Robot Mechanisms and Mechanical Devices Illustrateds on bone fracture repair - identifying important cellular characteristics ppt

Mechanical and mechanobiological influences on bone fracture repair - identifying important cellular characteristics Summary Fracture repair is a complex and multifactorial process, w

Mechanical and mechanobiological influences

on bone fracture repair

- identifying important cellular characteristics

A catalogue record is available from the Eindhoven University of Technology Library ISBN 978-90-386-1146-4

Copyright © 2007 by H Isaksson

All rights reserved No part of this book may be reproduced, stored in a database or retrieval system, or published, in any form or in any way, electronically, mechanically, by print, photoprint, microfilm or any other means without prior written permission of the author

Cover design: Jorrit van Rijt, Oranje Vormgevers

Printed by Universiteitsdrukkerij TU Eindhoven, Eindhoven, The Netherlands

Financial support from the AO Foundation, Switzerland is gratefully acknowledged

AO Foundation

Research

Mechanical and mechanobiological influences

on bone fracture repair

- identifying important cellular characteristics

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven,

op gezag van de Rector Magnificus, prof.dr.ir C.J van Duijn,

voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op maandag 26 november 2007 om 16.00 uur

door

Hanna Elisabet Isaksson

geboren te Linköping, Zweden

To my family and friends for all their

support through these years

Contents

Contents vii

Summary ix

List of original publications xi

1 Introduction 1

2 Bone fracture healing and computational modeling of bone mechanobiology 7

3 Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing 27

4 Corroboration of mechano-regulatory algorithms: Comparison with in vivo results 41 5 Bone regeneration during distraction osteogenesis: Mechano-regulation by shear strain and fluid velocity 55

6 A mechano-regulatory bone-healing model based on cell phenotype specific activity71 7 Determining the most important cellular characteristics for fracture healing, using design of experiments methods 91

8 Remodeling of fracture callus in mice can be explained by mechanical loading 107

9 Discussion and conclusions 123

Appendix A: Theoretical development of finite element formulation for modeling cellular activity………… 135

Appendix B: Taguchi orthogonal arrays and design of experiments methods 141

References 147

Samenvatting 163

Acknowledgement 165

Curriculum Vitae 167

Mechanical and mechanobiological

influences on bone fracture repair

- identifying important cellular characteristics

Summary

Fracture repair is a complex and multifactorial process, which involves a well-programmed series of cellular and molecular events that result in a combination of intramembranous and endochondral bone formation The vast majority of fractures is treated successfully They heal through ‘secondary healing’, a sequence of tissue differentiation processes, from initial haematoma, to connective tissues, and via cartilage to bone However, the process can fail and this results in delayed healing or non-union, which occur in 5-10% of all cases A better understanding of this process would enable the development of more accurate and rational strategies for fracture treatment and accelerating healing Impaired healing has been associated with a variety of factors, related to the biological and mechanical environments The local mechanical environment can induce fracture healing or alter its biological pathway by directing the cell and tissue differentiation pathways The mechanical environment is usually described by global mechanical factors, such as gap size and interfragmentary movement The relationship between global mechanical factors and the local stresses and strains that influence cell differentiation can be calculated using computational models

In this thesis, mechano-regulation algorithms are used to predict the influence of mechanical stimuli on tissue differentiation during bone healing These models used can assist in unraveling the basic principles of cell and tissue differentiation, optimization of implant design, and investigation of treatments for non-union and other pathologies However, this can only be accomplished after the models have been suitably validated The aim of this thesis is

to corroborate mechanoregulatory models, by comparing existing models with well characterized experimental data, identify shortcomings and develop new computational models of bone healing The underlying hypothesis throughout this work is that the cells act as sensors of mechanical stimuli during bone healing This directs their differentiation accordingly Moreover, the cells respond to mechanical loading by proliferation, differentiation or apoptosis, as well as by synthesis or removal of extracellular matrix

In the first part of this work, both well-established and new potential mechano-regulation algorithms were implemented into the same computational model and their capacities to predict the general tissue distributions in normal fracture healing under cyclic axial load were compared Several algorithms, based on different biophysical stimuli, were equally well able

to predict normal fracture healing processes (Chapter 3) To corroborate the algorithms, they

were compared with extensive in vivo experimental bone healing data Healing under two

distinctly different mechanical conditions was compared: axial compression or torsional rotation None of the established algorithms properly predicted the spatial and temporal tissue distributions observed experimentally, for both loading modes and time points Specific

inadequacies with each model were identified One algorithm, based on deviatoric strain and fluid flow, predicted the experimental results the best (Chapter 4) This algorithm was then employed in further studies of bone regeneration By including volumetric growth of individual tissue types, it was shown to correctly predict experimentally observed spatial and temporal tissue distributions during distraction osteogenesis, as well as known perturbations due to changes in distraction rate and frequency (Chapter 5)

In the second part of this work, a novel ‘mechanistic model’ of cellular activity in bone healing was developed, in which the limitations of previous models were addressed The formulation included mechanical modulation of cell phenotype and skeletal tissue-type specific activities and rates This model was shown to correctly predict the normal fracture healing processes, as well as delayed and non-union due to excessive loading, and also the effects of some specific biological perturbations and pathological situations For example, alterations due to periosteal stripping or impaired cartilage remodeling (endochondral ossification) compared well with experimental observations (Chapter 6) The model requires extensive parametric data as input, which was gathered, as far as possible, from literature Since many of the parameter magnitudes are not well established, a factorial analysis was conducted using ‘design of experiments’ methods and Taguchi orthogonal arrays A few cellular parameters were thereby identified as key factors in the process of bone healing These were related to bone formation, and cartilage production and degradation, which corresponded to those processes that have been suggested to be crucial biological steps in bone healing Bone healing was found to be sensitive to parameters related to fibrous tissue and cartilage formation These parameters had optimum values, indicating that some amounts

of soft tissue production are beneficial, but too little or too much may be detrimental to the healing process (Chapter 7)

The final part of this work focused on the remodeling phase of bone healing Long bone fracture remodeling in mice femora was characterized, including a new phenomenon described as ‘dual cortex formation’ The effect of mechanical loading modes on fracture-callus remodeling was evaluated using a bone remodeling algorithm, and it was shown that the distinct remodeling behavior observed in mice, compared to larger mammals, could be explained by a difference in major mechanical loading mode (Chapter 8)

post-In summary, this work has further established the potential of mechanobiological computational models in developing our knowledge of cell and tissue differentiation processes during bone healing in general, and fracture healing and distraction osteogenesis in particular The studies presented in this thesis have led to the development of more mechanistic models

of cell and tissue differentiation and validation approaches have been described These models can further assist in screening for potential treatment protocols of pathophysiological bone healing

