cellular behavior.

Taking the above into consideration, this work presents the development of a new mathematical model that simulates the evolution of chondrocytes from proliferative to hypertrophic state within one growth plate column, considering the influences of Ihh-PTHrP loop and mechanical loading. The mathematical model was solved using the Finite Element Method. The results obtained resembled in vivo chondrocytes behavior during hypertrophy in terms of synthesis of regulatory molecules and changes in cell height. The model presented here complements the available models and establishes the first step for the formulation of a global growth plate chondrocyte differentiation computational model. Moreover, this kind of model may be useful as a study platform to improve the understanding of how mechanical, structural and biochemical factors influence chondrocytes behavior within the growth plate under physiological and pathological conditions.

5.2 MATERIALS AND METHODS

Endochondral ossification process, responsible for longitudinal bone growth, relies on constant proliferation and hypertrophy of chondrocytes within the growth plate columns [23]. These events are regulated by biochemical and mechanical factors. Taking this into account, we formulated a mathematical model for the transition of chondrocytes from proliferative to hypertrophic states. The model considers the influence of mechanical loads and biochemical factors in the regulation of cell growth and it is based on the following assumptions:

 Hypertrophy is a process where growth occurs solely in the longitudinal direction of the bone, and it is controlled by mechanical and biochemical factors. Mechanical loads affect cellular size and morphology, while biochemical factors regulate chondrocytes differentiation and hypertrophy timing [15, 31, 179, 180, 182, 355].  The only biochemical factor considered was PTHrP-Ihh regulatory loop [23, 351]. Ihh is realeased by hypertrophic cell membrane and it stimulates PTHrP production.

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PTHrP, is synthetized in the borderline between resting and proliferative zones and is responsible for delaying hypertrophy [145, 146, 351].  Mechanical behavior of cells and extracellular matrix components was modelled as linear elastic based on the following facts: 1) large deformations were not contemplated; 2) growth plate is essentially an avascular structure that obtains its nutrients and oxygen supplies by diffusion form epiphyseal and metaphyseal vasculature [14, 23, 356, 357]; 3) our model considers only a portion of the growth plate assuming fluid flow periodicity; and 4) applied mechanical loading was static, thus according to previous works in such cases interstitial fluid does not influence the mechanical environment in the tissue [196].

Taking all this into consideration, the main model variables were: mechanical load, represented as the applied pressure P; and the concentrations of Ihh (SI ) and PTHrP (SP). In the following sections the work domain and the equations corresponding to cell growth and biochemical loop regulation will be described.

5.2.1 Mathematical Model

5.2.1.1 Domain description

The proposed model was implemented for the bidimensional domain shown in Figure 5-1. Such domain represents a segment of a growth plate column, corresponding to the zone of transition of chondrocytes from proliferative to hypertrophic state. The fragment modelled included eight chondrocytes between two cartilage zones located at the top and the bottom (Figure 5-1). Cells were modelled as ovoid structures of 8 x 20 μm2 according to data reported by Hunziker et al [31]. Pericellular matrix was modelled as the area surrounding the cells. At the lateral boundaries it was included an extracellular matrix area (Figure 5-1).

Figure 5-1. Work domain graphical description.

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Mechanical behavior was considered as linear elastic. Mechanical properties for each tissue are described in Table 5-1.

Table 5-1: Mechanical properties for each tissue included in the model. Tissue Young Modulus, E Poisson ratio (v) Reference (Pa) Chondrocyte 350 0.43 [358] Pericellular Matrix 48500 0.36 [359] Extracellular Matrix 500000 0.12 [359] Bone 11 x 109 0.3 [360]

Domain meshing was performed using 4-node elements. The meshed model included 4194 elements and 4343 nodes. Distributed tension and compression loads were applied to the upper boundary of the column, corresponding to magnitudes of +0.5x10-10 Pa and -0.5x10-10 Pa respectively (P on Figure 5-2). These values were arbitrary selected for this model as a proof of concept, since there is limited information regarding magnitudes of loading at tissue and cellular level. Movement restrictions were imposed to lateral and lower boundaries of the model as shown in Figure 5-2.

Figure 5-2: Boundary and load settings applied to the Ω domain.

Computer simulation was performed in 250 time steps corresponding to 250 hours of real time. Mechanical component was modelled using a lineal-elastic plane strain model [361]. Solving was performed using finite element analysis for spatial discretization and a backward Euler for temporal discretization. Numerical solution was calculated using a Fortran user developed subroutine.

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5.2.1.2 Biochemical loop

The only biochemical factors regulating hypertrophy in the model were given by Ihh and PTHrP concentrations and the interaction between these two molecules. Ihh is a morphogen synthetized by chondrocytes on the first stages of hypertrophy. It diffuses through the growth plate, stimulating PTHrP synthesis by resting chondrocytes [14-17, 23, 145, 146]. In turn, PTHrP inhibits Ihh synthesis indirectly by delaying hypertrophy, and maintaining cells in proliferative state (Figure 5-3) [15-17, 145, 146].

According to this, Ihh-PTHrP regulatory loop was modelled as a reaction-diffusion equation system that will be detailed in the following section.

Figure 5-3: Diagram representing Ihh-PTHrP regulatory loop. The scheme shows interactions between Ihh and PTHrP, as well as the influence of such molecules on proliferation and transition from proliferative to hypertrophic states (black arrow). Positive stimulus are indicated in green, while inhibition is indicated in red.

5.2.1.2.1 PTHrP concentration

PTHrP concentration (푆푃) increases due to presence of Ihh in the reserve zone (Boundary Γ푇 on Figure 5-4). Time changes in PTHrP concentrations are due to its diffusion through the extracellular matrix, its degradation and domain growth velocity:

푑푆푃 2 ln(2) + 푆푃∇ ∙ 퐯 = DP∇ SP − SP 5.1 푑푡 τP

Where 퐷푃 and τP represent PTHrP diffusion coefficient and half-life, respectively; and v domain growth velocity. The latter is related to the cell strain velocity tensor (휀̇) as follows:

푡푟(휀̇) = ∇ ∙ 퐯 5.2

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With tr (휀̇) as the trace of tensor 휀̇ (that will be described in cell growth section) and ∇ ∙ 퐯 the divergence of vector v. Developing equation 5.2, and considering that cell growth occurs only in the bone growth axis and that the model assumes plane strain conditions, equation 2 is reduced to [16, 23]:

휕푣 휀̇ = 푦 5.3 푦 휕푦

휕푣 Where 휀̇ and 푦 indicate the components of the tensor 휀̇ on the bone axial direction (y) and 푦 휕푦 the partial derivative of vector v, respectively.

Taking into account that, biologically, PTHrP is only produced in resting zone, the model considered that such production is circumscribed to the frontier between resting and proliferative zones. This border corresponds to the upper limit of the work domain (labeled as 훤푇 in Figure 5-4) [145, 146, 351]. Thus, equation 1 is subjected to the following boundary condition:

푆푃|Γ푇 = 휆푃 ∗ 휓푃(푆퐼) 5.4

Where 푆푃 represents PTHrP concentration in Γ푇 . 휆푃 term is a constant that indicates the amount of PTHrP in the frontier which is synthetized by resting cells or perichondrium; and

휓푃is a function that depends of Ihh concentration (푆퐼). The latter indicates that PTHrP is only produced after stimulation by Ihh (Figure 5-5) [15-17]. Thus, 휓푃(푆퐼) is given by:

푛 푆퐼 휓푃(푆퐼) = 푛 푇ℎ 푛 5.5 푆퐼 + 푡푆퐼

푆퐼 corresponds to Ihh concentration that is sensed by cells on the frontier Γ푇 which produces 푇ℎ 푛 PTHrP (Figure 5-4). 푆퐼 indicates the threshold Ihh concentration at which chondrocytes start synthetizing PTHrP. Value n represents the slope of the step-like function showed on Figure 5-5, which correspond to the PTHrP synthetic rate in response to Ihh concentrations sensed by PTHrP producing cells. Constant values used are shown in Table 5-2.

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Figure 5-4. Graphic representation of biochemical border conditions in the work domain.

Figure 5-5. Graphical representation of PTHrP concentration ([푆푃]) as function of Ihh concentration 푇ℎ 푛 ([푆퐼]). Threshold value for PTHrP synthesis stimulation is refered as 푆퐼 .

Additionally, since the column modelled presents periodicity, the PTHrP flux (∇푆푃|Γ ∙ 퐧) in the left (Γ퐿), right (Γ푅), and lower (Γ퐵) boundaries was assumed to be zero (Figure 5-4). This means that:

∇푆푃|Γ퐿,푅,퐵 ∙ 퐧 = 0 5.6

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5.2.1.2.2 Ihh concentration

Ihh is produced within cells at initial stages of hypertrophy and its concentration increase when PTHrP is absent. Taking this into account, and as described for PTHrP, time changes in Ihh concentrations are due to its diffusion through extracellular matrix, its degradation and domain growth velocity.

푑푆퐼 2 ln(2) + 푆퐼∇ ∙ 퐯 = DP∇ SI − SI 5.7 푑푡 τI

푆퐼 represents Ihh concentration, DI Ihh diffusion coefficient, τI Ihh half-life and v domain growth velocity.

Ihh is only produced during initial stages of hypertrophy, and the model considered that Ihh production occurs on cellular membranes (CM). In that way, equation 5.7 is subjected to the following boundary conditions:

푆퐼|퐶푀 = 휆퐼 ∗ 휓퐼(푆푃, 휏ℎ, 푡) 5.8

Where 푆퐼|퐶푀 indicates the Ihh concentration in the cell membrane of chondrocytes undergoing hypertrophy, 휆퐼 represents the Ihh concentration secreted through cell membrane, and 휓퐼(푆푃, 휏ℎ, 푡) function describes Ihh production. Such function depends on PTHrP concentration (푆푃), time frame of Ihh production ( 휏ℎ), and current time step of the hypertrophy process, denoted as time t (Figure 5-6). As described in literature, Ihh production within the growth plate is observed in the pre-hypetrophic zone, implying that such production occurs during first stages of hypertrophy [14, 23]. For this reason, it was assumed that the time frame for Ihh synthesis by a single chondrocyte (휏ℎ, Figure 5-6) is limited to the first 10 hours of hypertrophy. Thus, expression for 휓퐼(푆푃, 휏ℎ, 푡) term is given by:

푇ℎ 푛 푟 푆푃 휏ℎ 휓퐼(푆푃, 휏ℎ, 푡) = ( 푛 푇ℎ 푛) ( 푟 푟) 5.9 푆푃|퐶푀+ 푆푃 휏ℎ+ 푡

푇ℎ 푛 푆푃 represents a PTHrP threshold level perceived by the chondrocyte at which Ihh 푛 expression diminishes, 푆푃|퐶푀 refers to average PTHrP concentration in the cell membrane, 푟 휏ℎ represents the time frame of Ihh production (Figure 5-6), and t corresponds to the hypertrophy time. Terms r and n denote shape parameters of Ihh production graphic (Figure 5-7).

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Figure 5-6. Graphical representation of hypertrophy time (t), time frame of Ihh production ( 휏ℎ), and simulation time ( 푡푠).

As for PTHrP, it was assumed that Ihh flux at lateral and lower boundaries was zero, this implies that:

∇푆퐼|Γ퐿,푅,퐵 ∙ 퐧 = 0 5.10

Where ∇푆퐼 ∙ 퐧 represents Ihh flux normal to the contour direction and Γ퐿,푅,퐵 indicate left, right, and lower boundaries, respectively (Figure 5-4).

Figure 5-7. Graphical representation of Ihh concentration ([푆퐼]) as function of PTHrP 푇ℎ concentration([푆푃]). 푆푃 is the threshold PTHrP concentration value at which Ihh diminishes.

Additionally, half-life of such molecules was dependent of the following expression:

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휏 , 휏 = {푘1 퐼푛 푡ℎ푒 푒푥푡푟푎푐푒푙푙푢푙푎푟 푎푛푑 푝푒푟𝑖푐푒푙푙푢푙푎푟 푚푎푡푟𝑖푥 5.11 푃 퐼 푘2 퐼푛 푡ℎ푒 표푠푠𝑖푓𝑖푐푎푡𝑖표푛 푓푟표푛푡

Where 휏푃 and 휏퐼 are PTHrP and Ihh half-life times, respectively (Table 5-2). It was assumed that half-life times diminishes near the ossification front, due to the high amount of catalytic activity in this area which may affect morphogens half-life [45, 46, 110, 111].

5.2.1.2.3 Sensitivity analysis

In order to test model performance out of normal conditions, simulations were performed considering either decrease or complete absence of Ihh or PTHrP synthesis. Therefore, for PTHrP, 0% (PTHrP -/-); 25% and 50% of normal production rates were tested. In similar way, for Ihh, 0% (Ihh -/-); 1%; 5%; 10%; 25% and 50% were simulated. Simulations were performed in the absence of mechanical loading. As a proof of concept tensile and compressive loading were analyzed only for complete absence of Ihh and PTHrP.

5.2.1.3 Cell Growth

Hypertrophy is a process characterized by increase in cell volume, consequence of size increase of subcellular components [29, 362]. This process occurs gradually reaching the maximum size in approximately 24 hours [23]. In the model, cell growth was expressed in terms of cell deformation (휀푡) which depends upon hypertrophy time t and the mechanical loads inflicted.

Thus, cellular deformation is expressed by:

εt = εt−1 + ε̇∆t 5.12

Where εt indicates current cell deformation, εt−1 the deformation in the previous time step and ε̇∆t, the deformation induced by time increment. In this equation, ε̇ term accounts for cell strain velocity tensor (rate of cell deformation, as similarly described by Giorgi et al. 2014), which is expressed by [285]:

휀̇ = 훾(푡) ∗ 훼(휎푚푒푐) 퐧 ⊗ 퐧 5.13

Where 훾(푡) and 훼(휎푚푒푐) are fuctions that depend on hypertrophy time (t) and the loads imposed to the cell. n vector indicated the preferential growth direction and is defined as:

퐧푇 ≡ [0 1] 5.14

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Function 훾(푡) represents cell growth velocity (Figure 5-8). It was selected based on the behavior reported for chondrocytes undergoing hypertrophy [29, 363, 364]. This function is regulated by three shape parameters β, θ and K (Table 5-2). These stablish that once a chondrocyte starts hypertrophy (t = 0), it undergoes a rapid growth phase, followed by a progressive decrease in growth rate that finally stops at the maximum hypertrophy time (t = 24):

푡훽−1푒−푡⁄휃 훾(푡) = 5.15 퐾

In turn, the function 훼(휎푚푒푐) represents a scaling factor for cell deformation which depends on the average hydrostatic stress sensed by each cell after a load (P) is applied. This function agrees with the principles established by Hueter-Volkman law. Thus, it was assumed that if cell stress (휎푚푒푐) is within physiological limits, growth rate will be unaltered; otherwise, it will be modified depending on the magnitude of such stress [282]. Therefore, if the stress is below a value 휎푚𝑖푛, that represents a compressive hydrostatic stress, growth velocity will decrease. In contrast, if the stress is higher than a value 휎푚푎푥, that represents tensile stress, growth velocity will increase. Finally, if the stress is between 휎푚𝑖푛 and 휎푚푎푥, growth velocity will remain unaltered. Values for 휎푚𝑖푛and 휎푚푎푥 are shown in Table 5-2.

The function 훼(휎푚푒푐) is given by:

0.75 휎푚푒푐 < 휎푚𝑖푛 훼(휎푚푒푐) = {1 휎푚𝑖푛 ≤ 휎푚푒푐 ≤ 휎푚푎푥 5.16 1.25 휎푚푒푐 < 휎푚𝑖푛

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Table 5-2. Parameters used in the model. Parameter Description Value Comments Β Growth function shape parameters 8.5 Estimated Θ 1.4 hours Estimated K 1 x 105 Estimated -11 σmin Lower limit for α (αmec) function -1 x 10 Pa Estimated -11 σmax Upper limit for α (αmec) function 1 x 10 Pa Estimated 3 λP PTHrP production on RZ/PZ 1[mass units]/μm Estimated boundary N Slope of PTHrP production curve 4 Estimated 2 DP PTHrP diffusion coefficient 180000μm /hour [351]

vP PTHrP threshold for Ihh inhibition 0.5[mass Estimated units]/μm3 -4 vI Ihh threshold for PTHrP stimulation 1 x 10 [mass Estimated units]/μm3 2 DI Ihh diffusion coefficient 180000μm /hour [351] 3 λI Ihh production on cell membrane 1[mass units]/μm Estimated

τH Maximum Ihh production time 10 hours Estimated R Ihh production function shape 4 Estimated parameters

k1 Ihh/PTHrP half-life in cartilage 0.17 hours [351] -6 k2 Ihh/PTHrP half-life in bone 5.77 x 10 hours Estimated P Applied load ± 0.5x10-10 Pa +0.5x10-10 Pa for tension and -0.5x10-10 Pa for compression

Figure 5-8. Cell growth function 훾(푡). Graphical representation of the function 훾(푡) when β=8.5, θ=1.4 and K=1x105.