List of original publications

The work presented in this thesis was carried out at the AO Research Institute in Davos, Switzerland, and within the Bone- and Orthopaedic Biomechanics section of the department of Biomedical Engineering at Eindhoven University of Technology It resulted in the following peer-reviewed publications and manuscripts, referred to by their roman numerals The thesis also contains unpublished data

differentiation during fracture healing

Journal of Biomechanics, 39(8):1363-1562, 2006

during fracture healing: Comparison with in vivo results

H Isaksson, C.C van Donkelaar, R Huiskes, K Ito

Journal of Orthopaedic Research, 24(5):898-907, 2006

III Bone regeneration during distraction osteogenesis:

Mechano-regulation by shear strain and fluid velocity

H Isaksson, O Comas, J Mediavilla, W Wilson,

C.C van Donkelaar, R Huiskes, K Ito

Journal of Biomechanics, 40(9):2002-2011, 2007

H Isaksson, C.C van Donkelaar, R Huiskes, K Ito

Manuscript submitted for publication

of proper fracture healing, using design of experiments methods

Manuscript submitted for publication

C.C van Donkelaar, R Huiskes, K Ito

Manuscript submitted for publication

1

1

Despite their natural healing capacity and the extensive amount of research conducted in this area, delayed healing and non-union of bones are frequently encountered For example in the United States 5-10 % of the over 6 million fractures occurring annually develop into delayed

or non-unions (Praemer et al., 1992; 1999; Einhorn, 1995; 1998b) Bone fractures cost society large amounts of money every year in primary treatment, follow-up operations due to delayed

or non-unions, and the cost of lost employment Furthermore, ageing of the population is expected to increase the prevalence of fractures due to osteoporosis In the European Union, in the year 2000, the number of osteoporotic related fractures was estimated at 3.8 million, resulting in direct costs for osteoporotic fractures to the health care services of € 32 billion (Reginster and Burlet, 2006) It has been predicted that 40% of all postmenopausal women will suffer one or more fractures during their remaining lifetimes (Compston et al., 1998; Reginster and Burlet, 2006) Hence, prevention and effective treatment of such complications are desirable

It is well recognized that mechanical stimulation can induce fracture healing or alter its biological pathway (Rand et al., 1981; Brighton, 1984; Wu et al., 1984; Goodship and Kenwright, 1985; Aro et al., 1991; Claes et al., 1997; Rubin et al., 2001) New bone formation

is also related to the direction and magnitude of loading, affecting the internal stress state in the repairing tissue (Park et al., 1998; Augat et al., 2003; Bishop et al., 2006) However, the mechanisms by which mechanical stimuli are transferred, via cellular mediators, into a biological response remain unknown

Mechanobiology describes the mechanisms by which biological processes are regulated by signals to cells that are induced by mechanical loads (Roux, 1881; van der Meulen and Huiskes, 2002) When the mechanisms of mechanically-regulated tissue formation are understood and well defined at the cellular level, physiological conditions and pharmacological agents may be developed and used to prevent non-unions and, furthermore,

to help accelerate fracture repair and restore optimal function Computer modeling is having a profound effect on scientific research (Sacks et al., 1989) Many biological processes, including bone healing, are so complex that physical experimentation is either too time consuming, too expensive, or impossible As a result, mathematical models that simulate these complex systems are more extensively used In mechanobiology, these computational models

have been developed and used together with in vivo and in vitro experiments to quantitatively

determine the rules that govern the effects of mechanical loading on cells and tissue differentiation, growth, and adaptation and maintenance of bone Mechanical perturbations are

applied to a model geometry, and the local mechanical environment is calculated, using the finite element method The biological aspects of the computations are based on different premises for local mechanical variables stimulating certain cellular activities, for example cell proliferation, or changes in bone structure Computational models are gradually becoming more sophisticated with increasing computational power and mechanobiological knowledge Both experimental and computational studies are critical to advance our knowledge in mechanobiology Integration of the fields is important, since models can help interpret experiments and experiments can provide relationships and observations for model development

Using these principles, mechano-regulation algorithms were proposed to investigate the influence of mechanical stimuli on tissue differentiation These algorithms were extensively applied to study bone healing (Chapter 2.8) They have used strain invariants and fluid hydrostatic pressure or fluid velocity in different combinations as biofeedback variables

These algorithms need to be validated against direct in vivo data, before further developments

can follow Validation could help both the understanding of basic biology during bone regeneration and in developing clinical treatment protocols for fracture healing Additionally, validated models can be useful in designing new experiments, and theoretical models and animal experiments together can lead to new research questions and advances in mechanobiology However, to date validation attempts have not been carried out sufficiently This is partly due to the need for experimentally reliable and repeatable outcomes, and controlled mechanical environments These are rarely available, because the required conditions are very difficult to meet in an experimental setting Moreover, many experiments that are used for validation are originally carried out with other scientific questions in mind

The principles of bone healing are very similar to other bone forming processes Bone healing has great similarities to bone formation and growth during fetal development (Marks and Hermey, 1996; Ferguson et al., 1999) Furthermore, it appears that the understanding of principles in fracture repair may have implications beyond fracture treatment, with applications in tissue regeneration in general, such as during distraction osteogenesis, osseointegration of implants, and in tissue engineering Therefore, a better understanding of all the factors that influence the bone healing process in general, and mechanobiology in particular, will have important applications in skeletal generation and regeneration

1.2 Aims and outline of the thesis

The previous section identified the need for further research on mechanoregulatory mechanisms of bone healing The general objective of this work is to enhance the knowledge

of the role of mechanical factors in tissue differentiation during bone regeneration in general, and fracture healing in particular, by corroborating mechanoregulatory algorithms The fundamental hypothesis in these studies is that the local level of mechanical stimulation, using stress and strain invariants, determines the cell and tissue differentiation pathways The cells act as sensors, and they respond depending on their environment Mechanical stimulation influences where either fibrous tissue, cartilage or bone tissue forms by directing the

differentiation of mesenchymal cells into fibroblasts, chondrocytes or osteoblasts This thesis

develops methods for corroboration of computational models with direct in vivo experimental

data The general objectives are divided into specific aims and hypotheses, which are addressed in subsequent chapters The specific objectives with each chapter are specified below:

Chapter 2 – Literature review

• To provide a comprehensive literature basis to describe the current knowledge and previous research conducted in the area of bone healing and computational

mechanobiology

Chapter 3 – Comparing existing models

• To implement and compare several existing mechano-regulation algorithms with regards to their abilities to predict the normal fracture healing processes

• To investigate whether individual parameters such as strain invariants, i.e deviatoric strain or volumetric deformation, i.e pore pressure and fluid velocity can be used to predict tissue differentiation during normal fracture healing

Chapter 4 – Determining validation status and identify inadequacies

• To corroborate the mechano-regulatory algorithms with extensive in vivo bone healing

data from animal experiments, including interfragmentary conditions, different from those for which they were developed

• To reveal which of these algorithms reflect the actual mechanobiological processes the best, by analyzing the corroborations at time points representing early and late healing

Chapter 5 – Implementing volumetric growth

• To investigate whether mechano-regulation by octahedral shear strain and fluid velocity, the algorithm selected in Chapter 4, can predict the spatial and temporal tissue distributions observed during experimental distraction osteogenesis

• To study variations in predicted tissue distributions due to alterations in distraction rate and frequency

Chapter 6 – Developing a mechanistic cell model

• To develop a new model of tissue differentiation based on cell activity, including matrix and cell phenotype-specific descriptions of migration, proliferation, differentiation, apoptosis, matrix production and degradation, in order to overcome discrepancies identified in Chapter 4

differentiation and bone healing

Chapter 7 – Establishing the relative importance of cellular characteristics

• To determine the importance of each parameter in the mechanistic cell model, by

Chapter 8 – Characterizing post fracture remodeling in mice

• To experimentally describe the remodeling phase of fracture healing in mice

• To investigate the hypothesis that the differences during the remodeling phase of fracture healing observed in mice compared to larger mammals and humans, can be explained by a main difference in mechanical loading mode

Chapter 9 – Discussion

and to incorporate it with past research and future prospects

1.3 General approach

Two- and three dimensional finite element models were developed as adaptive models for tissue differentiation Poroelastic finite element formulations were used to calculate the biophysical stimuli and mass- or heat transfer finite element formulations were employed for the calculations of cellular activities Adapted tissue types (matrix production) regulated the

mechanical properties and could also alter the geometry of the tissue Results from in vivo

animal experiments were employed for a range of qualitative and quantitative comparisons between computational predictions and experimental data

Verification was ensured by assessing the ability of the model to solve the mathematical representations correctly and by performing convergence studies Validation was performed

by assessing the models ability to represent the mechanical and biological behavior of specific experimental outcomes (Figure 1-1) The software that was used to create the computational models and the origin of the experimental data employed, is described below

Figure 1-1: General scheme of the approach for validation of computational models The

research within this thesis focused on the left hand side, and the experiments required (right hand side) were adopted from other studies that were performed at the AO Research Institute

The numerical models developed in this thesis were implemented and solved with the following software: The overall framework of the tissue differentiation model was implemented and solved in Matlab (v 5.3-7.1 Mathworks) Depending on complexity, the finite element meshes where created using either Marc Mentat (MSC Software), ABAQUS CAE (v 6.3-6.5 Simulia, Dassault Systemés) or Matlab All finite element models were solved using ABAQUS (v 6.3-6.5 Simulia, Dassault Systemés) Parts of the codes were written in external programs in FORTRAN 77 or C++ The remeshing algorithm (Chapter 5), was modified based on existing code from Dr Jesus Mediavilla (2005) The biphasic swelling model adapted to implement volumetric growth in Chapter 5 originated from Dr Wouter Wilson (2005) The bone remodeling algorithm used in Chapter 8 was adopted from the theory

by Dr Ronald Ruimerman (2005) The mechanistic model in Chapter 6 and 7 was solved using

a special finite element formulation, developed for biological modeling of cell activity during this work The details are provided in Appendix A

For validation purpose, results from several animal experiments, originally carried out to answer other research questions were used (Figure 1-1, right side) The availability of experimental results, such as radiographs, histology, histomorphometry, mechanical testing, reaction force measurements and micro computed tomography were vital for the work presented in this thesis It allowed both quantitative and qualitative comparisons between computational predictions and experimental results, a strategy which is a necessity for

validations of theoretical models The in vivo ovine tibia fracture model employed in Chapter

4 was provided by Dr Nicholas Bishop, as part of his PhD studies (Bishop, 2007) The experimental ovine distraction model used in Chapter 5 is from Dr Ulrich Brunner’s MD habilitation research (Brunner, 1992) The murine experimental fracture healing data, which is part of Chapter 8, was conducted by Dr Ina Gröngröft, DVM, as part of her dissertation (Gröngröft, 2007)

2 Bone fracture healing and

computational modeling of

bone mechanobiology

This chapter provides a literature review of the topics addressed in this thesis It includes a brief description of bone morphology, the mechanisms by which it is generated, regulated and repaired, and the role that the cells play in these processes This is followed by an overview of skeletal disorders, in particular bone fractures and the healing process, including different forms of healing, and possible complications Thereafter, the influence of mechanics on bone healing and the current understanding of mechanobiology are summarized Finally, previous studies in the area of computational mechano-regulation of tissue differentiation are reviewed and theories and algorithms described

2.1 Bone and bone fracture

The adult human skeleton consists of 206 bones They act as a support framework for the body and protect the internal organs Together with the muscles and joints, they facilitate movement and participate in maintenance of the body’s mineral balance (Marks and Hermey, 1996)

2.1.1 Bone structure and composition

Morphologically, bones are classified as cortical or trabecular (cancellous) bone Cortical bone forms the outer shell of every bone It is compact, stiff and strong and has a high resistance to all loads: bending, axial and torsion, which are especially important in the shafts of long bones (Buckwalter et al., 1996a) In contrast, trabecular bone is a less dense, less stiff, open pore matrix, which acts as a mechanically efficient structure in supporting the thinner cortical shells

at the ends of long bones and in the vertebrae (Buckwalter et al., 1996a) The shafts of the long bones are referred to as the diaphyses, and the expanded ends as the epiphyses The ends

of the epiphyses are coated with articular cartilage and other bone surfaces are covered by a well vascularized soft-tissue layer, known as the periosteum The periosteum isolates and protects the bone from surrounding tissues and provides cells for bone growth and repair Similarly, the inner surfaces of the long bones are lined by the endosteum Bone marrow is the soft tissue that fills the medullary cavity of the long bones and the spaces between the trabeculae It serves as storage for precursor cells, which are involved in repair

Bone tissue can also be woven or lamellar Woven bone is laid down rapidly and has randomly oriented collagen fibers, and low strength In adults it is observed mainly at sites of repair, at tendon or ligament attachments and in pathological conditions In contrast, the collagen fibers in lamellar bone are aligned and are much stronger Woven bone is mostly replaced by lamellar bone during growth or repair (Buckwalter et al., 1996b)

Bone consists mainly of extracellular matrix (ECM), divided into organic and inorganic components The organic components consist primarily of type I collagen (Rossert and Crombrugghe, 1996), and the inorganic component consists primarily of hydroxyapatite and calcium carbonates (Marks and Hermey, 1996) The combination of organic fibers enclosed in

an inorganic matrix provides a stiff and strong composite structure, in which the mineral component resists compression and the collagen fibers resist tension and shear (van der and Garrone, 1991; Marks and Hermey, 1996) The remainder of the skeleton consists of cells and blood vessels There are four different cell types in human bones: osteoblasts, osteoclasts, bone lining cells, and osteocytes Osteoblasts are bone forming cells They line the surfaces of the bones and produce osteoid (Buckwalter et al., 1996a) Osteocytes are osteoblasts that became surrounded by bone matrix growing around them, forming a cavity, or “lacunae” They remain active in the maintenance of bone and are believed to regulate bone remodeling (Buckwalter et al., 1996b) Bone-lining cells, also called pre-osteoblasts, are found in the periosteal and endosteal surfaces Osteoclasts are multinucleated cells whose function is bone resorption They break down bone and release the minerals into the blood (Buckwalter et al., 1996b) Osteoblasts, osteocytes and bone-lining cells differentiate from mesenchymal stem cells, and osteoclasts from hemopoietic stem cells (Owen, 1970)

2.1.2 Bone formation and growth

Bone forms, grows and resorbs continuously, by remodeling processes The formation of bone occurs by two methods, intramembranous and endochondral ossification These are discussed

in greater depth in the following chapters, since both are prominent during bone healing

Briefly, intramembranous ossification occurs during formation of the ‘flat’ bones, for those in the skull, for example (Buckwalter et al., 1996b) It forms directly from basic mesenchymal tissue, by differentiation from pre-osteoblasts into osteoblasts, which lay down osteoid Intramembranous bone formation occurs as appositional growth on bone surfaces, thereby increasing their width (Buckwalter et al., 1996b) Endochondral ossification occurs in long bone formation and growth The bone develops from a cartilage template, which calcifies along a front and is replaced by bone as blood-capillaries tunnel through, providing bone forming cells (Buckwalter et al., 1996b)

About 5% of the skeleton is undergoing remodeling, or renewal, at any time Haversian remodeling is a process of resorption followed by replacement of bone, with little change in shape, and occurs throughout life (Marks and Hermey, 1996) A cluster of osteoclasts drill a tunnel into the bone, creating a cone Behind the tip, osteoblasts fill up the cone with new bone with living cells, connected to the capillaries within the canal (Buckwalter et al., 1996b) (Figure 2-1) Remodeling releases calcium and repairs micro damage It is also responsible for bone adaptation to the mechanical environment (Wolf, 1892), resulting in bone thickening in regions of increased stress and bone thinning in regions of decreased stress

Figure 2-1: Schematic diagram of haverisan remodeling (Reprinted from Rüedi et al (2007),

Copyright by AO Publishing, Davos, Switzerland)

2.1.3 Bone fracture

Bone fractures when its strain limit is exceeded A fracture disrupts the blood supply and causes damage to the surrounding tissues, resulting in hemorrhage, anoxia, cell death and aseptic inflammation (Simmons, 1985) Most fractures are caused by physical trauma The risk of fracture can increase when medical conditions, such as osteoporosis or cancer, weaken the bones

Bone fractures are classified by their appearance and the extent of damage to the surrounding tissues (Rüedi et al., 2007) All fractures investigated in this thesis were simple transverse fractures Particular treatment strategies are used for each fracture type, including external fixation, nailing and plating which are employed in Chapters 4, 5 and 8

2.2 Fracture healing

Fracture results in a series of tissue responses that remove tissue debris, re-establish the vascular supply, and produce new skeletal matrix (Simmons, 1985) Unlike the healing processes of other tissues, which produce scar tissue, bone has the ability to repair itself Once

a fracture has healed and undergone remodeling, the structure will have returned to the injury state There are two main types of fracture healing: Primary and secondary

of bone (Figure 2-2) Gradually the fracture is healed by the formation of numerous osteons It

is generally a slow process that can take months to years until healing is complete

Figure 2-2: Primary healing New osteons connecting the bone fragments across a fracture

line (Reprinted from Rüedi et al (2007), Copyright by AO Publishing, Davos, Switzerland)

2.2.2 Secondary healing

In contrast to primary healing, secondary healing occurs in the presence of some interfragmentary movement and is the process by which fractures heal naturally It involves a sequence of tissue differentiation processes by which the bone fragments are first stabilized by

an external callus (Rahn, 1987; Perren and Claes, 2000) Recovery of bone strength is generally more rapid than in primary healing

Stages of repair during secondary fracture healing

The process of bone repair by secondary healing can be divided into three overlapping stages – the inflammatory, reparative and remodeling phases Healing begins with inflammation which is followed by the formation of soft and hard callus during the reparative phase Finally the callus is resorbed by remodeling (Cruess and Dumont, 1985; Frost, 1989) This thesis

focuses on the reparative (Chapter 3-7) and remodeling (Chapter 8) phases of fracture healing The relative duration of these phases is shown in Figure 2-3

Figure 2-3: Phases of fracture healing and their relative length The figure has been

recreated based on Cruess and Dumont, (1975)

a) b) c)

Figure 2-4: Schematic drawing of the three main stages of fracture repair a) Inflammatory

phase, b) reparative phase and c) remodeling phase The figure has been adapted from Cruess and Dumont, (1975)