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5.3 RESULTS

As described in materials and methods, here we simulated the transition of chondrocytes from proliferative to hypertrophic state within a growth plate column. In physiological conditions, this process is controlled biochemically by Ihh and PTHrP production. Such transition is also affected by mechanical loading, thus in order to test how it affects hypertrophy, we simulated three different mechanical conditions: no loading, compressive loading and tensile loading. Additionally, in order to test model reliability, cases were simulated in which synthesis of Ihh or PTHrP has been was either diminished or abolished.

5.3.1 Physiological Cases

5.3.1.1 Unloaded case

Chondrocytes hypertrophy is characterized by gradual increase in cell area. The results obtained show that such increase took place in a period of 37 hours for each cell. This process started in the closest cell to the frontier between hypertrophic and proliferative zone (Black arrow on Figure 5-9). Once this cell finishes its growth, hypertrophy is repeated in the adjacent cells, thus at the end of simulation time (250 hours) 4 hypertrophic cell were observed. Maximum cell height for hypertrophic chondrocytes was 16.96μm in average, which corresponds to 100% increase in cell area (Figure 5-9, Figure 5-10, and Figure 5-11(a)). Such increase leads to 35% increase in total column height (Figure 5-12).

Ihh was produced by cells at first stages of hypertrophy (approximately first ten hours of hypertrophy). During that time, Ihh diffused through the extracellular matrix reaching the

PTHrP production edge (Γ푇) (Figure 5-4), located at the frontier between reserve and proliferative zones. Ihh presence there stimulated PTHrP production and diffusion through the column generating a decreasing gradient from top to bottom (Figure 5-10).

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Figure 5-9. Domain growth for unloaded case.

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Figure 5-10. Ihh and PTHrP concentration changes over time for normal cases (unloaded, tension and compression).

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Figure 5-11. Maximum cell height achieved during simulation time. A. Proliferative and Hypertrophic maximum cell heights for normal cases. B. Hypertrophic maximum cell height for pathological cases.

5.3.1.2 Compressive Load

Under compressive loads maximum hypertrophic cell height decrease around 13% compared to the unloaded case (Figure 5-11(a)). Furthermore, changes in shape were observed in proliferative cells, especially those located near the frontier between reserve and proliferative zones (Figure 5-10). These changes resulted in a decrease in proliferative cells height (Figure 5-11(a)).

Additionally, in comparison to the unloaded case, a restriction in total column growth was observed corresponding to 6% reduction in final column height (Figure 5-12).

5.3.1.3 Tensile load

Under tensile loads maximum cell height increased by 24% compared to the unloaded case (Figure 5-11(a)). In addition, proliferative cells located near the frontier with reserve zone suffered higher deformation compared to the observed in the compressive case (Figure 5-10and Figure 5-11(a)). Such changes resulted in a 16% increase in column cell height

109 respect to the unloaded case (Figure 5-12). Furthermore, it was observed a change in morphology in the upper part of the column (Figure 5-10).

Figure 5-12. Final column height at the end of simulation time for all cases.

5.3.2 Biochemical sensitivity analyses

Results obtained in the simulations including alterations in the biochemical regulatory loop (Ihh -PTHrP) are shown in Figure 5-11(b), Figure 5-12, Figure 5-13 and Figure 5-14.

When Ihh or PTHrP production was completely abolished, premature hypertrophy of all chondrocytes within the column was observed. Hypertrophic cells reach an average final cell height of 17.7 μm in the first 27 hours of simulation (Figure 5-13 and Figure 5-14), and final column height increased 27% compared to the normal unloaded case (Figure 5-12). In addition, similar to the results obtained for the normal cases, maximum column and hypertrophic cell height were affected by loading, resulting in decrease for compressive cases and increase under tension (Figure 5-11(b), Figure 5-13 and Figure 5-14). In terms of PTHrP and Ihh concentrations, the results showed that absence of Ihh caused suppression of PTHrP production (Figure 5-13). In contrast, absence of PTHrP caused simultaneous production of Ihh in all cells within the column (Figure 5-14).

Analyses performed using partial deficiency in either Ihh or PTHrP synthesis revealed that the model was more sensitive to changes in the latter. This was evidenced by the gradual effect observed in premature hypertrophy of chondrocytes that was proportional to PTHrP alteration. Thus, by decreasing 50% the rate of PTHrP at 250 hours a total of 5 cells hypertrophied, while a 75% decreased resulted in hypertrophy of 6 cells (Figure 5-15). In contrast, the model demonstrated to be highly tolerant to alterations to Ihh levels. Therefore, cell hypertrophy was unaltered up to 95 % decrease of Ihh levels (Figure 5-16).

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Figure 5-13. Ihh and PTHrP concentration changes over time when Ihh production is suppressed (unloaded, tension and compression).

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Figure 5-14. Ihh and PTHrP concentration changes over time when PTHrP production is abolished (unloaded, tension and compression).

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Figure 5-15. Ihh and PTHrP concentration changes over time when PTHrP production is decreased. A. Results for 50% decrease in PTHrP production. B. Results for 25% decrease in PTHrP production.

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Figure 5-16. Ihh and PTHrP concentration changes over time when Ihh production is decreased. A. Results for 90% decrease in Ihh production. B. Results for 95% decrease in Ihh production. C. Results for 99% decrease in Ihh production.

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5.4 DISCUSSION AND CONCLUSIONS

Here it is presented the formulation of a two-dimensional mathematical model of proliferative to hypertrophic state transition of growth plate chondrocytes. The model considered such process in cells aligned in columns, which constitute the basic structural unit in the growth plate [31, 179, 365]. The model integrates the influence of both mechanical loading and the Ihh-PTHrP biochemical regulatory loop in the transition process. These two parameters have been extensively reported in literature as important regulators of chondrocyte hypertrophy [15-17, 179-182, 270, 278].

Previous computational approaches have been developed in order to formulate and simulate mathematical models of cellular hypertrophy. For example, van Donkelaar et al. considered cell hypertrophy as the consequence of a mechanical process that involves mechanical loading, cellular osmotic pressure, synthesis and degradation of collagens and proteoglycans [353]. However, these authors did not consider the effect of biochemical factors in their model. Other models, such as the ones presented by Garzón-Alvarado et al. and Narváez- Tovar et al. have considered the combined effect of mechanical loading and the Ihh-PTHrP regulatory loop on hypertrophy [281, 282, 287, 288]. Nevertheless, such studies focus on changes in columnar morphology and ossification front progression. Based on these facts, the model herein proposed analyzes in detail the combined effect of mechanical and biochemical factors in the process of cell hypertrophy within a column of the growth plate.

Histological analyses of growth plates from different species show that, during hypertrophy, chondrocytes increase their cell area. Such growth is anisotropic in the preferential bone growth axis, and leads to changes in cell height [15, 31, 355]. Maximum cell height attained by a hypertrophic chondrocyte varies according to age and animal species. For example, Hunziker et al., report maximum cell heights between 31.2μm and 18.2μm in growth plates isolated from proximal tibia of rats of 21 and 80 days old respectively [31]. In turn, Weise et al., report maximum cell heights around 20μm for 12 weeks old rabbits [37]. The results obtained by our model resemble cell height achieved in older animals (Figure 5-11A). In fact, our data differed from the aforementioned values for adult rats (80 days old) and rabbits (12 weeks old) around 7%. In contrast, a difference of around 49% was observed when compared with data for younger rats. Such differences may be related to physiological variations regarding cell growth velocity during different development stages that may be controlled by additional biochemical factors not considered in this model [31].

In addition to physiological conditions, this model simulated abnormal cases where either Ihh or PTHrP production was blocked (Ihh-/- or PTHrP -/-, respectively). In both cases, the premature hypertrophy observed within the column can be explained considering that the main function of the Ihh-PTHrP regulatory loop is to promote proliferation by delaying

115 hypertrophy (Figure 5-13; Figure 5-14). Such behavior agrees with observations from previous experimental studies and the phenotype displayed by PTHrP and Ihh mutants that show shorter bones due to accelerated chondrocyte hypertrophy [15, 16, 45, 151, 154, 155]. In contrast, interpretation of the results obtained with the partial alterations of Ihh or PTHrP is hampered by the lack of information available regarding the effects of partial deficiencies in vivo, since the animal models available were developed using null mutations [147, 151, 155]. Furthermore, in humans there is limited knowledge about the phenotypes associated to mutations in the genes coding for these proteins. Thus, up to now there are no reports of skeletal displasyas associated to mutations in PTHrP, however mutations in it receptor (PTHR1) have been identified as the cause of two types of severe chondrodysplasyas: Blomstrand´s lethal chondrodysplasia and Jansen’s metaphyseal chondrodysplasia [366]. On the other side, mutations in the gene coding for Ihh have been identified in two milder forms of skeletal dysplasias: acrocapitofemoral dysplasia and brachydactily type A1 [28]. Therefore, although the apparently more severe clinical compromise observed in PTHrP pathway alterations may coincide with our finding that chondrocyte hypertrophy is more sensitive to PTHrP alterations in the model (Figure 5-15; Figure 5-16), it is not possible to make definitive conclusions since the model described here is a micro scale specific cell behavior model that only considers a segment of the growth plate and a limited number of regulating factors.

Regarding the mechanical influence on hypertrophy process, the model allowed the analysis of the physical effects of mechanical loading on growth plate chondrocytes and prediction of growth velocity. Results show that loads primarily affected cell morphology (Figure 5-10). In fact, for compressive loads, the decrease in cellular maximum cell height observed may be attributed to the restrictive effect exerted by such loading, limiting the intercellular space (Figure 5-11). As for the tensile loads, the observed cell height increase may be explained by the fact that, widening of the intercellular space may have favored cellular growth (Figure 5-11). Both, results for compressive and tensile loading, agree with previous literature reports showing that mechanical loading induces changes in proliferative and hypertrophic zones [21, 183, 190].

Despite the fact that our model accurately reproduces hypertrophy process and gives light on short term effects of Ihh-PTHrP regulatory loop and mechanical loading on columnar chondrocytes behavior, this model does not allow to make analysis on bone growth rates. This limitation is related to the absence of reserve zone and proliferation process in our model, which are important elements involved in growth regulation [21, 23, 183]. Additionally, interactions between mechanical loading and the biochemical loop were not considered, even though several authors have described a dependent relationship between Ihh or PTHrP expression and mechanical stimulation [234, 235, 243, 340].

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In conclusion, the mathematical implementation used in this work allowed the development of a computational model that resemble biological behavior of growth plate columnar chondrocytes in vivo, however for appropriate validation physiological quantitative data will be necessary. This work is a first approach for the development of integral computational models that allow studying combined effects of physical and biochemical stimuli on biological processes taking place within the growth plate based on the available knowledge. These models provide valuable platforms for developing theoretical approximations on mechanisms associated to growth plate response to physiological and pathological conditions. Furthermore, the analysis of those interactions may provide emerging properties of biological systems. Such information might be useful to complement and direct experimental approaches, in order to improve our knowledge of biological processes such as long bone growth.

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6 STUDY OF GROWTH PLATE PATHOLOGY IN THE RAT MODEL OF MUCOPOLISACCHARIDOSIS TYPE VI. AN EXPERIMENTAL AND COMPUTATIONAL APPROACH.

6.1 INTRODUCTION

Mucopolisaccharidoses (MPS) are a group of diseases characterized by a severe skeletal compromise [47, 316, 367]. These diseases are caused by genetic defects that impair normal intracellular catabolism of glycosaminoglycans (GAGs). As a consequence, partially degraded GAGs are accumulated within cells and in the extracellular matrix (ECM) of different tissues including articular cartilage and growth plate [47, 316, 367].

Growth plate is a highly organized tissue responsible for longitudinal bone growth. Histologically it is characterized by the presence of four distinct zones: resting, proliferative, hypertrophic and calcification. Moreover, chondrocytes present in this tissue display a characteristic columnar arrangement parallel to growth axis [14, 23]. Studies in humans and animal models have revealed structural abnormalities within the growth plate of MPS affected individuals including: resting zone chondrocytes enlargement; low proliferation rates; and loss of columnar arrangement [316, 368-374]. Additionally, it has been observed an accumulation of GAG-rich material in the ECM of the tissue as well as disturbances in other major components such as collagen type II [374, 375].

Growth plate ECM plays a key role in the physiological function of this structure as it provides structural support maintaining the columnar cellular organization required for longitudinal growth [20, 38, 52]. In addition, ECM acts as a regulator of biochemical and biophysical environment within the tissue, a function that is shared with pericellular matrix (PCM) [20, 38, 52, 71-73]. Therefore, the biochemical alterations of MPS tissues characterized by partially degraded GAGs accumulation intra and extracellularly, are expected to generate structural changes within ECM and PCM. We hypothesize that such alterations may result in a modification of the cellular organization as well as mechanical and biochemical environment within growth plate, leading ultimately to abnormal cellular behavior within the tissue. However, these issues have been poorly explored in genetic

118 diseases, in which basic research has been focused on biochemical and molecular researches [376, 377].

As an initial approximation to such hypothesis, here we studied the growth plate pathology in the rat model of MPS VI or Maroteaux-Lammy syndrome, a MPS subtype caused by the deficiency of a lysosomal enzyme involved in dermatan sulfate (DS) and chondroitin 4 sulfate (C4S) catabolism (aylsulfatase B) [47, 378]. The rat model of MPS VI displays an important skeletal compromise and alterations in the growth plate [374]. However, such abnormalities have been documented at advanced stages of the disease. Moreover, there is little information available regarding their progression during long bone growth in this or other MPS animal models. In addition, the pathophysiological mechanisms underlying growth plate abnormalities in this and other MPS and their impact in bone development are still largely unknown [316, 370].

Taking the above into account, in this work a description of mechanical and histological alterations of growth plates in a rat model of MPS VI is performed. The experimental approach presented in this chapter was performed in collaboration with Schuchmann’s lab of the genetics and genomic department of Mount Sinai. With the information obtained from this part, a computational analysis was implemented to shed light on potential consequences of morphological and mechanical alterations on growth plate function and bone growth. The results were analyzed taking into account the histological evidence and contrasted to normal bone development. This work is the first step towards the development of new methodological approaches focused in understanding the molecular and mechanical aspects involved in the pathophysiology of MPS, a necessary step for the development of more effective therapies.

6.2 MATERIALS AND METHODS

6.2.1 Animals

Wild type and MPS VI Sprague-Dawley rats were used. All rats were raised at the Mount Sinai School of Medicine following NIH and USDA guidelines regarding animal care and use. Rats were euthanized using carbon dioxide inhalation. Three animals were included per group for histological and immunohistochemical analyses. Eight wild type and and five MPS VI animals were used for mechanical testing.

6.2.2 Sample Collection

Distal femurs were isolated from 4-day, 1-month, and 3-month-old rats. Samples for histology and immunohistochemistry were fixed in buffered 10% formalin; those for biomechanical analyses were conserved at -80°C until testing. All the experimental analyses

119 were performed in Schuchmann’s lab in the genetics and genomics department at the Mount Sinai School of Medicine.

6.2.3 Histological analysis

Samples were serially dehydrated through ethanol/xylene and embedded in paraffin. Prior dehydration and embedding, 1 and 3 month-old samples were decalcified in Cal-Ex (Thermo Fisher Scientific, Waltham MA) for 3 to 7 days. Embedded samples were sectioned at 5 µm thickness obtaining coronal sections of the femur. Cover slides were rehydrated through xylene/ethanol/water and stained with Harris modified hematoxylin and eosin Y (H&E, Sigma Aldrich, St. Louis MO) and Toluidine Blue (TB, Sigma Aldrich, St. Louis MO) following standard protocols.