Inflammation

The inflammatory phase begins simultaneously with the occurrence of the fracture (Figure 2-4a) During the trauma, blood vessels, the periosteum and the surrounding soft tissues are ruptured and a haematoma (blood cloth) forms The haematoma serves as an important source

of haematopoeitic cells and platelets that initiate the inflammatory response (Buckwalter et al., 1996b) Large numbers of signaling molecules, including cytokines and growth factors, are released (Bolander, 1992) The disruption of the blood supply also causes bone necrosis at the edges of the fracture ends Many of the cytokines released have angiogenic functions to restore the blood supply Also, pluripotent mesenchymal stem cells invade the haematoma at this time Cell division is first observed along the periosteum, and within a few days the activity is increased along the entire area next to the fracture, where it remains high for weeks (McKibbin, 1978)

Mesenchymal cells, originating from the periosteum, endosteum, bone marrow, and possibly the vasculature of the muscle-tissue surrounding the haematoma (Postacchini et al., 1995; Iwaki et al., 1997; Gerstenfeld et al., 2003b), migrate towards the fracture region No cells originate from the actual fracture gap The mesenchymal cells and the inflammatory cells form

a loose granulation tissue Mesenchymal cells proliferate, to later differentiate down specific pathways to become fibroblasts, chondrocytes, or osteoblasts, which generate fibrous tissue, cartilage and bone, respectively These cells proliferate and generate a callus (Bostrom and Asnis, 1998) The ends of the fractured bone themselves do not appear to participate in the initial reaction, and become necrotic, indicated by the empty osteocyte lacunae at the fractured ends (McKibbin, 1978)

Repair

The repair phase can be divided into the formation of hard callus (intramembranous ossification) and the formation of soft callus (endochondral ossification) Once the blood supply has started to be re-established and mesenchymal cells have invaded, callus formation begins (Figure 2-4b)

Intramembranous ossification

The first bone to be formed is laid down beneath the periosteum This rapid formation of woven bone begins several millimeters away from the fracture gap (Einhorn, 1998b) This bone is produced by committed osteoprogenitor cells that are already present in the cambium layer of the periosteum (Owen, 1970) It occurs within the haematoma when a group of mesenchymal or osteoprogenitor cells start producing osteoid at an ossification center Ossification extends progressively from the bony surface, pushing the surrounding soft tissue away Mineralized bone replaces the osteoid, and as the ossification centers expand, and eventually fuse Formation of these external bony cuffs proceeds in the direction of the fracture gap (McKibbin, 1978; Brighton, 1984)

Endochondral ossification

Concurrently, callus formation through endochondral ossification occurs at and around the fracture gap The soft callus consists of fibrous and/or cartilaginous connective tissues, which have differentiated from the mesenchymal stem cells During this stage, chondrocytes within the matrix proliferate and generate cartilaginous tissue Eventually these chondrocytes hypertrophy, and the cartilage calcifies The calcified cartilage acts as a stimulus for the ingrowth of new blood vessels (Webb and Tricker, 2000) The amount of cartilage present is variable, and dependent on the amount of movement (McKibbin, 1978) The formation of cartilage usually begins at the cortical bone ends and expands radially The bone formation occurs step by step toward the fracture plane The formation of endochondral bone is dependent on the existence of blood capillaries, which originate from the periosteal callus The process of endochondral bone formation strongly resembles the embryonic development of long bones (Ferguson et al., 1999) Angiogenesis occurs in parallel with endochondral ossification, eventually leading to erosion of mineralized cartilage and deposition of bone (Mark et al., 2004)

Remodeling

Once bony bridging of the callus has occurred and reunited the fracture ends, the processes of bone remodeling and resorption become the dominant activities in the callus (Figure 2-4c) The woven bone is gradually replaced by lamellar bone (Marsh and Li, 1999) During this process the medullary cavity is reconstituted It is thought that fluid shear stresses in bone modulate the remodeling activities, leading to osteocyte apoptosis and osteoclast recruitment (Bakker et al., 2004) Eventually, osteonal remodeling of the newly formed bone tissue and of the fracture ends restores the original shape and lamellar structure of the bone (Einhorn, 1998b) Resorption of the endosteal callus coincides with re-establishment of the original blood supply

2.3 Requirements for bone healing

Fracture healing is influenced by many variables including mechanical stability, electrical environment, biochemical factors and vascular supply Many of the basic influences of these factors on connective tissue response during fracture healing are poorly understood However,

biochemical and mechanical interactions are recognized as most important

The most dominant mechanical factors identified are the fracture geometry and the magnitude, direction and history of the interfragmentary motion These factors determine the local strain field in the callus The distribution of local strain in the healing tissue is believed to provide the mechanobiological signal for regulation of the fracture repair process that stimulates cellular reactions One of the most dominant mechanical factors is the fracture geometry, described by fracture pattern and gap size For example, even simple transverse fractures that lack careful repositioning and adequate fixation, can result in delayed union or non-union (Koch et al., 2002) Small gaps are beneficial for a fast and successful healing process, while larger gaps result in delayed healing, with decreased size in the periosteal callus and reduced bone formation in the fracture gap (Augat et al., 1998) The amount of interfragmentary movement is dictated by external load and fixation stability A stiff fixator limits the stimulation of callus formation, while flexible fixation enhances callus formation Unstable fixation can lead to excessive motion and result in non-union (Kenwright and Goodship, 1989; Claes et al., 1995) However, the effect of the interfragmentary movement depends on the size

of the fracture gap (Claes et al., 1998)

The direction of the interfragmentary movement influences the healing process Moderate axial interfragmentary movement is widely accepted to enhance fracture repair by stimulating formation of periosteal callus and increasing the rate of healing (Kenwright et al., 1991;

Larsson et al., 2001) Shear movements, however, have resulted in contradicting results Experimental studies have shown that shear movements at the fracture site result in healing with decreased periosteal callus formation, delayed bone formation in the fracture gap, and inferior mechanical stability, compared to healing with axial movement (Yamagishi and Yoshimura , 1955; Augat et al., 2003) However, other experimental investigations have demonstrated superior healing under shear, compared to axial interfragmentary motion (Park

et al., 1998; Bishop et al., 2006) Furthermore, clinical studies have shown shear movement to

be compatible with successful healing (Sarmiento et al., 1996) Hence, the effect of shear, compared to axial motion, appears to be sensitive to timing, magnitude, and/or gap size (Augat

et al., 2005) These studies have all investigated shear at the level of a whole bone However,

it is still uncertain how that translates to shear at the tissue and cell level That translation can

be investigated with computational tools

During the course of healing, the callus stabilizes the fracture by enlarging its cross sectional area and increasing its stiffness through tissue differentiation The interfragmentary movement decreases with healing time, as the callus stiffens Finally, the hard callus bridges the bony fragments and reduces the interfragmentary movement to such a low level that bone formation can occur in the gap The rate of reduction of interfragmentary movement appears to be related

to the initial interfragmentary movement, with larger movements having a faster decline (Claes et al., 1998)

2.3.2 Biochemical factors

Soft tissue coverage and blood supply

Over the last few decades, the importance of restoration of the soft tissues surrounding the fracture has become emphasized (Rüedi et al., 2007) Restoration of blood supply is important

in providing the biological environment, necessary for fracture healing The nutrient artery in the intramedullary canal, the capillary-rich periosteum and metaphyseal vessels are all important in providing cells with oxygen, nutrients and chemical factors, such as growth factors and cytokines (Rüedi et al., 2007)

Growth factors

Several growth factors and cytokines are known to be involved in the process of skeletal tissue repair and remodeling (Bostrom and Asnis, 1998; Lieberman et al., 2002) Many factors have been studied in isolation However, the interactions and feedback mechanisms are still far from being understood A short summary of known effects are provided below

Members of the transforming growth factor beta (TGF-β) supergene family, which include the bone morphogenic proteins (BMPs), have been shown to control a number of processes during skeletal development and repair Although these proteins are closely related, both structurally and functionally, each has a distinct temporal expression pattern and a potentially unique role

in bone healing (Aspenberg, 2005; Einhorn, 2005) TGF-β factors promote proliferation and differentiation of mesenchymal precursor cells into osteoblasts, osteoclasts and chondrocytes (Linkhart et al., 1996) They also appear to stimulate both endochondral and intramembranous

bone formation BMP signaling leads to activation of genes for proliferation and differentiation along the chondrogenic and osteogenic pathways BMP2 and BMP7 (OP1) seem to have similar effects and were shown to induce bone locally and speed-up skeletal defect repair Fibroblast growth factors (FGFs) and insulin growth factors (IGFs) can increase callus size and strength (Kawaguchi, 1994), by increasing proliferation of chondrocytes and osteoblasts, and stimulation of angiogenesis (Schmidmaier et al., 2004) Platelet-derived growth factors (PDGFs) stimulate osteoblast and osteoclast cell proliferation (Bourque et al., 1993; Sandberg et al., 1993) Furthermore, several cytokines (interleukins and tumor necrosis factors) affects processes during skeletal repair (Bolander, 1992; Sandberg et al., 1993) Prostaglandins stimulate osteoblastic bone formation and inhibit remodeling by decreasing osteoclast activity (Bakker et al., 2001), and hormones, such as estrogen and parathyroid hormones, also affect the healing potential (Aspenberg, 2005) Elucidating these interactions will be an important task for future research

2.4 Delayed and non-unions

There is no universally accepted definition of delayed or non-union A general definition of delayed union is a more than average time lapse to achieve clinical healing (Biasibetti et al., 2005) One commonly used description is that a delayed union occurs when periosteal callus formation ceases prior to complete union, delaying union to the late endosteal healing phase (Babhulkar et al., 2005) Non-union can be defined by the failure of both the endosteal and periosteal callus formation (Babhulkar et al., 2005) Sclerosis, a stiffening and hardening of the tissues in the medullary canal, occurs when the fracture remains open or becomes filled with scar tissue, which is usually fibrous in nature Occasionally a fibro-cartilaginous pseudoarthrosis or ‘false’ joint forms (Figure 2-5) Some types of non-unions, such as pseudoarthrosis and hypertrophic non-unions are usually treated mechanically Other types of non-unions related to infection, aseptic or septic tissues are treated biologically Treatments can also include the use of traditional bone grafts

Figure 2-5: Non-union represented by a mid-diaphyseal femur fracture, which resulted in a

pseudoarthrosis formation (Reprinted from Rüedi and Murphy (2000), Copyright by AO Publishing, Davos, Switzerland)

Non-union can be associated with patient factors, characteristics of the fracture, type of treatment, and pharmacological factors Patient factors can include smoking, diabetes and vascular insufficiency, and muscle quality, as well as nutritional status, anemia, and growth hormone deficiency Smoking is related to an increased rate of delayed union because of the vascoconstrictive effects of nicotine (Raikin et al., 1998; Hollinger et al., 1999) Moreover, injury sites and high-energy injuries that lead to extensive soft tissue damage are associated with higher rates of non-union Treatment techniques can also impede fracture healing, with inadequate immobilization or mobilization, fracture distraction, periosteal stripping and repeated manipulations being common examples Furthermore, cytostatics work by killing cells that proliferate quickly Hence, it has a negative effect on bone regeneration (Sauer et al., 1982) Corticosteroids and non-steroidal anti-inflammatory drugs impair the inflammatory response, and therefore impair healing (Einhorn, 2003; Gerstenfeld et al., 2003a)

2.5 Distraction osteogenesis

Distraction osteogenesis (DO) is a bone regeneration process, which was first performed by the Russian physician Ilizarov (Ilizarov, 1989a; 1989b) Ilizarov created an osteotomy on a patient to correct a severe deformity of the lower limb To avoid stretching nerves and blood vessels, his strategy was to use percutaneous wires to transfix the bone proximal and distal to the osteotomy site, and to use them to gradually distract the ends of the bone at a steady rate

He assumed that this treatment would create a large gap in the osteotomy site, which would require a subsequent bone graft procedure However, when he attempted to perform the bone graft operation, he found that the gap was completely filled with new bone (Ilizarov, 1989a) This method has become adopted world wide as the primary procedure for limb lengthening, correcting deformities and treating non-unions due to trauma, infection or tumor (Richards et al., 1998; Einhorn, 1998a)