6.2.4 Immonuhistochemistry

Paraffin embedded samples were immunostained for Collagen II. The Ultravision Detection System (Lab Vision Corporation, Fremont CA, TR-15-HD) was used to detect the Col II (Santa Cruz Biotechnology, TX, sc-28887) antibody signals. Briefly, sectioned slides were baked at 65°C for 1 hour, deparaffinized and rehydrated through serial xylene/ethanol gradients to deionized water. Antigen retrieval was performed using 1% proteinase K for 15 minutes at 37°C. Slides were blocked using hydrogen peroxide and the specific kit components. They were then incubated in anti-Col II antibody solution containing 5% serum and 0.1% Tween-20 at 4°C overnight (at 1:250 dilution). The following day, the slides were brought to room temperature (RT) and incubated in secondary antibody solution for 30 minutes at RT (biotinylated goat anti-rabbit). The slides were then incubated in streptavidin peroxidase for 10 minutes and imaged with DAB chromogen until the tissues turned brown. Hematoxylin was used as a counterstain.

6.2.5 Quantitative analysis of growth plates

Three histomorphometric parameters were measured to describe growth plates in normal and MPS VI animals (Figure 6-1A):

1. Total growth plate thickness (GP) 2. Resting + Proliferative zone thickness (RPZ) 3. Hypertrophic zone thickness (HZ)

Measurements were performed on 10x-magnified images according to Valteau et al. [189]. A minimum of 90 measures were obtained for each group through evaluation of at least 3

120 images per individual (1 image x 3 independent sections). 10 measures were performed per image and a total of 3 animals were included per group.

Figure 6-1. Image processing for quantitative analysis of growth plate characteristics. A. Evaluation of total growth plate (GP) and zonal thickness (Resting-proliferative zones—RPZ; Hypertrophic zone—HZ). Sample image from a normal 1-month-old WT animal using 10X magnification. B. Grid used for evaluation of columnar organization per zone (PZ: Proliferative zone; Pre-HZ: Pre- hypertrophic zone; HZ: Hypertrophic zone) according to the described in [379]. Sample image from a normal 1-month-old WT animal using 20X magnification. Scale bars in A and B represents 100µm.

In addition, a quantitative description of growth plate columnar organization in proliferative, pre-hypertrophic and hypertrophic zones in normal and MPS VI animals was performed. Such analyses were performed following the protocol published in [379] which is detailed in Appendix D. Briefly, grid based cell quantifications were performed on 20x-magnified images (Figure 6-1B). At least 3 images per individual (1 image x 3 independent sections) were analyzed.

Four parameters were analyzed (Figure 6-2) as defined in [379] (see Appendix D):

1. Cellular density (C) 2. Column density (CD) 3. Density of isolated cells (CI) 4. Column orientation (α).

Since the parameter CI illustrate the quality of columnar arrangement within growth plate, the results obtained for this parameter are reported as the proportion of isolated cells among the total cell within a field (CI/C).

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All measurements were performed by image analysis using the ImageJ Java source code tool in a blind manner by the investigator. Results per zone were averaged and expressed as cell per area (mm2).

Figure 6-2. Graphical representation of the cell distribution descriptors along the different physeal zones. The cells in gray conform a column and the isolated ones are colored in black. The axis labeled as A (in green) symbolizes the line that links the geometric centers of the cells that conform the column, while the axis labeled as B represents the transversal axis to the one in the preferential bone growth. α represents the column orientation angle. Image taken from [379].

6.2.6 Mechanical testing

Elastic modulus from 4-day-old samples was assessed via axial unconfined compression tests using an electroforce testing instrument 3200 series (Bose corporation, Eden Prairie, MN). The specimens were tested in a fluid bath consisting of PBS solution by applying a quasi- static compression scheme. Thus, specimens were subjected to slow compressive ramps at a 0.01mm/s rate. Stress-strain curves were plotted and elastic modulus corresponded to the calculated slope using the data points between 50 and 90% of the maximum strain in stress- strain curves.

6.2.7 Statistical analysis

Results are presented as mean ± standard error mean (n= 3) with replicas for each sample. To determine levels of significance of the differences between normal and MPS VI, results were analyzed using Mann-Whitney test. Differences were considered significant at p < 0.05. Graph Pad Prism Version 3.1 (Graph Pad Software, San Diego Ca, USA) was used for statistical analysis.

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6.2.8 In silico analysis of epiphyseal stress distribution

In order to analyze the potential impact of changes in mechanical properties after the onset of secondary ossification center in MPS VI animals, the stress distribution pattern within the epiphysis was analyzed using finite element analysis. For such purposes the generic computational model described in chapter 3 was used. Only the morphology corresponding to straight L2-W2- configuration at Stage 2 was used, taking into account that it is the morphology that better resembles the growth plate localization and size expected to occur between 4-day-old and 1-month-old samples. Various theoretical scenarios were addressed by altering cartilage’s Young modulus (E) either by increasing or decreasing up to 60% the values used for normal conditions in chapter 3 (E = 6.0MPa). Such simulations were performed taking into account that dermatan sulfate accumulation is expected to affect growth plate ECM structure and subsequently mechanical properties although it is uncertain the magnitude of such changes. In fact, within the growth plate, PG containing DS (decorin and biglycan) are present in resting and proliferative zones, where they have been found in association to collagen type II fibers and seems to be implicated in regulating fibrillogenesis through interactions mediated by DS chains [38, 41, 57, 380-383]. Furthermore, it has been proposed that DS chains within proteoglycans may play important roles during development by mediating ECM organization [384]. In addition, changes in the magnitude of Young modulus have been evidenced for other cartilaginous tissues in MPS animal models and other pathologies like osteoarthritis that involve abnormal ECM structure [385-387]. Results from this part were analyzed in terms of osteogenic index (see chapter 3 and 4 for further description) distribution, since at this stage results shown in chapter 3 suggest that it might be a good indicator of mechanical stimulation of ossification within epiphysis and growth plate.

A second theoretical scenario was used for analyzing the impact of morphological changes observed in 1-month-old MPS VI animals. For such purposes, the model described in chapter 4 was used to generate morphologies similar to the observed in 1-month-old normal and MPS VI animals. Results were analyzed in terms of octahedral shear stress (S) and hydrostatic pressure (P).

Lastly, columnar misalignment observed in 1-month-old MPS VI growth plates was simulated using the mechanobiological model for cell hypertrophy described in chapter 5. For such purposes the morphology used was adjusted by inclining the cell column 30° respect to the growth axis but maintaining the size for PCM described in chapter 5 (Figure 6-3). The model included a wider ECM zone, corresponding to the observed in MPS VI growth plates (Figure 6-3). Material properties, constrains, and formulation of biochemical parameters within the model were used as described before (Chapter 5 - materials and methods). Simulations were performed without mechanical loading.

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Figure 6-3. Work domain graphical description.

6.3 RESULTS

6.3.1 Growth Plate Histological Characteristics

At 4 days of age, MPS VI animals did not display any abnormalities either in terms of growth plate zones size, nor columnar arrangement (Figure 6-4; Table 6-1). Furthermore, a region of hypertrophy in the central portion of epiphyses suggestive of secondary ossification center development was observed likewise in both populations (data not shown).

Figure 6-4. Histological characteristics of growth plates from 4-day-old WT and MPS VI rats. A. Histological sections stained with hematoxylin and eosin images at 4X (Left) and 20X (Right) magnification. Scale bars correspond to 100µm. B. Cell density results per zone. C. Column density

(CD) results per zone. D. Results for isolated cells ratio per zone. Open and black bars correspond to Wild Type (WT) and MPS VI rats, respectively. Result are reported per growth plate zone as follows: proliferative (PZ), pre-hypertrophic (pre-HZ) and Hypertrophic (HZ) zones.

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Similar to the observed for 4-day-old animals, no statistically significant differences were observed in the thickness of growth plates of 1-month-old animals (Table 6-1). However, at this age, disturbances in the zonal structure of those growth plates were evidenced, consisting of a decrease in hypertrophic zone thickness (Table 6-1). Furthermore, quantitate analysis of columns within the growth plate revealed alterations in chondrocytes distribution along the different zones of the growth plate in MPS VI animals compared to wild type (Figure 6-5). Such abnormalities also involved proliferative zone, where a reduced number of chondrocytes was found in MPS VI samples (Figure 6-5B), which also displayed a lower tendency to arrange in columns as evidenced by decreased columnar density and increased rate of isolated cells (Figure 6-5C and D). In contrast, increased cell density was observed in pre-hypertrophic and hypertrophic zones (Figure 6-5B).

Table 6-1. Histomorphological measurements of wild type and MPS VI growth plates.

Age Parameter Wild type MPS VI Growth plate thickness (µm) 659.04 ± 96.28 539.5 ± 136.26 Resting-Proliferative zone thickness 461.83 ± 87.24 319.15 ± 118.35 4 days (µm) Hypertrophic zone thickness (µm) 197.11 ± 29.74 220.35 ± 33.02 Growth plate thickness (µm) 466.62 ± 46.16 381.68 ± 81.23 Resting-Proliferative zone thickness 225.17 ± 34.63 241.24 ± 59.75 1 month (µm) Hypertrophic zone thickness (µm) 241.11 ± 31.61 140.43 ± 41.74* 3 months Growth plate thickness (µm) 224.49 ± 33.98 244 ± 78.4 *Statistically significant difference when compared to WT (p<0.05).

In terms of columnar orientation, no statistically significant differences were observed in the mean angle of columns between wild type and MPS VI animals in all zones. However, the latter displayed higher variations (Table 6-2).

In addition, qualitative observation of 1-month-old growth plates showed changes in growth plate morphology when compared with wild type animals, displaying a more pronounced M shape (Figure 6-5A). In addition, a broader zone of cartilage towards the epiphyseal side of the plate (orange arrows in Figure 6-6A and B), as well as in the articular surface of the epiphysis (Black arrows in Figure 6-6B), which were not observed in wild type animals. In addition, cell size seems to be diminished in MPS VI growth plates (Figure 6-5A).

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Table 6-2. Column orientation angle and coefficient of variation for wild type and MPS VIgrowth plates. Column orientation angle Variation coefficient of α

(α)* (%)* Growth plate Wild type MPS VI Wild type MPS VI Age zone Proliferative 86.77 89.38 33 28 4 days Pre- Hypertrophic 88.53 85.99 28 39 Hypertrophic 90.24 91.18 22 22 Proliferative 93.82 84.05 15 20 1 month Pre- Hypertrophic 92.15 82.48 17 23 Hypertrophic 89.4 81.51 13 21 3 months Total growth plate 92.23 86.69 17 24 *Results presented correspond to the average value.

Figure 6-5. Histological characteristics of growth plates from 1-month-old WT and MPS VI rats. A. Histological sections stained with hematoxylin and eosin. Images at 10X magnification. Scale bars correspond to 100µm. B. Sample image of grid used for quantification of columnar organization. Histological sections stained with hematoxylin and eosin. Images at 20X magnification. Scale bars correspond to 100µm. Grids used for quantifications in the different zones are indicated in colors (white for proliferative zone; red for pre-hypertrophic zone; and yellow for hypertrophic zone). C.

Cell density results per zone. D. Column density (CD) results per zone. E. Results for isolated cells ratio (CI/C) per zone. For C, D, and E open and black bars correspond to Wild Type (WT) and MPS VI rats, respectively. Results are reported per growth plate zone as follows: proliferative (PZ), pre- hypertrophic (pre-HZ) and Hypertrophic (HZ) zones. The symbol (*) indicates statistically significant difference (p < 0.05).

126

Finally, 3-month-old MPS VI animals showed no alterations neither in growth plate thickness or morphology (Figure 6-7A; Table 6-1). However, complete loss of zonal arrangement in the internal structure of the growth plate was observed (Figure 6-7A). In consequence, quantitative analysis for these samples was performed using a 50x50 µm grid for all the growth plate for normal and MPS VI samples. Such analyses revealed a decrease in both cell and columnar density (Figure 6-7B and C). Moreover, a high proportion of cells were not organized forming columns as evidenced by the increase in isolated cell ratio (Figure 6-7D). Similarly to the observed for 1-month-old samples, a higher variation in column angles was observed in MPS VI growth plates (Table 6-2).

Figure 6-6. Microscopic images of distal femur epiphyses of WT and MPS VI animals. A. Growth Plate. B. Articular surface. Histological sections stained with hematoxylin and eosin. Images at 10X magnification. Scale bars correspond to 100µm. Orange arrows show epiphyseal side of the growth plate. Black arrows show the articular surface.

127

Figure 6-7. Histological characteristics of growth plates from 3-month-old WT and MPS VI rats. A. Histological sections stained with hematoxylin and eosin. Images at 10X magnification. Scale bars correspond to 100µm. B. Cell density results per zone. C. Column density (CD) results per zone. C. Results for isolated cells ratio (CI/C) per zone. Open and black bars correspond to Wild Type (WT) and MPS VI rats, respectively. Result are reported per growth plate zone as follows: proliferative (PZ), re-hypertrophic (pre-HZ) and Hypertrophic (HZ) zones. The symbol (*) indicates statistically significant difference (p < 0.05).

To further characterize the abnormalities observed in older MPS VI animals, the two main components of growth plate extracellular matrix were analyzed: GAG (by toluidine blue staining) and collagen type II (Col II) (by immunohistochemistry). Immunostaining for col II showed stronger staining in wild type animals compared to MPS VI, difference that becomes even more evident in 3-month-old animals (Figure 6-8). In contrast, only 3-month- old MPS VI animals showed differences with the WT group. In these animals the strong blue staining indicates GAGs accumulation in these animals.

128

Figure 6-8. Histology-based analysis of extracellular matrix composition in wild type and MPS VI rats. In the left side of both panels immunohistochemistry for collagen type II (Col II) is shown. In the right side images of toluidine blue stained samples are shown (TB). Scale bars correspond to 100µm.

6.3.2 Mechanical Testing

When evaluating mechanical behavior under compression, no statistically significant differences were observed in calculated Young modulus between samples from MPS VI and wild type rats (Figure 6-9).

Figure 6-9. Calculated Young Modulus (E) in chondroepiphyses of 4-day-old wild type and MPS VI rats. Results from compression tests performed for wild type (WT) and MPS VI samples (n=8 and n=5 respectively). No significant differences were observed.

129

6.3.3 In silico analyses

In order to further understand the consequences of the observed morphological abnormalities within MPS VI growth plate in terms of mechanical environment and cellular behavior, computational modelling was used.

Although no mechanical changes were observed at 4 days old (Figure 6-9), there is uncertainty regarding the mechanical properties that MPS VI growth plates may display in older animals. Therefore computational modeling was used to predict the effect of increases or decreases in Young modulus (E). Results showed that general stress distribution patterns were poorly affected by such changes, even when a 60% increase (E=9.6) or decrease (E=2.4) of the initial young modulus (E=6.0) are considered (Figure 6-10).

Figure 6-10. Osteogenic Index (OI) distribution considering different Young modulus (E) values. E is expressed in MPa. Value used for simulation in chapters 3 and 4 (initial Young modulus) was 6.0 MPa. Increases or decreases were considered as percentage changes based on initial Young modulus as explained in the text (see material and methods).

In addition, the effect of the morphological changes observed between 1-month-old MPS VI and wild type rats was analyzed (Figure 6-6). Results showed that growth plate morphology affected values of shear stress and hydrostatic pressure, rather than their distribution patterns. The morphologies observed in MPS VI growth plates were related to higher shear stress values and absolute magnitude of hydrostatic pressure (Figure 6-11).

130

Figure 6-11. Predicted stress distribution within wild type and MPS VI growth plates at 1 month of age. A. Octahedral shear stress (S). B. Hydrostatic pressure (P).

Finally, the effect of columnar misalignment on cellular behavior was analyzed using a mechanobiological model for cell hypertrophy. Results showed that only by altering cell distribution within the domain, gradients of PTHrP and Ihh are severely disturbed causing delay in the hypertrophy process and subsequently growth of the structure (Figure 6-12). Therefore, in the misaligned model after 250 hours 2 out of 8 cell underwent hypertrophy with an increase of the cell column of 25%, while in a column perfectly aligned with growth axis 4 out of 8 cells completed that lead to 39% increase in column height (Figure 6-12).

6.4 DISCUSSION

Mucopolysaccharidoses (MPS) are genetic diseases that severely compromise hyaline cartilage structure by altering tissue composition due to the accumulation of partially degraded glycosaminoglycans (GAGs) [47, 316]. These abnormalities have proven to affect not only adult hyaline cartilage but also transient cartilage located at the growth plate, disturbing the process of endochondral ossification [316]. Although great effort has been made on describing articular cartilage pathology and skeletal abnormalities in MPS and developing novel molecular therapies, little is still known regarding the characteristics and basic pathophysiological mechanisms associated to growth plate pathology in MPS. Thus, in this context, this work gives a detailed description of growth plate pathology observed in MPS and provides information regarding the onset and development of the observed

131 abnormalities. Furthermore, this work constitutes the first approximation to pathophysiological mechanisms taking place within growth plates in these diseases from a mechanical and structural point of view using a combined computational and experimental approach.