This biological phenomenon seems to contradict some of the earlier basic assumptions about the formation of bone and the way in which mechanical forces affect osteogenesis (Einhorn, 1998a) Researchers have believed that compression, weight bearing and stress-generated potentials in bone lead to osteogenesis On the contrary, distraction (tension) has never been thought to be a stimulus for osteogenesis and in fact, most surgeons consider a fracture that is subjected to tension to be at risk of becoming a non-union (Einhorn, 1998a) However, the outcome has been shown predictable and reproducible DO is usually separated into three phases: the latency phase, immediately following osteotomy, the distraction phase, during which the active distraction of the bony segments take place, and the consolidation phase, which finally leads to bony union The rate of bone formation during DO is directly related to distraction rate (Ilizarov, 1989b; Li et al., 1999; 2000), frequency (Ilizarov, 1989b; Aarnes et al., 2002; Mizuta et al., 2003) and the local strain/stress generated in the distraction gap (Li et al., 1997; 1999) In distraction osteogenesis bone forms just as rapidly as during fracture healing, and as long as distraction force is applied, bone regeneration can be sustained almost indefinitely (Einhorn, 1998a) Hence, it is a suitable model for studying the potential mechanisms that stimulate bone formation and examination of the role of mechanical forces

2.6 Stem cell and tissue differentiation

In general, stem cells may be characterized as cells which have the capacity for extended renewal, as well as the ability to produce differentiated cells to maintain tissue structure and renew tissue after damage (Bianco et al., 2001; Triffitt, 2002) Mesenchymal stem cells (MSC)

self-in adult organisms are known to exist self-in several locations, self-includself-ing the marrow, periosteum and muscle-connective tissues, all which are potentially important during bone healing (Postacchini et al., 1995; Iwaki et al., 1997; Gerstenfeld et al., 2003b) The MSCs have so far been difficult to recognize and there are still no markers to exclusively identify mesenchymal stem cells In a healthy tissue there is little stem-cell activity with stem cells resting in a stable non-proliferating state and this state being maintained until more cells are required for tissue regeneration or repair (MacArthur et al., 2004) However, upon large disturbances, or where additional tissue is required, stem cells are capable of producing tissue progenitor cells, which then differentiate, whilst at the same time maintaining a stem cell pool

MSCs can differentiate towards several highly different cell phenotypes, including fibroblasts, chondrocytes or osteoblasts (Figure 2-6) These differentiated cells begin to synthesize the extracellular matrix of their corresponding tissues Several factors influence which lineage pathways the cell and tissue differentiation will take These factors include biochemical signaling molecules (Chapter 2.3.2) and mechanical conditions (Chapter 2.3.1) (Ashhurst, 1986; Sandberg et al., 1993) Bone marrow-derived MSCs play an important role as progenitors of skeletal tissue components, in skeletal morphogenesis and healing (Baron, 1999; MacArthur et al., 2004) Consequently, the understanding of MSC-derived cell proliferation and differentiation is of great interest in tissue regeneration, as well as from clinical and tissue-engineering perspectives (Yang et al., 2001; Rose and Oreffo, 2002; Cancedda et al., 2003)

Figure 2-6: Mesenchymal lineage pathways displayed by the end-stage phenotypes and the

possible differentiation pathways a MSC can take The differentiation of a pluripotent MSC goes through a multi-step series of changes in response to environmental stimuli before the end-state cell phenotype is reached The figure was adapted from Caplan and Bruder (2001)

2.7 Mechanobiology

The principle of mechanobiology is that biological cellular processes are regulated by signals, generated by mechanical loading, a concept dating back to Roux (1881) Mechanobiology aims to determine how loads are transferred to the tissues, how the cells sense these loads, and how the signals are translated into the cascade of biochemical reactions that stimulate cell expression and cell- or tissue differentiation (van der Meulen and Huiskes, 2002)

Computational mechanobiology attempts to determine the quantitative rules that govern the effects of mechanical loading on tissue differentiation, growth, adaptation and maintenance The biological side of the computation is based on the premise that local mechanical variables stimulate cell expression to regulate matrix composition, density or structure Modeling considerations include force application at the boundary, force transmission through the tissue matrix, mechanosensation and transduction by cells, cell gene expression, and transformation

of extracellular matrix characteristics All these parts are combined in a computer simulation model These processes must be represented by variables, parameters and mathematical relationships Some of these are known, or can be measured (e.g morphology, mechanical tissue properties, external loading characteristics), whereas others have to be estimated

2.8 Computational mechanobiological models

Many biological processes, including bone healing, are so complex that physical experimentation is either too time consuming, too expensive, or impossible As a result, mathematical models became increasingly important Finite element modeling was first introduced into orthopaedic biomechanics in 1972 to evaluate stresses in human bones (Brekelmans et al., 1972; Huiskes and Chao, 1983) Since then finite element models have been used, for example, to design and analyze implants, to obtain fundamental mechanical knowledge about musculoskeletal structures, and to investigate time-dependent adaptation processes in tissues (Huiskes and Hollister, 1993; Prendergast, 1997) By combining the power of computers with the knowledge of mechanobiology, theories have been proposed in terms of computer algorithms, to explain how the mechanical environment influences tissue growth, maintenance, remodeling and degeneration The theories have then been tested using finite element models Some of the proposed algorithms regarding tissue differentiation and bone healing are described below

2.8.1 Early theories

Pauwels’ theory

In 1960, Pauwels proposed the first rigorous theoretical framework by which the effects of mechanical forces on tissue differentiation pathways occur through mechanical deformation of the tissues (Pauwels, 1960) Building on initial work by Roux (1881), Pauwels suggested that tissues were suited to sustain distinct mechanical stressing Fibrous tissue forms in regions of tension, since collagen fibres are highly resistant exclusively to tensile stressing Cartilaginous tissue forms fluid-filled spherical structures around chondrocytes, which swell osmotically, and are suited to support hydrostatic pressure only Hence, he identified strain and pressure, as

two distinct stimuli, stimulating or allowing fibrous tissue and cartilage, respectively Primary bone formation requires a stable, low-strain mechanical environment and endochondral bone formation will proceed only after the soft tissues have stabilized the environment sufficiently

to create this low strain environment (Pauwels, 1960) (Figure 2-7)

Figure 2-7: Pauwels scheme for differentiation of mesenchymal cells into musculoskeletal

tissues, depending on the combination of volumetric and deviatoric deformation components

(Pauwels, 1960) This figure is created based on Pauwels (1960)

The fundamental concept in Pauwels’ theory was that in the case of a healing fracture, it is impossible for direct bone formation to bridge an unstable gap without being destroyed Therefore the purpose of the intermediate tissues is to stabilise and stiffen the fracture callus and to create a mechanically undisturbed environment where bone can form Pauwels’ theory was based on clinical observation and logic, but he did not have the means of measuring or calculating the tissue strains or stresses in detail