To better understand growth plate pathology in MPS, initially we assessed the cellular organization within growth plates at different developmental stages in the rat model of MPS VI. This model reproduces the bone pathology observed in humans, in fact the affected animals present with smaller bodies, shorter limbs than normal and display facial dysmorphia that become evident between 1 and 2 months of age [374]. Based on this information, the time points here studied corresponded to a neonatal stage (day 4); the second was selected around the onset of clinical signs and before sexual maturity (1 month); and lastly growth plates of young adult animals (3 month) were analyzed, since at this age the animals display all phenotypical abnormalities characteristic of the disease in rats.

Results from histological evaluation were comparable to the observed phenotype in humans, where MPS VI is characteristically a progressive disease. In fact, MPS VI patients are usually asymptomatic during the first year of life and skeletal abnormalities become evident during early childhood [378, 388]. In a similar way, no histological changes were observed in newborn MPS VI rats (4-days-old). Furthermore, structural abnormalities in these animals started to become evident by 1 month of age involving all three evaluated zones: proliferative, pre-hypertrophic and hypertrophic. Abnormalities observed were primarily related to cell density rather than columnar arrangement. Cellular abnormalities identified in 1-month-old MPS growth plates seem to indicate a rapid transition from proliferative to hypertrophic zones since cell density was decreased in the former and increased in the latter. In addition, most of the cells within MPS VI growth plates were found in pre-hypertrophic zone, suggesting that although more cells started hypertrophy, this process may be slower (Figure 6-5B). Such hypothesis is consistent with the observed retardation in epiphyseal ossification, evidenced by the wider hypertrophic cartilage present surrounding the secondary ossification center in 1-month-old MPS VI animals (Figure 6-5A). Similar proliferative zone involvement has been observed in MPS VII mouse model, although not hypertrophic zone compromise was observed. Furthermore in the MPS VII model, loss of proliferative chondrocytes was associated to decrease in cell proliferation, which may be an additional mechanism involved in the alterations observed in MPS VI rats that was not addressed in this study [370]. In addition, previous studies have reported reduced metaphyseal trabecular density in then MPS VI rat model [389]. Such findings might be related to the altered hypertrophy process, however, it was not assessed in this study.

132

Figure 6-12. Ihh and PTHrP concentration changes over time for a normal and an inclined growth plate column. Images showing the diffusion patterns observed for PTHrP (upper panel) and Ihh (Lower panel) at time 0, 37 and 250 (hours) of simulation using the mechanobiological model described in chapter 5. Results correspond to the simulations performed using morphologies corresponding to a growth plate column aligned with the longitudinal bone growth axis (left) and an inclined column (right).

133

In addition, contrasting to the cell density increase observed in the hypertrophic zone of 1- month-old MPS VI rats, the thickness of this zone was reduced. These results suggest a decrease in cell size in affected animals that, although not measured, was qualitatively evident in microscopic images (Figure 6-5A). Such findings differ from the observations made in the MPS VI cat model in which higher and vacuolated cell were identified in hypertrophic zones, although a similar compromise of proliferative zone was describe [372]. These differences may be related to changes in GAG composition of cartilage among different species, leading to different degrees of accumulation and cell involvement [390, 391]. However, further histological studies are required to analyze the progression of intracellular storage in growth plate chondrocytes of MPS VI animals, since in this study we only analyzed samples from young animals (up to 3 months). Furthermore, the histological technique used in this study does not allow to observe in detail the presence of vacuolization or storage material within chondrocytes.

Growth plate histological alterations were progressive; for instance in young adult animals (3-month old) growth plate architecture was completely lost, displaying not only a severe loss of cellularity but also a misalignment with the bone growth axis (Figure 6-7; Table 6-2). In rats, growth continues up to 28 to 30 weeks. Therefore, the abnormalities observed at 3 months take place long before growth slows down, which normally occurs around 6 months of age [35]. Considering that bone longitudinal growth is directly related to columnar and zonal arrangement and hypertrophy, our findings are consistent with, and may explain the development of shorter limbs in MPS VI rats [21].

In sum, histological analysis revealed a severe alteration of growth plate structure due to the biochemical pathology in MPS VI animals, however there is limited knowledge regarding the possible pathological mechanisms leading to this alterations. Based upon what has been observed in other tissues and other animal models, in MPS VI it is expected an accumulation of GAGs in the extracellular environment (ECM and PCM) [316, 370, 372, 392-394]. Furthermore, dermatan sulfate (DS) accumulation in MPS VI may alter ECM and PCM structure, considering that DS containing proteoglycans have been found in association to collagen type II fibers and seems to be implicated in regulating fibrilogenesis through interactions mediated by DS chains [38, 41, 57, 380-383]. Our results support this idea by demonstrating that although GAGs accumulation within growth plates of MPS VI rats was only evident by 3 months of age, collagen staining revealed altered patterns already in 1- month old animals (Figure 6-8). On one hand, this has important implications since collagen may be involved in maintaining columnar arrangement within the growth plate by forming fibrils orientated parallel to the growth axis in proliferative an hypertrophic zones [63, 64, 81, 83, 85, 395]. In addition GAGs are responsible for providing cartilage compression resistance [20, 38, 41]. Thus structural abnormalities observed in MPS VI animals may have

134 implications in cellular organization as well as mechanical environment within the tissue. Taking this into account and to better characterize the progressive storage of GAG within MPS VI growth plates, quantitative analysis are required. Such analyses should be the focus of future studies.

As a first approximation to the mechanical alterations associated to MPS VI, the Young modulus of epiphyseal cartilage was assessed in newborn animals (4-day-old). Although no changes were observed at this stage, this results correlate well with the normal structure observed at this age (Figure 6-1; Figure 6-9). Despite these results and taking into account the aforementioned ECM abnormalities observed at 1 and 3 month-old animals, it might be expected that such mechanical properties may be altered later during development (Figure 6-8). In fact, alterations in the stiffness of the cartilaginous tissue from the nucleus pulposus have been reported in the canine model of MPS VII and the rat model of MPS VI [386, 387].

Since it is difficult to predict the mechanical alterations within MPS VI growth plates, due to the mixed alteration of collagen and GAGs observed, computational modeling was used to predict the consequences of potential changes in Young’s modulus. Therefore, as a proof of concept, we analyzed mechanical environment considering either increases or decreases in growth plate Young modulus.

For such purposes, an epiphysis with a small secondary ossification center was modeled taking into account that such configuration is expected between 4 days (completely cartilaginous epiphysis) and 1 month (completely ossified epiphysis)[15, 16]. Our results suggested that changes in Young’s modulus do not change stress distribution within the growth plate, at least within the considered range (Figure 6-10). Therefore, according to our simulations, there are no changes in stress patterns that may correlate to the abnormalities observed in 1-month old growth plates, suggesting that changes in mechanical properties might not be a determining factor in the progression on early stages of growth plate pathology. It is important to consider that these affirmations are made based on the results of a generic computational model and in order to make more accurate predictions, it will be necessary to further analyze experimentally the occurrence of mechanical alterations in MPS VI growth plates beyond the neonatal period.

In addition to the changes in ECM components, the morphological changes observed by histological analysis in 1-month-animals may also be a factor altering mechanical environment in MPS VI growth plates as discussed in chapters 3 and 4. In fact, it is outstanding that despite the differences observed at 1 month, both groups display similar growth plate morphology by 3 months. These results may suggest that MPS VI animals develop the well-defined M shape prematurely. When the mechanical environment was

135 analyzed in silico, it was observed that such morphology displays a higher hydrostatic pressure which has been associated to ossification inhibition (Figure 6-11). A similar morphology is acquired by 3-month old wild type animals, which may be associated to the decrease in bone growth rates expected to occur normally between 8 and 16 weeks [35]. Thus, MPS VI growth plates may be sensing an inhibitory mechanical environment prematurely which may be an additional factor contribution to bone growth impairment.

Lastly, taking into account that loss of columnar arrangement was the most striking feature in 3-month-old MPS VI rats (Figure 6-7), the potential effect of columnar disorganization on growth plate function was assessed using an in silico mechanobiological model. Therefore, a model where chondrocytes were not aligned to the bone longitudinal growth axis was considered (Figure 6-3). Our results support the idea that columnar orientations may be an important factor affecting normal hypertrophy, since it was observed that only by modifying cell arrangement, there was a disturbance in biochemical environment that severely delayed cell hypertrophy in the model (Figure 6-12). This correlates to the initial abnormalities observed in 1-month-old animals that, although did not lost columnar arrangement, displayed a higher variability in columnar organization and an important delay on chondrocyte hypertrophy as discussed above. Based on these observations we hypothesize that primary biochemical abnormality in MPS VI leads to changes in extracellular matrix structure that promotes chondrocytes disorganization within the growth plate. As a consequence normal biochemical gradients responsible for growth plate normal regulation are affected leading to complete disruption of the normal endochondral ossification process. Such scenario may be possible considering, the observed alterations from early stages the expression collagen and the proposed role of DS chains in collagen nets assembly. Furthermore, appropriate ECM structure has been suggested as one of the factors involved in promoting and maintaining columnar organization, as evidenced by animal models. In fact preservation of columnar arrangement until 1 month may explain why these animals did not display evident skeletal abnormalities at that age despite the other histological alterations identified (Figure 6-5).

6.5 CONCLUSION

In conclusion, our results do not support the hypothesis of altered mechanical environment as a key factor involved in early stages of bone pathology in MPS, although it may contribute to inhibit ossification at later stages. In turn, our experimental and computational data suggest that the main consequence of GAG accumulation on growth plate is chondrocytes disorganization within the plate, probably associated to an abnormal ECM structure. The evidenced presented here, provides additional information about the potential mechanisms

136 involved in the disease. Thus, our data suggest that loss of columnar arrangement may be an important pathophysiological mechanism leading to loss of growth plate normal function, although it might not be the only one. In fact, alterations in intracellular signaling pathways involving STAT and JAK pathways have been described as involved in growth plate pathology in MPS VII mice [370]. Moreover alteration in BMP and TGF signaling, authophagy, and inflammation have been described as playing a role in cellular dysfunction in lysosomal storage diseases, although their role in growth plate pathology in MPS has been poorly studied [316, 396, 397]. Therefore, although our results require further experimental confirmation, the combined experimental and computational approached used here, allowed the definition of a new research path in order to better understand the growth plate pathology in MPS that can be applied to other genetic chondrodysplasias. This kind of studies contribute greatly to elucidate pathological mechanisms in these diseases and may expand the understanding of bone pathology in order to improve development of therapeutic approaches.

137

7 FINAL CONCLUSIONS AND PERSPECTIVES

Long bone development is a complex process that starts during embryological period and lasts until the end of adolescence in humans [16]. This process has been extensively studied, especially on those aspects regarding the mechanical and biochemical regulation of endochondral ossification during early prenatal stages [15, 16, 45, 181, 182]. During postnatal life, long bone growth relies on the normal function of the growth plate. Although this structure has been extensively studied from a morphological point of view, especially in normal conditions, most of the experimental approaches developed in order to analyze the effect of mechanical and biochemical factors have been analyzed in terms of growth rates and tissue level morphological effects [14, 21, 23]. Therefore, details regarding the mechanical and biochemical environments within growth plate form still a largely unexplored field. Subsequently, information about the pathophysiological mechanisms associated to growth plate abnormalities identified in several acquired and genetic bone dysplasias are not well understood.

Taking this into account, this work gives insight in mechanical and morphological aspects of the growth plate and their influence in long bone development in the context of normal and pathological conditions. For such purposes, a set of in silico mechanical and mechanobiological models were formulated as a platform to develop theoretical approximations to growth plate physiology and its pathologies. Such models were based on experimental evidence available in literature regarding normal bone growth and novel evidence generated during the development of this thesis using a genetic chondrodysplasia as a prototype of pathological condition. The approximation presented in this work is based on computational modelling, since it has demonstrated to be advantageous for predicting changes in the tissues resulting from mechanical loads using different morphological scenarios, events that are difficult to approach using in vivo models [175, 181, 277, 279, 283- 287, 327, 331]. Furthermore, in silico modeling allows the analysis of relationships between physical, structural and biochemical factors and their interactions based on the experimental

138 evidence available in order to improve our knowledge of biological processes. In fact, they provide a theoretical scenario that allows the identification of emerging properties of biological systems that might be useful to complement and direct experimental approaches [270, 272].

The work here presented includes, first, a study of the stress distribution on growth plate during different stages of bone development (Chapter 3). Such analyses revealed a mechanical stress gradient that seems to correlate with the histological arrangement of the growth plate which may have biological implications [14, 23, 333]. Our results suggest that mechanical stimuli may affect similarly growth plate and epiphyseal ossification [277, 333]. Additionally, within the growth plate such stimuli illustrate variations during each stage of bone development. According to our data, a completely mechanical approximation to bone development highly resembled biological behavior during initial stages, although it failed to do so once epiphyseal ossification is completed [34, 333]. At this stage, given the stress distribution characteristics, mechanical stimuli within growth plate may gain a preserving role rather than a stimulus for ossification [277, 333]. Such behavior suggests that mechanical stimuli may play different roles depending on the bone developmental stage. These observations were further supported by the results obtained when mechanical stimuli were analyzed in the context of growth plate morphological evolution (Chapter 4).

Although the results of this part present some limitations, since mathematical formulation rely on simplifications regarding loading schemes and morphological details, this model served as a proof of concept and allowed the identification of the impact of growth plate morphology and ossification front position in the mechanical environment of the developing epiphysis and growth plate. Furthermore, the obtained results encourage the development of more detailed computational models that consider the morphological and loading complexity of a specific bone in order to validate the results here presented and obtain more accurate data. In addition, further studies will require to consider more complex mechanical models for performing biomechanical analysis, as well as, take into account the boundary conditions between different tissues.

As a second step, a two-dimensional mathematical model of proliferative to hypertrophic state transition of growth plate chondrocytes was formulated as a platform to analyze in silico the cellular behavior within the growth plate (Chapter 5). The model considered such process in a single growth plate column, integrating the influence of both mechanical loading and the Ihh-PTHrP biochemical regulatory loop in the transition process, leading to results that are in good agreement with published experimental and computational findings [31, 183, 186- 188, 190, 282, 362]. The results of this model need to be analyzed in a theoretical scenario; extrapolation to the in vivo context may be limited considering that this is a model

139 circumscribed to a segment of the growth plate and takes into account only a selected set of biochemical and mechanical factors. Therefore, this model constitutes a first approximation to the development of mechanobiological models that can be used to study mechanical and biochemical interactions taking place in biological processes. In fact, the formulation to this model leads to the identification of some knowledge gaps that need to be filled and that must be the focus of future works. These include more detailed information regarding the impact of specific mechanical stimuli on: 1) synthesis of biochemical specific morphogens, such as Ihh/PTHrP; 2) chondrocyte proliferation; 3) zonal transitions from resting to proliferative zone or proliferative to hypertrophic zone; 4) column formation.

Finally, a mechanical, structural and biochemical approximation to growth plate pathology in in MPS VI was studied as a prototype of a genetic chondrodysplasia that presents late onset growth plate involvement. Thus, this work provides novel information regarding the progression of histological and biochemical abnormalities observed in the rat model of the disease (Chapter 6). Our results provided evidence that, in this disease, the main factors involved in growth plate pathology are delayed chondrocyte hypertrophy and columnar disorganization. Based on these observations, the in silico models developed in chapters 3 to 5 were used to explore some hypothesis regarding the pathophysiological mechanisms involved: 1) growth plate alterations are caused by alterations in mechanical properties; 2) Morphological changes observed at early stages potentiate growth plate disorganization by altering stress distribution patterns; and 3) columnar disorganization leads to abnormal biochemical environment disturbing the normal hypertrophy process. The results obtained supported the last hypothesis as the most probable scenario in this disease, and opens at least two areas of research that constitute the interest of future experimental analysis: characterizing mechanical properties of growth plates in advanced stages of the disease and identifying the expression patterns of specific morphogens within the growth plates of affected animals at different developmental stages.

In conclusion, this thesis provides new data about the mechanical environment within the growth plate along different stages of long bone development, an aspect that, to the best of our knowledge, has been not been addressed in previous works. The good agreement observed between the computational models developed and experimental evidence suggests that the theoretical framework presented in this thesis provides useful tools for further analyses of growth plate biology. Moreover, the results obtained contribute to broaden the knowledge about mechanical influence on the process of long bone growth and establish the basis for developing more detailed computational and experimental studies in this field. Lastly, the combined experimental-computational strategy used here for analyzing growth plate pathology in MPS VI constitutes a novel methodological approach to study growth plate involvement in pathological scenarios, a necessary step in order to gather basic knowledge

140 regarding bone pathology in genetic disease that might be useful in the future for developing novel therapeutic approaches.

141

APPENDIX A.

Growth plate stress distribution implications during bone development: a simple framework computational approach.

Manuscript published in the journal of Computer methods and programs in biomedicine, corresponding to partial results of Chapter 3:

Guevara JM, Moncayo MA, Vaca-Gonzalez JJ, Gutierrez ML, Barrera LA, Garzon-Alvarado DA. Growth plate stress distribution implications during bone development: a simple framework computational approach. Computer methods and programs in biomedicine 2015;118:59-68.

142

c

o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 8 ( 2 0 1 5 ) 59–68

jo urnal homepage: www.intl.elsevierhealth.com/journals/cmpb

Growth plate stress distribution implications

during bone development: A simple framework

computational approach

a b b b

J.M. Guevara , M.A. Moncayo , J.J. Vaca-González , M.L. Gutiérrez ,

a b,∗

L.A. Barrera , D.A. Garzón-Alvarado

a

Institute for the Study of Inborn Errors of Metabolism, Pontificia Universidad Javeriana, Bogotá, Colombia

b

Biomimetics Laboratory and Numerical Methods and Modeling Research Group (GNUM), Instituto de Biotecnología

(IBUN), Universidad Nacional de Colombia, Bogotá, Colombia

a r t i c l e i n f o a b s t r a c t

Article history: Mechanical stimuli play a significant role in the process of long bone development as

Received 28 April 2014 evidenced by clinical observations and in vivo studies. Up to now approaches to understand

Received in revised form stimuli characteristics have been limited to the first stages of epiphyseal development. Fur-

22 September 2014 thermore, growth plate mechanical behavior has not been widely studied. In order to better

Accepted 8 October 2014 understand mechanical influences on bone growth, we used Carter and Wong biomechanical

approximation to analyze growth plate mechanical behavior, and explore stress patterns for

Keywords: different morphological stages of the growth plate. To the best of our knowledge this work is

Epiphyseal stress distribution the first attempt to study stress distribution on growth plate during different possible stages

Long bone development of bone development, from gestation to adolescence. Stress distribution analysis on the epi-

Mechanical stimulus physis and growth plate was performed using axisymmetric (3D) finite element analysis in

Growth plate a simplified generic epiphyseal geometry using a linear elastic model as the first approxi-

mation. We took into account different growth plate locations, morphologies and widths,

as well as different epiphyseal developmental stages. We found stress distribution dur-

ing bone development established osteogenic index patterns that seem to influence locally

epiphyseal structures growth and coincide with growth plate histological arrangement.

© 2014 Elsevier Ireland Ltd. All rights reserved.

ends of the diaphysis establishing the epiphysis [2]. Toward

1. Introduction

the end of gestation the secondary ossification center (SOC)

forms in the central part of the epiphysis, followed by radial

Long bone embryological development is a complex process

growth until a completely ossified epiphysis is attained [3].

that derives from mesenchymal cells that condense and then

Thus, developmentally long bone epiphyses can first be com-

differentiate into chondrocytes to form a cartilaginous mold.

pletely cartilaginous, followed by SOC formation, ending with

The ossification process starts with establishment of the pri-

a completely ossified epiphysis at different stages of human

mary ossification center (POC) in the central part of the future

development: gestation, child-hood, and puberty [1–3].

bone or diaphysis [1]. The cartilaginous mold enlarges at both

∗

Corresponding author at: Carrera 30 No 45-03 Edificio 407, Oficina 202A, Bogota, Colombia. Tel.: +57 1 3165000x11202 14062;

fax: +57 1 3165333.

E-mail address: [email protected] (D.A. Garzón-Alvarado).

http://dx.doi.org/10.1016/j.cmpb.2014.10.007

0169-2607/© 2014 Elsevier Ireland Ltd. All rights reserved.

60 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 8 ( 2 0 1 5 ) 59–68

In the appendicular skeleton cartilage growth tissue

remains between the diaphysis and epiphysis in a region iden-

tified as the growth plate. Histologically the growth plate is

arranged in three zones: reserve, proliferative, and hyper-

trophic [1,4,5]. This zone is responsible for longitudinal growth

and characteristic shape acquisition. Other growth plate char-

acteristics, such as location within the bone, morphology, and

width, change according to bone type and age [6]. This is illus-

trated in the work published by Kandzierski et al. evidencing

that the growth plate morphology of a proximal femoral epiph-

ysis can resemble a concave meniscus at the age of four. With

increasing age, at seven the growth plate becomes straight,

as a ridged non-uniform line. Last, the growth plate assumes

the form of an arch at the beginning of puberty [5–10]. In

addition, growth plate’s width also changes through life, with

a wider growth plate during early stages and diminishing

progressively until its disappearance toward the end of adoles-

cence [8,11,12]. These changes are controlled by several factors

including genetic, biochemical, and mechanical [13]. The lat-

ter has been widely recognized as a regulator of growth rate,

modifying cell populations in proliferative and hypertrophic

states as well as matrix synthesis as evidenced by in vivo and

in vitro studies [14–17].

Various theoretical approaches have been performed in

order to understand mechanical regulation. Approaches range

from stress distribution analysis within the developing tissue

[18–22], to more complex models that integrate biochemical

and mechanical factors [23–25]. All of them have only consid-

ered events occurring in the epiphysis, not taking into account

growth plate characteristics or behavior. Furthermore, up to

now stress distribution on the epiphysis and growth plate

through different stages of bone development has not been

studied.

Using an axisymmetric (3D) finite element analysis we

devised a bone with generic geometry to explore stress

distribution on the growth plate during different stages of epi-

physeal ossification. The aim of this work was to shed light

on stress distribution within the growth plate during differ-

ent stages of epiphyseal ossification, and establish the effect

of growth plate morphology on epiphyseal stress distribu-

tion and vice versa. Results derived from this work will help

elucidate mechanical events taking place within the growth

plate and epiphysis during long bone growth. Additionally, the

information generated may be useful to formulate hypotheses Fig. 1 – Generic bone geometry. (A). Generic bone geometry

regarding mechanical influences on biological events taking description and scale. (B and C) Growth plate

place in normal and pathological bone growth scenarios. characteristics. (B) Widths. Representative sample for

straight morphology. W1: Thin, W2: Medium, W3: Thick.

(C) Locations. Representative sample for straight

morphology. L1: Low, L2: Middle, L3: High. (D) Morphologies

corresponding to W2, L2.

2. Materials and methods

To understand long bone mechanical behavior at different

2.1. Model

growth stages we performed a computational analysis using

linear elastic model solved by fine element analysis (FEA).

A 3D axisymmetric model of a generic bone was designed

For numerical analysis a set of partial differential equations

(Fig. 1), taking into account that several human long bones epi-

was implemented using Fortran (Formula Translating System,

physis have a similar shape during early embryological stages

New York, USA) programming language. Equation solving and

such as the proximal femur head, with bone’s longitudinal

results visualization were performed using ABAQUS v 6.1. and

length of 25 mm and epiphyseal radius of 10 mm (Fig. 1A). For

TECPLOT 360 (Tecplot Inc., Bellevue, WA, USA), respectively.

simplification the same morphology was maintained for latter

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 8 ( 2 0 1 5 ) 59–68 61

Table 1 – Tissue material properties. Elastic modulus and Poisson’s ratio for cartilage, bone, and Ranvier’s grooves as

established by Piszczatowski [29].

a

Tissue Elastic modulus (E)(MPa) Poisson ratio () Location within the model

Cartilage 6.0 0.495 Epiphysis (cases 1 and 2)Growth plate

Trabecular bone 345.0 0.300 Trabecular bone

SOC (Case 2)

Epiphysis (case 3)

Fibrous tissue 10.0 0.300 Ranvier’s grooves

a

See Fig. 1. SOC: Secondary Ossification Center.

developmental stages. The model included four regions: dia-

physis, growth plate, Ranvier’s grooves, and epiphysis (Fig. 1A).

In addition, different combinations between growth plate

morphologies and secondary ossification centers were eval-

uated: straight, concave, convex and irregular morphologies

(Fig. 1B–D). Here a linear elastic model is used, although car-

tilage is a highly hydrated tissue, since it is based on Carter’s

model which does not consider fluid flow velocity in contrast

to other approximations reported in the literature [26,27]. Fur-

thermore, the load applied was static and constant. Linear

elastic models have proven to be as reliable as poro-elastic

constitutive models for cartilage stress distribution analysis

in previous reports, thus here we the former considering its

simplicity for a first approximation to growth plate mechan-

ical environment [28]. Material properties for each zone are

described in Table 1. For simulations elastic modulus and Pois-

son’s ratio in different tissues were as follows: diaphysis was

designated as trabecular bone, Ranvier’s grooves, a mechan-

ical support structure, as fibrous tissue, and growth plate as

cartilage.

Although there is a drastic change in material properties

between growth plate region and diaphysis, analyses were per-

Fig. 2 – Loading conditions, constrains and data analysis.

formed in order to evaluate the impact of material transition

(A) Contour figure showing symmetry axis and constrains

in stress distribution. For such purposes, a transition zone was

used. Load position is indicated with arrows. (B). Growth

created between growth plate and diaphysis. This zone gen-

plate sections used for osteogenic index (OI) distribution

erates a gradual change of material properties from cartilage

analysis (Paths H1, H2 and H3) are marked with

(top) to bone (bottom); the transition in material properties

discontinuous lines. Each path corresponds to a histological

was given by:

section of the growth plate: reserve zone (blue), proliferative

E zone (pink) and hypertrophic zone (red). (For interpretation

E = E + y − y

TRANSITION ZONE GROTH PLATE ( GROTH PLATE)

y of the references to color in this figure legend, the reader is

referred to the web version of this article.)

where

E = E − E

BONE GROTH PLATE

And y is the transition zone width and y any point within the based on high osteogenic index (OI) areas obtained in case

transition zone. E is the young modulus of that zone. 1 simulations as shown in Supplementary Fig. 2 (see Section

The proof of concept was performed using a straight growth 2.3 for further information); thus SOC geometry varies in size

plate. These analyses showed a minor impact of material and shape, including circles and differently oriented ellipses

change on growth plate stress distribution, as such, a similar as shown in Supplementary Fig. 3. For case 3, it was used the

pattern was observed with or without a transition zone. Some same morphology as for case 1, but epiphysis was considered

changes in diaphyseal stress pattern were observed, however as trabecular bone instead cartilage (Fig. 1 and Table 1).

since this zone is already ossified, stress distribution in such Four growth plate morphologies were simulated for each

zone is not relevant for the purposes of this study (Supple- of the aforementioned cases: straight, concave, convex, and

mentary Fig. 1). irregular. Additionally, different widths and location of the

Long bone epiphyses were identified at three different growth plate were modeled trying to resemble the conditions

stages resembling chronological bone development: first com- of different bones as shown in Fig. 1. Three growth plate width

pletely cartilaginous (case 1), SOC formation (case 2), and sizes were used (W1: thin, W2: medium, W3: thick, corre-

completely ossified epiphysis (case 3). For case 2, SOC size sponding to 0.125, 0.25 and 0.5 mm respectively). Last, three

and shape was designed individually for all conditions tested locations within the epiphysis (L1: low, L2: middle, L3: high)

62 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 8 ( 2 0 1 5 ) 59–68

Fig. 3 – Cartilaginous epiphysis OI distribution. (A) Representative sample for OI value with simulations on straight growth

plate in three different localizations and medium width (L1, L2, L3, W2 case 1). (B) Maximum OI values obtained in the

central region of epiphysis for all localizations, morphologies, and widths.

were simulated for each morphology (Fig. 1B–D). To construct relation for P and S, named osteogenic index (OI) as an indica-

different locations, configuration L2 was used as reference and tor of mechanical stimuli influence on the ossification process

L1 and L3 were achieved by moving the growth plate to upper given by:

or lower L2 edge, respectively.

A total of 36 morphologies were used for simulations.

OI = S + kP (1)

For meshing, conventional quadrilateral elements were used.

Convergence analysis showed an optimum element size of

0.01 meshing length units (Supplementary Fig. 4). The number where k is an empirical constant that was tested with values

of element varied among morphologies ranging from approx- between 0.2 and 2 (Supplementary Fig. 5). However for all sim-

imately 16.000 to 20.000. ulations k = 0.5 was used, since this value closely resembles a

biological setting as described by Carter et al., where a region

2.2. Loading conditions and constrains of low OI in the articular cartilage region is observed and high

values of OI for the predicted area of secondary ossification

For the model, Y axis was taken as symmetry axis; addition- center, which was clearly distinguished within the epiphyses

ally zero displacement constraints for Y axis at the lower edge [18].

of the geometry was established. Loads were applied on the OI is a scalar parameter integrating the competing effects of

upper arch. In order to be able of doing unitary comparisons, octahedral normal stress and octahedral shear stress. The OI

the load applied in the simulation corresponds to a pressure can be used to predict which regions of a cartilaginous skele-

of 1 MPa (Fig. 2A) similar to tests made in [21,30]. tal element are likely to ossify first (high OI values) and which

are likely to remain cartilaginous (low OI values)[18]. Taking

this into account, OI distribution was analyzed only in carti-

2.3. Data analysis

laginous structures within the model that include epiphysis

(only for cases 1 and 2) and growth plate.

Simulation results were analyzed in terms of octahedral nor-

In order to characterize mechanical environment within

mal stress (P) and octahedral shear stress (S). According to

the growth plate for all conditions simulated OI distribution

studies developed by Carter and Wong cartilage formation

was determined in the horizontal plane using sections named

resulted from octahedral normal stress, and bone was the

Path H1, H2 and H3 (Fig. 2B).

result of octahedral shear stress [18]. They defined a numerical

Fig. 4 – Osteogenic Index (OI) distribution in an epiphysis with SOC. (A) Representative sample for OI value with simulations

on straight growth plate in three different localizations and medium width (L1, L2, L3, W2 case 2). (B) Maximum OI values

obtained in regions flanking SOC horizontally.

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 8 ( 2 0 1 5 ) 59–68 63

Fig. 5 – Growth plate osteogenic index (OI) distribution for all conditions simulated. Representative sample for simulations

on straight growth plate.

ossification in the central region of the cartilaginous epiphysis.

3. Results

In order to understand SOC’s effect on epiphyseal stress distri-

bution we simulated a cartilaginous epiphysis with cartilage

3.1. Growth plate effect on epiphyseal stress

material properties surrounding a central area with trabe-

distribution

cular bone characteristics as specified in Table 1 (case 2). As

expected, the appearance of a bone structure within the epiph-

Epiphyseal stress distribution analysis during the earliest

ysis (SOC) leads to changes in epiphyseal OI pattern compared

stages of bone development with a completely cartilaginous

to a completely cartilaginous epiphysis (case 1). Osteogenic

epiphysis was performed (case 1). Stress distribution pat-

index (in cartilage tissue) attained the highest values in the

tern for all simulations demonstrated peak octahedral normal

area surrounding SOC, mainly at horizontal flanking sites,

stress (P) beneath the loading area. Furthermore, highest val-

reaching even higher values than for case 1 (Fig. 4). OI val-

ues for octahedral shear stress (S) were observed in the central

ues seemed to be affected principally by growth plate location

zone of the epiphysis. Likewise, highest OI values were also

(Supplementary Fig. 3).

centrally located as observed for S (Supplementary Fig. 6).

For case 3, representing a completely ossified epiphysis,

Osteogenic index distribution was evaluated for different

this value was not analyzed for the epiphysis since OI repre-

growth plate locations, morphologies, and changes in width.

sents ossification stimulus on cartilaginous tissue. Therefore,

We observed OI distribution changes mainly associated with

we only evaluated OI values in the growth plate for case 3.

growth plate localization (Fig. 3, Supplementary Fig. 2). A

growth plate in the lower position (L1) presented the highest

value for OI in the center with a vertical elongated distribu- 3.3. Growth plate stress distribution

tion that flattened as growth plate location became closer to

the loading area (L3) (Fig. 3A). Maximum osteogenic index val- Because the growth plate is responsible for bone’s longitudi-

ues within the epiphysis, showed a marked decreased value nal growth, OI value distribution was specifically analyzed for

for a growth plate located at L3 compared to L2 and L1 (Fig. 3B). different growth plate characteristics (localization, morphol-

ogy, and width). In addition, we simulated these events for

all epiphyseal developmental stages (cases 1, 2, and 3). A het-

3.2. SOC effect on epiphyseal stress distribution erogeneous OI distribution was observed for all simulations

performed (Fig. 5).

During bone development toward the end of gestation sec- To characterize OI horizontal value pattern for all simula-

ondary center of ossification (SOC) is formed. This involves tions we performed three different paths (Path H1, H2, and

64 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 8 ( 2 0 1 5 ) 59–68

4. Discussion and conclusions

Several computational approaches have explored the mechan-

ical environment in developing bones prior to SOC onset,

establishing possible associations between mechanical stim-

ulus and biological responses [18–22,25,28,30]. However, few

studies have addressed such aspects for the growth plate or

explored changes during development. In fact, to the best of

our knowledge this study is the first approach to understand

stress distribution on epiphysis and growth plate during dif-

ferent long bone developmental stages. This work is based

on Carter et al. [18] scalar parameter integrating octahedral

normal stress and octahedral shear stress to predict the ossi-

fication process. Contrasting to previous works that focused

mainly on SOC development, here Carter’s approximation was

applied for analyzing growth plate mechanical behavior in dif-

ferent bone development stages, in order to explore possible

correspondence between stress patterns and morphological

characteristics of the growth plate. As one the main find-

ing of the study, we observed a mechanical stress gradient

that seems to correlate with histological arrangement of the

growth plate. As such, prior to complete epiphyseal ossifi-

cation OI patterns coincide with growth plate histological

organization (reserve, proliferative, hypertrophic) which may

be involved in stimulating longitudinal bone growth. Addi-

tionally, it was observed that complete epiphyseal ossification

has an impact on growth plate stress distribution favoring

its maintenance rather than ossification. Furthermore, our

results suggests that mechanical stimuli may play a deci-

Fig. 6 – Horizontal growth plate OI value pattern during sive role on epiphyseal development as well as growth plate

different developmental stages. Representative sample for ossification, in particular during early stages of development,

straight growth plate L2, W2. Results obtained from Paths in agreement with the increasing in vivo and in vitro evi-

H1: resting zone (—), H2: proliferating zone (–) and H3: dence regarding mechanical effect on long bone development

hypertrophic zone (–). (A) Case 1. (B) Case 2. (C) Case 3. [14,17,31].

Results for cartilaginous epiphysis (case 1), which resem-

bles embryological development (second trimester) up to the

first year of life in humans [5,6,10], agree with those presented

H3). These paths illustrate OI values across the growth plate,

by Carter et al. under similar loading conditions and con-

starting from the center to Ranvier’s grooves for resting (H1),

strains. Epiphyseal areas with considerable OI values allow

proliferating (H2), and hypertrophic (H3) zones. Since high OI

predicting SOC localization and morphology [18]. Based on our

values predict cartilaginous tissue ossification, path results

results for case 1, SOC appearance is predicted in the epiphy-

could help establish an association between mechanical stim-

seal central zone despite growth plate location, morphology

ulation and a biological response. For cartilaginous (case 1) and

and width (Fig. 3, Supplementary Figs. 2–3).

SOC (case 2) epiphyses growth plate OI distribution demon-

Furthermore, according to our results future SOC character-

strated similar behavior. The highest OI value was observed

istics depend mainly on growth plate location (Fig. 3). A similar

in Path H1, with a decreasing tendency for Paths H2 and H3

pattern is observed during development for the appendicular

(Fig. 6A and B). However, for a completely ossified epiphysis

skeleton. In bones such as the femur which presents a medi-

(case 3) we observed a drastic change in OI value distribution

ally located growth plate, SOC develops as a rounded structure

(increased in negative magnitude), with parabolic tendency

(corresponding to L2 simulation). Whereas in bones such as

(Fig. 6C). Additionally, for Path H1 OI increased concomitantly

the radius, with a growth plate located near the loading area

with growth plate thickness (data not shown).

(corresponding to L3 simulation) SOC acquires a flattened

According to bone developmental stages growth plate

shape [6]. In addition, we observed decreased OI value in the

acquires different morphologies [8]. We performed simula-

SOC region for a growth plate located near the loading area

tions for straight, concave, convex, and irregular morpholo-

(L3). For this particular growth plate localization we suggest

gies. Results showed association between morphology and OI

low OI values could be associated with a mechanical stimulus

distribution pattern (Fig. 7, Supplementary Figs. 7–9). Horizon-

that may result in delayed SOC apparition. Biologically, such

tal OI value pattern for Path H1 was dependent on growth plate

events occur in bones such as the radius and hand and feet

morphology and epiphyseal developmental stage. For case 1,

phalanges, in which ossification occurs after the first year of

horizontal OI value pattern was greatly affected by growth

life [6].

plate morphology in particular for the Path H1 (Fig. 8).

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 8 ( 2 0 1 5 ) 59–68 65

Fig. 7 – Osteogenic index distribution according to growth plate morphology. Representative sample simulations for each

growth plate morphology (L2, W2, case 1).

With SOC appearance, our results show a non-uniform we suggest OI values in this structure can be an indicator

stress redistribution that lead to higher OI values laterally of expected growth rate. Within the growth plate OI values

rather than vertically, resulting in an ovoid growth trend were affected by all variables studied: localization, morphol-

(Fig. 4). Such results seem to resemble SOC growth pattern for ogy, and width (Figs. 5 and 7. Supplementary Figs. 7–9) with

bones such as the distal femur [6,9]. Additionally, as for case lower (L1) thick (W3) growth plate achieving the maximum

1, OI values and distribution seem to be affected mainly by value. The characteristics above mentioned are comparable

growth plate localization (Supplementary Fig. 3). to histological findings during embryological stages for lower

In sum, cases 1 and 2 simulation results suggest that SOC limb bones in humans and other mammals. In such cases

development was only affected by changes in growth plate growth plate is wider and present high growth rates [5,32]. Tak-

location (Fig. 2). For all cases simulated SOC was predicted to ing this into account, it is possible to suggest that mechanical

appear in the epiphyseal central zone, similar to in vivo SOC stimulus may contribute to the increased growth rate in that

development in most human bones [6]. However, it is well period.

known that SOC number and morphology varies among dif- Additionally we obtained a decreasing trend in OI values

ferent skeletal elements [6]. Previous studies have suggested from the epiphyseal to the diaphyseal end of the growth plate.

other factors can affect SOC appearance and shape such as Our results evidenced OI peak values in the reserve zone

epiphyseal contour and load localization [18,22]. In this study (Figs. 5–7), with OI values comparable to those observed in the

such conditions were constant (round epiphyseal shape – cen- epiphysis. The reserve zone is in charge of providing cells to

tral load). Thus, additional studies are required to evaluate the proliferative zone assuring growth process continuity [33].

together growth plate location and epiphyseal shape for spe- Moreover, it has been proposed that resting chondrocytes may

cific cases to understand how their interactions might affect synthesize biochemical factors, responsible for growth orien-

epiphyseal development [18]. tation and inhibition of hypertrophy in the proliferative zone.

Carter and Wong proposed OI as a mechanical stimula- These events favor growth plate histological organization in

tion indicator for ossification. As such, high OI values may distinct zones [33–36].

be related to increased ossification velocity [18]. Since long Based on the observed changes in OI values among

bone growth results from ossification within the growth plate, the areas corresponding to reserve, proliferation, and

Fig. 8 – Growth plate horizontal OI value distribution according to morphology. Representative sample simulations for each

growth plate morphology (L2, W2, case 1). Results obtained from Path H1.

66 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 8 ( 2 0 1 5 ) 59–68

Fig. 9 – Comparison between simulation results and imaging evidence for proximal femur epiphysis. For simulation (I) high

growth rate regions are shown in white (arrows). Predicted morphology is depicted in black. In images (II) growth plate is

highlighted in yellow. Images of 4, 7, 10 and 12 year-old boys. Image modified from [8]. (For interpretation of the references

to color in this figure legend, the reader is referred to the web version of this article.)

hypertrophic zones we suggest that mechanical stimulus proximal femur head. The results from simulations performed

could be associated with triggering changes in cellular behav- in this study were compared with human bone development

ior. As such, high OI values in the reserve zone may be events reported by Kandzierski et al., 2012, demonstrated

stimulating cells to start to proliferate or synthesize biochem- epiphyseal growth plate changes during femur development

ical factors or both, particularly in early stages of development from image studies (Fig. 9)[8,9]. In our simulation regions with

(cases 1 and 2). Mechanical regulation can be acting as an high OI values (similar to those observed in epiphysis) predict

epigenetic regulator of protein synthesis (29). high ossification rates. According to this, for example, results

Reports in the literature show an association between for concave L3W2-case 2, irregular L3W2-case 3, and convex

mechanical stimulus and differentiation process as well as L3W1-case 3 growth plates resemble the trend observed for the

synthesis of morphogens [17,37–40]. Furthermore, octahedral proximal femur at 4, 7 and 12 years of age respectively (Fig. 9).

normal stress has been reported to linearly increase chon- Thus, evidencing correspondence between stress patterns and

drocyte membrane lipid packing and lipid desaturase gene morphological characteristics. However, it is important to take

expression (36). It is well documented membrane biochem- into account that some of the morphologies evaluated do not

ical properties modulate signal transduction [41]. Therefore, correspond to physiological states, for example width growth

we suggest, for a completely cartilaginous epiphysis as well plates and complete ossified epiphysis.

as an epiphysis with SOC, the mechanical load observed as The results obtained are highly influenced by the unique

a high OI value in the reserve zone, could be a contributing load scheme considered, thus it is important to consider that

factor to biochemical changes initiated by these cells. in vivo each bone has specific loading characteristics that are

The final stage of epiphyseal development results in a com- related to bone interactions with muscles, ligaments and other

pletely ossified structure (case 3) this occurring during late bones. Taking this into account, even though here we observed

infancy. The results obtained for this case show low OI values a trend that correlate with some biological findings, to derive

in the growth plate central region increasing toward Ran- more accurate biological conclusions particularized simula-

vier’s grooves (Figs. 5 and 6C), comparable to those obtained tions for specific bones should be performed.

by Piszczatowski [42]. Such low central values, according to This work constitutes an initial approach to mechanical

Carter and Wong, may be interpreted as a mechanical stimulus environment during different stages of long bone develop-

favoring cartilage preservation rather than promoting ossifi- ment. For this reason to better analyze the net impact of

cation [18]. On the other hand, toward Ranvier’s grooves high growth plate morphology on epiphyseal stress distribution

OI values suggest active ossification. The above mentioned OI and vice versa, the computer model was established based on

behavior may lead to disbalanced growth forcing the growth several simplifications regarding epiphyseal geometry, load-

plate to achieve a convex morphology. ing conditions and the model used for mechanical behavior

In this study we performed stress distribution analysis analysis. Despite such limitations, the model used revealed

for all combinations among the variables considered (growth important information related to epiphyseal and growth plate

plate geometry, location, width and epiphyseal ossification stress distribution and the ossification process. Biological rel-

state). This allowed an approximation to the growth plate sit- evance of our findings should be confirmed through bone

uation for a wide range of long bones; that is the case for specific models that take into account poroelasticity and

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growth plate chondrogenesis, Endocrinology 143 (2002) [39] Q.Q. Wu, Q. Chen, Mechanoregulation of chondrocyte

1851–1857. proliferation, maturation, and hypertrophy: ion-channel

[34] M.B. Goldring, K. Tsuchimochi, K. Ijiri, The control of dependent transduction of matrix deformation signals, Exp.

chondrogenesis, J. Cell. Biochem. 97 (2006) 33–44. Cell Res. 256 (2000) 383–391.

[35] E. Karimian, A.S. Chagin, L. Savendahl, Genetic regulation of [40] T. Xu, K. Yang, H. You, A. Chen, J. Wang, K. Xu, C. Gong, J.

the growth plate, Front. Endocrinol. (Lausanne) 2 (2011) 113. Shao, Z. Ma, F. Guo, J. Qi, Regulation of PTHrP expression by

[36] O. Nilsson, E.A. Parker, A. Hegde, M. Chau, K.M. Barnes, J. cyclic mechanical strain in postnatal growth plate

Baron, Gradients in bone morphogenetic protein-related chondrocytes, Bone 56 (2013) 304–311.

gene expression across the growth plate, J. Endocrinol. 193 [41] K. Montagne, H. Uchiyama, K.S. Furukawa, T. Ushida,

(2007) 75–84. Hydrostatic pressure decreases membrane fluidity and lipid

[37] Y.Y. Shao, L. Wang, J.F. Welter, R.T. Ballock, Primary cilia desaturase expression in chondrocyte progenitor cells, J.

modulate Ihh signal transduction in response to hydrostatic Biomech. 47 (2013) 354–359.

loading of growth plate chondrocytes, Bone 50 (2012) 79–84. [42] S. Piszczatowski, Geometrical aspects of growth plate

[38] Q. Wu, Y. Zhang, Q. Chen, Indian hedgehog is an essential modelling using Carter’s and Stokes’s approaches, Acta

component of mechanotransduction complex to stimulate Bioeng. Biomech. 14 (2012) 93–106. APPENDIX B. Supplementary Material Appendix A – Chapter 3

Supplementary 1. Analysis of the effect of material properties transition on epiphyseal stress distribution.

In order to evaluate the impact of material transition in stress distribution, a transition zone was created between growth plate and diaphysis. This zone generates a gradual change of material properties from cartilage (top) to bone (bottom); the transition in material properties was given by:

∆퐸 퐸 = 퐸 + (푦 − 푦 ) 푇푅퐴푁푆퐼푇퐼푂푁 푍푂푁퐸 퐺푅푂푊푇퐻 푃퐿퐴푇퐸 ∆푦 퐺푅푂푊푇퐻 푃퐿퐴푇퐸

Where

∆퐸 = 퐸퐵푂푁퐸 − 퐸퐺푅푂푊푇퐻 푃퐿퐴푇퐸

And ∆y is the transition zone width and y any point within the transition zone. E is the Young’s modulus of that zone.

The proof of concept was performed using a straight growth plate. These analyses showed a minor impact of material change on growth plate stress distribution, as such, a similar pattern was observed with or without a transition zone. Some changes in diaphyseal stress pattern were observed, however since this zone is already ossified, stress distribution in such zone is not relevant for the purposes of this study (Figure B1).

153

Figure B1. Analysis of the effect of material properties transition on epiphyseal stress distribution. A. In gray is marked the transition zone denoted as ∆y. B-C. Results showed distribution of Osteogenic Index (OI) in absence or presence of a transition zone (TZ) in the epiphysis (B) and growth plate (C). TZ1: ∆y=1 mm TZ2: ∆y=3 mm TZ3: ∆y=5 mm TZ4: ∆y=8 mm TZ5: ∆y=11 mm.

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Supplementary 2: Cartilaginous epiphyseal (Stage 1) osteogenic index (OI) distribution for all simulations performed.

Figure B2. Cartilaginous epiphyseal (Stage 1) osteogenic index (OI) distribution for all simulations performed.

155

Supplementary 3: Osteogenic index (OI) distribution in an epiphysis with SOC (stage 2) for all simulations performed.

Figure B3. Osteogenic index (OI) distribution in an epiphysis with SOC (stage 2) for all simulations performed.

156

Supplementary 4: Mesh convergence analysis.

A mesh convergence analysis was performed using different mesh sizes on a configuration corresponding to stage 1. Results showed a similar OI distribution pattern with mesh sizes below 0.01 (Figure B4). Based on such results 0.01 was selected for all analysis.

Figure B4: Osteogenic Index (OI) distribution using different mesh sizes corresponding to 66.050 elements (0.005 mesh size); 16.404 elements (0.01 mesh size); 2711 elements (0.025 mesh size); 676 elements (0.05 mesh size); 192 elements (0.1mesh size). A. Epiphyseal OI distribution. B. Growth plate Oi distribution. *Mesh size is referred in Meshing length units.

157

Supplementary 5: Optimum k value estimation.

An analysis was performed in order to determine the optimum k value using different values on a configuration corresponding to stage 1. Results showed that with a value of 0.5 results corresponded better to the in vivo epiphyseal ossification as referred by Carter and Wong (Figure B5) [277].

Figure B5: Osteogenic index distribution using different k values for calculation.

158

Supplementary 6-7-8: Osteogenic index distribution for non-straight morphologies.

Figures corresponding to the observed OI distribution for irregular (Supplementary 6 -- Figure B6), convex (Supplementary 7 -- Figure B7) and concave (Supplementary 8 --Figure B8) morphologies.

159

Figure B6: Osteogenic index distribution on irregular growth plate in three different localizations, for all epiphyseal developmental stages, and all widths.

160

Figure B7: Osteogenic index distribution on convex growth plate in three different localizations, for all epiphyseal developmental stages, and all widths.

161

Figure B8: Osteogenic index distribution on concave growth plate in three different localizations, for all epiphyseal developmental stages, and all widths.

162

APPENDIX C Supplementary results chapter 4

Morphologies used for analysis of stimuli behavior through normal human femur development

Figure C1. Sample images of morphologies displayed by human proximal femur at different ages. Compilation generated based on images reported in literature [319, 326, 343-347].

Changes in stimuli mean values (퐃̅) and variations (퐂퐕) during growth

163

Figure C2. Changes in stimuli mean values (D̅) and variations (CV) during growth. The results presented correspond to the values of each stimulus obtained in each of the growth plate morphologies shown in Figure C1. A. Shear stress B. Axial stress C. Hydrostatic pressure D. Osteogenic Index. Solid line: mean value of stimulus. Dashed line: Variance of the stimulus along the growth plate.

164

APPENDIX D. A quantitative and qualitative growth plate description: a simple framework for chondrocytes columnar arrangement evaluation

Manuscript published in the journal of Computer methods and programs in biomedicine, corresponding to methodology used in Chapter 6:

Guevara JM, Castro-Abril HA, Barrera LA, Garzón-Alvarado DA. A Quantitative And Qualitative Growth Plate Description: A Simple Framework For Chondrocytes Columnar Arrangement Evaluation. Journal of Mechanics in Medicine and Biology. (doi: 10.1142/S0219519416500548)

165

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Journal of Mechanics in Medicine and Biology Vol. 16, No. 2 (2015) 1650054 (15 pages) °c World Scientific Publishing Company DOI: 10.1142/S0219519416500548

A QUANTITATIVE AND QUALITATIVE GROWTH PLATE DESCRIPTION: A SIMPLE FRAMEWORK FOR CHONDROCYTES COLUMNAR ARRANGEMENT EVALUATION

JOHANA MARIA GUEVARA Institute for the Study of Inborn Errors of Metabolism Pontificia Universidad Javeriana, Bogota, Colombia [email protected]

HECTOR ALFONSO CASTRO-ABRIL Numerical Methods and Modeling Research Group (GNUM) Universidad Nacional de Colombia, Bogota, Colombia [email protected]

LUIS ALEJANDRO BARRERA Institute for the Study of Inborn Errors of Metabolism Pontificia Universidad Javeriana, Bogota, Colombia [email protected]

DIEGO ALEXANDER GARZÓN-ALVARADO* Numerical Methods and Modeling Research Group (GNUM) Universidad Nacional de Colombia, Biomimetics Laboratory Institute of Biotechnology Universidad Nacional de Colombia, Bogota, Colombia [email protected]

Received 18 February 2015 Revised 5 June 2015 Accepted 15 June 2015 Published

The growth plate is a cartilaginous structure located in the metaphysis of long bones, char- acterized histologically by its stratification and columnar arrangement. It is responsible for assuring longitudinal growth. Evaluation of growth plate histological characteristics has been traditionally performed using qualitative observation; however, some quantitative approaches have been reported using complex techniques. Here, we propose a simple quantitative images based analysis in order to evaluate objectively columnar arrangement within growth plate. For this, we defined six descriptors that were condensated in a geometric tensor. This tensor could be used as a single parameter to evaluate the growth plate organization. Validation of the tensor was performed with growth plate microphotographs of three healthy species (rat, pig

*Corresponding author.

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and rabbit) and an abnormal one (Csf1tl/Csf1tl rat) found in specialized literature. According to our results, the descriptors and the tensor give a complete picture of the organization of the growth plate, reflecting the expected stratification and columnar arrangement of the cells within the tissue. This methodology could be a reliable tool for evaluation of growth plate structure for research and diagnostic purposes, taking into account that it can be easily implemented.

Keywords: Growth plate; columnar organization.

1. Introduction The epiphyseal plate, physis or growth plate is a cartilaginous structure located in the metaphysis of bones; it is responsible for longitudinal long bone growth until final bone length is attained. Within this structure a continuous transition process of cartilage to bone occurs, known as endochondral ossification. It is characterized by a differentiation process that implies phenotypic and functional changes in the main cellular type present in cartilage, the chondrocyte, favoring mineralization of the extracellular matrix (ECM) and recruitment of osteoblasts, forming bone.1–3 Growth plate is a highly organized structure that is histologically arranged in three zones: The first and nearest to the epiphysis is called reserve zone, composed by round slow-proliferating cells denominated resting chondrocytes. Most likely these cells are precursors of the second zone or proliferative, which is characterized by flat proliferating chondrocytes, arranged as a stack of coins aligned to the lon- gitudinal growth axis. Finally, the third zone or hypertrophic is formed by chon- drocytes that stop proliferation and suffer hypertrophy, increasing their cell volume up to 10-fold. Furthermore, hypertrophic chondrocytes promote extracellular matrix calcification and finally undergo apoptosis, generating a zone of calcified cartilage in contact with diaphyseal bone.1–3 Normal bone growth relies on proper growth plate chondrocyte differentiation and columnar arrangement.1,4 Furthermore, several genetic and epigenetic condi- tions are related with abnormalities in those processes that finally lead to altered long bone growth and shape.5–7 Such abnormalities have been documented by his- tological analysis of growth plates obtained from animal models and human sam- ples. Those plates have been described quantitatively in terms of widths of growth plate regions, number of proliferating cells and growth rates, however columnarity is usually evaluated by qualitative observations that lack precise and comparable parameters.6,7 There are some reports in literature regarding cell density per zone, cell per column and even 3D morphology of columns for normal growth plates in different species. However, up to now there are no clear parameters for columnarity evaluation.8–11 In order to improve the morphological evaluation of growth plate structure, here we aim to find quantitative descriptors of growth plate columnar quality in terms of spatial orientation and cellularity. For such purposes, we analyzed growth plate histological images and derived six evaluation parameters. In addition, using those parameters we proposed a tensor that condensed all the information. This

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quantitative indicator of growth plate columnar quality could be a useful tool for those interested in a detailed histological evaluation of growth plates, and may be used in human and other animals in clinical and research contexts. Additionally, the measures here proposed may be used as source data for development of computa- tional models of growth plates.

2. Materials and Methods In order to perform a quantitative description of growth plate columnar organiza- tion, we defined five independent parameters: cellular density, C; column density,

CD; density of isolated cells, CI; column orientation, n; and NCy/NCx cell ratio, r. These were measured on growth plate histological images shown in Fig. 1, corre- sponding to three species: rat, rabbit and pig,9,12–14 using a zone dependent grid. For grid design, we calculated cell height and diameter for each physeal zone using microphotographs scale bars as reference. Based on these values, and considering that cell size is similar among species,9,15 zone grid dimension was determined according to the average inter-species cell size on each physeal zone, in order to

(a) (b) (c)

(d) (e) (f)

Fig. 1. (Color online) Histological images of the different species considered. (a) 21 day old wild type (wistar) rat. (b) 35 day old wild type (wistar) rat. (c) 80 day old wild type (wistar) rat. (d) 28 day old Csf1tl/Csf1tl rat. (e) 240 day old miniature pig. (f) 42 day old New Zealand white Rabbit. Taken from scale bars: 100 m (Images (a)–(c)); 400 m (image (d)) and 200 m (images (e), (f)).

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Table 1. Details of the grid used for measurements on each image.

Species Age (Days) Growth plate zone Grid cells used

Wild Type Wistar Rat 21 PZ 60 Pre-HZ 20 HZ 15 35 PZ 70 Pre-HZ 20 HZ 10 80 PZ 45 Pre-HZ ND HZ 20 Csf1tl/Csf1tl rat 28 PZ 135 Pre-HZ 20 HZ 10 New Zealand White Rabbit 42 PZ 100 Pre-HZ ND HZ 12 Miniature Pig (Sus scrofa Domesticus) 240 PZ 24 Pre-HZ 10 HZ 3

Note: PZ: Proliferative Zone; Pre-HZ: Pre-Hypertrophic Zone; HZ: Hypertrophic Zone; ND: No Data available.

assure that at least two cells fit entirely within a field. Thus, the field size was 33:33 33:33 m2 for reserve and proliferative zones, 50 50 m2 for pre-hyper- trophic and 100 100 m2 for hypertrophic zone. Details about the grid used for measurements are shown in Table 1.

2.1. Parameter description 2.1.1. Cell density (C) Cell density was defined as the total number of cells within a grid field, including only those cells whose area was completely inside the square. Data obtained from all fields were averaged per zone and expressed as cells per area (mm2Þ.

2.1.2. Column density (CD) Column density expresses the total number of columns within a grid field. Here, a column was defined as two or more stacked cells (see Fig. 2), with a distance among them no greater than the average cell height within the field. Additionally, the geometrical centers of the cells within the column must be aligned in a way such that the connection among them by a straight line is allowed. Data obtained from all fields were averaged per zone and expressed as number of columns per area (mm2).

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Fig. 2. (Color online) Graphical representation of the cell distribution descriptors along the different physeal zones. The cells in gray conform a column and the isolated ones are colored in black. The axis labeled as A (in green), symbolizes the line that links the geometric centers of the cells that conform the column, while the axis labeled as B represents the transversal axis to the one in the preferential bone growth.

2.1.3. Isolated cell density (CI ) This parameter was defined as the number of cells within a field that do not belong to a column (Fig. 2). Data obtained from all the fields were averaged per zone and normalized to an area of 1 mm2.

2.1.4. Column orientation () As an indicator of column orientation, the angle () formed between the line that connects the geometrical centers of each cell within the column (which is the column axis) and the axis orthogonal to the longitudinal bone growth axis was measured (Fig. 2).

2.1.5. NCy/NCx cell ratio (r) The anisotropic cell concentration per field (r) was defined as the ratio of the number of cells in the column axis with respect to the cells in the orthogonal direction.

2.2. Structural geometric tensor of the growth plate (R*) The geometric tensor that expresses the anisotropic structure of growth plate (Eq. 2) was initially defined by Garzon–Alvarado et al.16 It describes the cellular pattern within a control area with side L (see Fig. 3). This tensor is given by: rffiffiffiffiffi C ¼ ð þðr Þ Þ; ð Þ R r I 1 n n 1 where C corresponds to cell density within the control area, r the anisotropic cell concentration, and n the column direction vector. I indicates the identity matrix.

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The original description was used for a theoretical scenario where all cells within a field belonged to columns; these were perfectly orientated with the longitudinal growth axis. In order to adapt the tensor R to describe a more realistic situation in an in vivo growth plate, we included an additional parameter regarding the number of isolated cells within a control field.

2.2.1. Mathematical description of the modified geometric tensor R*

The density of isolated cells (CI ) and the total cell density within a field are related by the following equation

CI ¼ C CC; ð2Þ

where C corresponds to the total number of cells within a control field, CC repre- sents the number of cells that belong to a column (Fig. 2) and CI the number of isolated cells. Note that CC is dependent on both C and CI , since these two were directly measured from histological images. Dividing Eq. (2) by C, we obtain: C C I ¼ C : ð Þ C 1 C 3

We defined the ratio of isolated cells over the total number of cells (CI /C)as. Thus, Eq. (4) is rewritten as: C ¼ C : ð Þ 1 C 4 Clearing C in Eq. (4), we obtain:

CC C ¼ : ð5Þ 1 Replacing C from Eq. (5) in Eq. (1), we obtain the modified geometric tensor R*: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CC R ¼ ðI þðr 1Þn nÞ; ð6Þ ð1 Þr

where CC , , r, I and n represent the aforementioned parameters. To understand the biological relevance and descriptive properties of the tensor, it is important to highlight that for calculation two coordinate systems were used: A global and a local one. The former corresponds to an axis parallel to the longitudinal bone growth axis (denoted as Y ) and an axis orthogonal to it (denoted as X); while the latter, is formed by the longitudinal axis of the column (denoted as Y 00) and an axis perpendicular to it (denoted as X00). Taking into account that all parameters were measured in the local coordinate system, tensor R will also be expressed in the column local coordinate system, and it will be expressed as tensor R c. Thus, column direction vector n will always correspond to the principal growth direction of the column: n ½01: ð7Þ

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Developing Eq. (6) for the local system, the expression for the tensor R C is as follows: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cc 10 R ¼ : ð8Þ c ð1 Þr 0 r

Based on Eq. (8), it is observed that there are r times more cells in the principal growth direction contributing to growth (in that direction) than in any other di- rection. This information is valid for any column within a field; however, it is insufficient to accurately describe the impact of growth plate columnar ori- entation on bone growth. To do this, it is necessary to consider the relationship between local and global coordinate systems. As observed in Fig. 3, local coordinate system is rotated an angle with respect to the global coordinate system. Based on this phenomenon, one system can be transformed into another by employing a transformation matrix (T), which is expressed by the following equation:  cos sin T ¼ ; ð9Þ sin cos

with corresponding to the rotation angle of the local coordinate system with respect to the global. Thus, one can transform tensor R c (expressed in the local coordinate system) into a new tensor R g (expressed in the global coordinate system) by using the following expression:

T R g ¼ T R cT: ð10Þ

Fig. 3. (Color online) Graphical description of the two coordinate systems used for tensor R* calcula- tion. Column local coordinate system (X0–Y ) is depicted in orange, while global coordinate system (X–Y) is represented in black. Column direction vector n and its orthogonal direction n? are indicated in purple.

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Developing Eq. (10), the final expression for tensor R g tensor is obtained: R g ¼ R 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 CC CC CC 6 2 þ r 2 ðr 1Þ 7 6 ð Þrcos ð Þrsin ð Þrcos sin 7 6 1 1 1 7 ¼ 6 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 7: 4 CC CC CC 5 ðr 1Þ cos sin sin2 þ r cos2 ð1 Þr ð1 Þr ð1 Þr ð11Þ This new tensor (R g) represents a general state of growth where the term R11 is an indicator of the number of cells per unit of length in the direction orthogonal to bone growth axis (X), while the term R22 provides information associated to the con- tribution to bone growth in the main bone growth axis (Y ). Finally, the terms R12 and R21 may be interpreted either as a measure of the number of cells participating in the distortion of the longitudinal bone growth or as the total lost in longitudinal bone growth potential. All these components are expressed in terms of cells per unit of length. It is worthwhile noting that rotation angle () and column orientation angle () are related by the following expression:

¼ 90 þ : ð12Þ

An alternate procedure for obtaining Eq. (11) can be derived by expressing local direction vector n in the global coordinate system. Thus, for a positive rotation angle (Fig. 3), vector n takes the following form:

ng ½sin cos ; ð13Þ

where ng represents the direction vector n expressed in the global coordinate system. Formulation of tensor R is performed directly on the global coordinate system: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CC R ¼ R ¼ ðI þðr 1Þn n Þ: ð14Þ g ð1 Þr g g

In this case, the parameters CC, and r do not change since they are invariant to the transformation. Developing the above equation, we obtain the following: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  CC 10 sin R ¼ R ¼ þðr 1Þ ½sin cos ; ð15Þ g ð1 Þr 01 cos sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 CC 10 sin sin cos R g ¼ R ¼ þðr 1Þ : ð16Þ ð1 Þr 01 sin cos cos2

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Simplifying and rearranging terms, this expression results in the same one obtained in Eq. (11).

3. Results and Discussion The quantitative growth plate cellular organization analysis was performed as de- scribed in materials and methods. In the first place, differences among normal growth plates are shown by highlighting inter-species variability. In the second place, comparison between rat normal and abnormal growth plates is reported. Finally, results of the geometric tensor R* are shown for all species.

3.1. Normal growth plates Table 2 shows results of the five independent parameters directly measured in the images analyzed. Values for each parameter present a high dispersion, mainly due to the presence of high amounts extracellular matrix leading to areas of low cellularity. Such situation is more evident in proliferative zone for all cases (Fig. 1). Despite this, we observed that the number of cells (C), column density (CD) and r tended to decrease from proliferative to hypertrophic zones. This reduction could be related to the fact that cells increase in size and volume as they hypertrophy, occupying more space within a field, which results in less cells per area. Furthermore, our findings agree with previous histological analyses performed in rat, mice and human growth plates, as reported by Hunziker and Schenk, Buck- walter et al. and Kember and Sissons, respectively.8–10 Column orientation showed similar behavior among zones, with angles ranging from 87 to 107. For all species, the orientation of the columns tended to a value of 90 in the hypertrophic zone, which implies that here columns tend to align to the growth axis. Data is summarized in Table 2. The total number of isolated cells (CI Þ per unit section were similar among the analyzed growth plates (Table 2). However, when expressing CI as a proportion of the total number of cells within a certain section field (term from Eq. (5)), we observed greater values for the pre-hypertrophic zone compared to those found in the proliferative and hypertrophic zones (Fig. 4). This suggests that within the latter zones, cells tend to belong to a column, reflecting a high degree of columnar organization. In contrast, high CI =C in pre-hypertrophic zone may suggest that cells within the same column lack hypertrophy synchronicity, resulting in transient disturbance of columnar arrangement in this progression zone.

3.2. Abnormal growth plate In order to test the potential of the proposed parameter for evaluating growth plate normality, we analyzed an image of the growth plate of the toothless rat (Csf1tl/ Csf1tlÞ, a mutant strain that has been reported to have deficient column formation and abnormal differentiation zones.12 Results show that in comparison to the

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Table 2. Average values for column cell density (C), columnar density (CD), sloping angle () and NCy/NCx cell concentration ratio (r).

Age Growth CD CI Species (Days) plate zone C [cells/mm2] – (SD) [cell columns/mm2] – (SD) [cells/mm2] – (SD) () – (SD) r – (SD)

Wild type wistar Rat 21 PZ 2938.48 (2006.14) 780.53 (672.56) 704.01 (683.27) 100 (14.87) 2.62 (1.02) Pre-HZ 2140 (759.78) 460 (195.75) 400 (224.78) 96 (19.72) 2.72 (1.15) HZ 1126.67 (278.95) 260 (98.56) 213.33 (124.59) 91 (8.34) 1.34 (0.64) 35 PZ 2635.71 (1915.77) 668.57 (587.19) 411.43 (713.54) 88.63 (10.52) 3.22 (1.13) Pre-HZ 1520 (1018.56) 440 (340.89) 300 (447.21) 92.96 (7.34) 1.92 (1.02) HZ 1120 (113.53) 340 (96.6) 180 (131.66) 98 (14.18) 1.00 (0.55)

1650054-10 80 PZ 3040.5 (1906.4) 714.21 (475.09) 550.96 (532.57) 93 (11.12) 3.08 (1.42) Pre-HZ ND ND ND ND ND HZ 1720 (735.28) 500 (255.47) 320 (246.24) 94 (9.81) 2.38 (1.33) Csf1tl/Csf1tl rat 28 PZ 1176.75 (1091.44) 258.48 (428.83) 244.87 (422.74) 82.24 (29.83) 2.11 (0.4) Pre-HZ 1100 (500.53) 140 (242.79) 200 (242.79) 91.58 (14.03) 2.33 (0.44) HZ 1270 (290.78) 330 (82.33) 330 (82.34) 91.43 (16.83) 1.2 (0.35) New Zealand White Rabbit 42 PZ 1962 (1684.37) 549 (441.18) 81 (288.74) 89 (2.23) 3.44 (1.07) Pre-HZ ND ND ND ND ND HZ 1975 (635.5) 358.33 (79.3) 75 (96.53) 90 (0.54) 1.62 (0.89) Miniature Pig (Sus scrofa 240 PZ 3037.5 (2233.31) 937.5 (621.23) 337.5 (639.85) 93 (15.23) 2.32 (0.91) Domesticus) Pre-HZ 2360 (831.6) 600 (388.73) 720 (957.77) 91 (18.40) 1.74 (0.69) 2 HZ 1200 (529.15) 300 (100) 233.33 (152.75) 87 (15.35) 1.15 (0.38) nd Reading Note: PZ: Proliferative Zone; Pre-HZ: Pre-Hypertrophic Zone; HZ: Hypertrophic Zone; ND: No Data available. July 28, 2015 8:47:41am WSPC/170-JMMB 1650054 ISSN: 0219-5194 2nd Reading

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Fig. 4. Comparison of isolated cell proportion between species. ND: No Data available.

proliferative zone of the growth plates of wild type rats of similar ages (21 and 35 days old), the mutant showed a decrease in C and CD (Table 2). Additionally, higher CI /C ratio was observed for the proliferative zone, indicating an increase in isolated cells per field (Fig. 4). This was also observed in the pre-hypertrophic zone. Regarding column orientation, mean values of the orientation angles of wild type and mutants showed no relevant differences. However, when variations of such angles inside each zone were analyzed, abnormal growth plate demonstrated higher variability (Table 3 and Fig. 5). This agrees with the observed columnar dis- turbances in the Csf1tl/Csf1tl rat, compared to normal rats (Fig. 5).

Table 3. Differences in the variation coefficients of the column sloping angle between wild type Wistar rats and mutant (Csf1tl/Csf1tl rat).

Species Age (Days) Growth plate zone Variation coefficient of (%)

Wild Type Wistar Rat 21 PZ 16.45 Pre-HZ 20.65 HZ 9.2 35 PZ 11.86 Pre-HZ 14.47 HZ 15 80 PZ 12.63 Pre-HZ ND HZ 9.91 Csf1tl/Csf1tl rat 28 PZ 36.27 Pre-HZ 21.56 HZ 18.41

Note: All data were analyzed for each physeal zone. PZ: Proliferative Zone; Pre-HZ: Pre- Hypertrophic Zone; HZ: Hypertrophic Zone; ND: No Data available.

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(a) (b)

(c) (d)

Fig. 5. Orientation angle distribution in wild type and mutant rat. (a) proliferative zone; (b) hyper- trophic zone; (c) orientation vector of a normal rats and (d) orientation vector of Csf1tl/Csf1tl rat. Results of 21 day old wild type rat.

Based on the obtained results, we conclude that C, CD, CI =C and the variation coefficient of were the most sensitive descriptors for quantitative measurement of growth plate columnar alterations displayed by Csf1tl/Csf1tl rats. Although such parameters must be evaluated in other abnormal cases in order to validate our results, they constitute a promising tool for quantitative analysis in research and diagnostic scenarios, since they may provide objective measurements to distinguish clearly normal and abnormal cell organization.

3.3. Geometric tensor R* data Tensor R* is a 2 2 matrix that describes the distribution of cells in a control field.

Position 1,1 of the tensor, denoted by R*11, represent, the number of columnar cells per unit length aligned with the X axis; position 2,2 (R*22), represent, the number of columnar cells per unit length aligned with the Y axis. Positions 1,2 (R*12) and

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(a)

(b)

(c)

Fig. 6. Results corresponding to nondimensional component ðI þðr 1Þn nÞ of R*ij tensor. (a) Results for *R11. (b) Results for *R12 ¼ *R21 and (c) Results for *R22.

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2,1 (R*21) indicate the number of columnar cells per unit length that are deviated from the Y axis.

Figure 6 shows the results of tensor R*. Values for R*11 show differences among species and growth plate zones. In particular, we observed differences in the pro- liferative and prehypertrophic zones of the analyzed rat growth plates. This may be related to the high cell volume changes between zones in such growth plates (Fig. 1).

Results for R*12 and R*21 showed that deviated cells of the proliferative zone were greater than the corresponding number in the hypertrophic zone, implying that, as columns reach this zone, they tend to align with the bone growth axis. This behavior could favor a uniform cell distribution along the ossification front and therefore a uniform growth behavior was also observed in the mutant growth plate. This finding may suggest that, despite the abnormalities, there is a tendency to favor growth in the bone longitudinal axis. However, for the mutant, there is still loss of growth potential energy due to the high angle variability observed in this plate reflected

(Fig. 5). Such behavior is reflected by the higher values of R*12 and R*21 observed for Csf1tl/Csf1tl rats in Fig. 6.

Results of R*22 show a zone dependent behavior for all species, with values decreasing as the zone changed from proliferative to hypertrophic. This trend may be explained by the fact that hypertrophic cells are greater in size and volume compared to cells in other zones, occupying more space within the control field.1,2

Thus, R*22 trend can be compared to the hypertrophy process, which is similar among species. Furthermore, in the Csf1tl/Csf1tl rat, it was similar to the wild type rats. This reflects that, as observed in Fig. 1(d), the hypertrophy process still occurs, despite growth plate abnormalities.

Additionally, R*22 values in the proliferative zone for all normal rats growth plates clustered around a mean value of 2.95, while the corresponding value in the

mutant rat was 2.09. This finding suggests that, for this particular mutant, the R*22 position for the proliferative zone may be sensitive to abnormal changes in growth plate organization. This reflects that the main disturbance in Csf1tl/Csf1tl rats occurs in column formation, as stated by Gartland et al.12

4. Conclusion In this paper, we present an intuitive and straightforward images based method- ology in order to quantitatively describe growth plate morphology. This method- ology provides five objective parameters that allow to quantitatively represent age-related and inter-species differences in cell distribution for each growth plate zone. With those parameters, we calculated a geometric tensor R* which gives a complete and unified picture of columnar behavior in the plate, while conserving its sensitivity to the above mentioned changes. In addition to the proper description of growth plate characteristics, the descriptors were also able to identify the abnormal behavior of the toothless rat (Csf1tl/Csf1tlÞ growth plate, especially in terms of column density and isolated cell

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density. These abnormalities were as well pictured by tensor R* supporting its proposed role as a global quantitative descriptor of growth plate columnar quality. In conclusion, although further evaluation using other species may be required, our results suggest that the descriptors herein described could be a useful tool for evaluating histological changes in growth plates for research and diagnostic purposes.

References 1. Burdan F, Szumilo J, Korobowicz A, Farooquee R, Patel S, Patel A, Dave A, Szumilo M, Solecki M, Klepacz R, Dudka J, Morphology and physiology of the epiphyseal growth plate, Folia Histochem Cyto 47:5–16, 2009. 2. Ham AW, Cormack DH, Ham’s Histology, Chap. 12, Lippincott, Philadelphia, USA. Bone, 1987. 3. Karsenty G, Kronenberg HM, Settembre C, Genetic control of bone formation, Annu Rev Cell Dev Biol 25:629–648, 2009. 4. Mackie EJ, Tatarczuch L, Mirams M, The skeleton: A multi-functional complex organ: the growth plate chondrocyte and endochondral ossification, J Endocrinol 211:109–121, 2011. 5. Azouz EM, Teebi AS, Eydoux P, Chen MF, Fassier F, Bone dysplasias: An introduction Canadian Association of Radiologists journal, Can Assoc Radiol J 49:105–109, 1998. 6. Krakow D, Rimoin DL, The skeletal dysplasias, Genet Med 12:327–341, 2010. 7. Rimoin DL, Cohn D, Krakow D, Wilcox W, Lachman RS, Alanay Y, The skeletal dysplasias: clinical-molecular correlations, Ann N Y Acad Sci 1117:302–309, 2007. 8. Buckwalter JA, Mower D, Ungar R, Schaeffer J, Ginsberg B, Morphometric analysis of chondrocyte hypertrophy, J Bone Joint Surg Am 68:243–255, 1986. 9. Hunziker EB, Schenk RK, Physiological mechanisms adopted by chondrocytes in reg- ulating longitudinal bone growth in rats, J Physiol 414:55–71, 1989. 10. Kember NF, Sissons HA, Quantitative histology of the human growth plate, J Bone Joint Surg Br 58-B:426–435, 1976. 11. Moss-Salentijn L, Moss ML, Shinozuka M, Skalak R, Morphological analysis and computer-aided, three dimensional reconstruction of chondrocytic columns in rabbit growth plates, J Anat 151:157–167, 1987. 12. Gartland A, Mason-Savas A, Yang M, MacKay CA, Birnbaum MJ, Odgren PR, Sep- toclast deficiency accompanies postnatal growth plate chondrodysplasia in the toothless (tl) osteopetrotic, colony-stimulating factor-1 (CSF-1)-deficient rat and is partially re- sponsive to CSF-1 injections, Am J Pathol 175:2668–2675, 2009. 13. Bries AD, Weiner DS, Jacquet R, Adamczyk MJ, Morscher MA, Lowder E, Askew MJ, Steiner RP, Horne WI, Landis WJ, A study in vivo of the effects of a static compressive load on the proximal tibial physis in rabbits, J Bone Joint Surg Am 94E:1110–1111, 2012. 14. Congdon KA, Hammond AS, Ravosa MJ, Differential limb loading in miniature pigs (Sus scrofa domesticus): A test of chondral modeling theory, J Exp Biol 215:1472–1483, 2012. 15. Stokes IA, Clark KC, Farnum CE, Aronsson DD, Alterations in the growth plate as- sociated with growth modulation by sustained compression or distraction, Bone 41:197– 205, 2007. 16. Garzon-Alvarado DA, Narvaez-Tovar CA, Silva O, A mathematical model of the growth plate, J Mecha Med Biol 11:1213–1240, 2011.

1650054-15 APPENDIX E. LIST OF PUBLICATIONS

Results of the work presented of this thesis have been published in The Journal of Computer Methods and Programs in Biomedicine (Chapter 3). In addition, the methodology developed for the histological analyses performed in chapter 6 was published in The Journal or Mechanics in Medicine and Biology (Chapter 6). Both publications are attached as Appendix and correspond to the following references:

 Guevara, J.M., et al., Growth plate stress distribution implications during bone development: a simple framework computational approach. Comput Methods Programs Biomed, 2015. 118(1): p. 59-68

 Guevara, J. M., et al. A quantitative and qualitative growth plate description: a simple framework for chondrocytes columnar arrangement evaluation. Journal of Mechanics in Medicine and Biology. doi:10.1142/S0219519416500548

In addition, part of the work (Chapter 3) has been submitted for publication to The Journal or Mechanics in Medicine and Biology.

During the development of this thesis, other publications have been made dealing with: histological image analysis; expression of lysosomal enzymes expression during the process of chondrogenesis; the effect of acid ceramidase treatment on chondrocytes implantation on rats; and effect of biophysical stimuli on in vitro cultures of chondrocytes. Such publications are not included in the manuscript and correspond to the following references:

 Gutierrez Gomez M.L., Guevara Morales J.M., Barrera Avellaneda L.A., Semi- automatic grading system in histologic and immunohistochemistry analysis to evaluate in vitro chondrogenesis. Universitas Scientiarum v.17 fasc.2 p.113 – 123, 2012

 Gutierrez Gomez M.L, Guevara Morales J.M., Garzon Alvarado D.A., Barrera Avellaneda L.A. Aggrecan catabolism during mesenchymal stromal cells in vitro chondrogenesis. Animal Cells And Systems v.17 fasc.4 p.243 - 249, 2013

181

 Vaca-González JJ, Guevara JM, Vega JF, Garzón-Alvarado DA. An In Vitro Chondrocyte Electrical Stimulation Framework: A Methodology to Calculate Electric Fields and Modulate Proliferation, Cell Death and Glycosaminoglycan Synthesis. Cellular and Molecular Bioengineering 2015:1-11.

 Frohbergh ME, Guevara JM, Grelsamer RP, Barbe MF, He X, Simonaro CM, et al. Acid ceramidase treatment enhances the outcome of autologous chondrocyte implantation in a rat osteochondral defect model. Osteoarthritis Cartilage. 2015 Oct 30. pii: S1063-4584(15)01369-2. doi: 10.1016/j.joca.2015.10.016. .

Finally this work has been presented as a poster or oral presentation in:

 Exploratory analysis of growth plate mechanical environment during bone development: a computational model. Guevara JM., Moncayo MA., Vaca JJ., Gutierrez ML., Barrera LA., Garzón-Alvarado DA. 13th International Symposium on Mucopolysaccharidoses and Related Diseases, Sauipe, Bahia, Brazil, August 13-17, 2014 (Poster).

 Histological and mechanical characterization of growth plates in a MPS VI rat model. Guevara J, Frohbergh M, Garzón-Alvarado DA, Barrera LA, Schuchman E, Simonaro CM. SSIEM 2015 Annual Symposium. Lyon, France, September 1-4, 2015. (Poster)

 Evaluation of the role of mechanical stimuli in growth plate morphological evolution during long bone development. Guevara JM, Castro HA, Moncayo MA, Barrera LA, Garzón-Alvarado DA. VI International Conference on Computational Bioengineering. Barcelona, Spain, September 14-16, 2015

 A mathematical model for growth plate columnar organization. Castro HA, Guevara JM, Barrera LA, Garzón-Alvarado DA. VI International Conference on Computational Bioengineering. Barcelona, Spain, September 14-16, 2015

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