Interfragmentary strain theory

Perren and Cordey proposed that tissue differentiation is controlled by the resilience of the callus tissues to strain (Perren, 1979; Perren and Cordey, 1980) Their main idea was that a tissue that ruptures or fails at a certain strain level cannot be formed in a region experiencing strains greater than this (Figure 2-8)

Figure 2-8: Perren and Cordey’s ideas were based on how much elongation each tissue type

can tolerate This figure is created based on Perren and Cordey (1980)

The interfragmentary strain is determined by taking the longitudinal fracture-gap movement and dividing it by the size of the gap As a tissue in the fracture gap stiffens, the interfragmentary strain is reduced allowing healing by progressive tissue-differentiation from the initial granulation tissue, to fibrous tissue, cartilaginous tissue and finally bony tissue However, the hypothesis only considered longitudinal or axial strains; important strain contributions from radial and circumferential strains were neglected

2.8.2 Single phase models

Carter’s mechanobiological hypothesis

history explained tissue differentiation over time Later, Carter and colleagues developed their ideas and proposed a more generalised mechano-transduction model (Carter et al., 1998) (Figure 2-9) When the tissue is subjected to high tensile strains (above the tension line) fibrous matrix is produced Production of cartilaginous matrix is predicted to occur under high pressure, i.e to the left of the pressure line, since this tissue can support and resist hydrostatic pressure When the hydrostatic pressure is very low, i.e to the right of this line, formation of bone occurs No specific threshold values were specified for tension or pressure lines

Figure 2-9: Mechanobiological model as proposed by Carter et al., (1998) Two lines

separate the different predicted tissue types, one line based on tensile strain and one line based on hydrostatic pressure This figure is created based on Carter et al (1998)

The studies of Carter et al were the first to employ finite element analysis to explore relationships between local stress/strain levels and differentiated tissue types They modeled the tissue in the callus as a single solid (linear elastic) phase The first tissue differentiation scheme was tested with a model of a developing joint to determine whether this approach could predict the emergence of secondary ossification centres (Carter and Wong, 1988) Using the refined model, predictions for endochondral ossification during fracture healing, and healing around orthopaedic implants were investigated (Giori et al., 1995; Carter et al., 1998; Carter and Beaupre, 2001) Carter’s studies stressed that a good blood supply is necessary for

Carter’s mechanobiological model has also been used in other studies For example, computational studies of oblique fractures (Blenman et al., 1989), pseudoarthrosis formation (Loboa et al., 2001), asymmetric clinical fractures (Gardner et al., 2004) and distraction osteogenesis (Morgan et al., 2006) have been performed based on Carters mechanobiological model However, none of the studies predicted tissue differentiation adaptively over time

Claes and Heigele’s fracture healing model

Claes and associates performed an interdisciplinary study comparing data from animal experiments, finite element analysis and cell cultures to assess the influence of gap size and interfragmentary strain on bone healing (Claes et al., 1995; 1997; 1998) Based on histological observation, Claes and Heigele (1999) formulated a mechano-regulation algorithm, similar to that of Carter For the first time, they quantified thresholds for when the various tissues were

to form (Figure 2-10) The finite element analysis performed, as a basis for the threshold determination, was a solid hyperelastic analysis, performed at a few specific time points during fracture healing The comparison of histology with mathematical analyses of stress and strain allowed attribution of intramembranous bone formations to local strains of less than 5% The 5% limit for bone formation was also supported by cell-culture experiments involving stretching of osteoblasts (Claes et al., 1998) Compressive hydrostatic pressures greater than -0.15 MPa and strains smaller than 15% appeared to stimulate endochondral ossification, with all other conditions corresponding to areas of connective fibrous tissue or fibrocartilage Their theory was based on observations that bone formation occurs mainly near calcified surfaces

Figure 2-10: The fracture healing model proposed by Claes and Heigele (1999), including

threshold values for when each tissue type will form This figure is created based on Claes and Heigele (1999)

The fracture healing algorithm from Claes and Heigele has also been used by others Gardner and Mishra (2003) studied a clinical fracture and found favourable correlations with the algorithm Moreover the model has been combined with other rules of bone healing, using an

iterative finite element analysis controlled by a ‘fuzzy logic’ algorithm (Ament and Hofer, 2000) Rules were based on cell culture experiments and histological investigations, specifically incorporating vascularity to successfully simulate the main patterns of fracture healing The combination of Claes and Heigele’s algorithm and ‘fuzzy logic’ rules was also used by Simon et al (2004) to investigate differences between shear and axial stimulation, and

by Shefelbine et al (2005) to study healing of trabecular bone fracture

2.8.3 Biphasic adaptive models

In recent years biphasic and poroelastic finite element formulations became available for modelling fluid-saturated solid materials External loading is resisted by the linear combination of stress in the solid matrix and pressure of the fluid The solid matrix deforms according to its elastic modulus and fluid flows at a rate proportional to the pressure gradient and the permeability, according to Darcy’s Law Depending on the theoretical implementation, the solid and fluid components can be assumed as incompressible, such that the rate of change of solid volume and fluid volume are equal, or the solid can be compressible while the fluid is incompressible This type of formulation leads to time-dependent behaviour of the material, as fluid is extruded from and redistributed within the solid matrix The poroelastic formulation was originally proposed to model soil mechanics (Biot, 1941) and the biphasic formulation was proposed by Mow to model cartilage behaviour (Mow et al., 1980) The theories are slightly different but have been shown similar in outcomes (Prendergast et al., 1996)

Prendergast and Huiskes

In a biphasic analysis of a tissue differentiation experiment around a spring piston implanted

in the femoral condyles of dogs, it was found that local tissue fluid pressure does not change

as the tissues differentiate (Soballe et al., 1992a; 1992b; Huiskes et al., 1997; Prendergast et al., 1997) It was also found that the stresses on tissues are not only generated by the tissue matrix, but also to a large extent by the drag forces from interstitial fluid flow (Huiskes et al., 1997; Prendergast et al., 1997) This indicated the need for dynamically loaded, biphasic models, because these effects could not be examined with static or linear elastic representations It was concluded that interstitial fluid flow and pressure need to be investigated as potential signalling variables Prendergast et al introduced a model of tissue differentiation based on a biphasic poroelastic finite element model of the tissues, found experimentally at a loaded implant interface (1997) They proposed two biophysical stimuli: solid shear (deviatoric) strain in the solid phase and fluid velocity in the interstitial fluid phase, where high magnitudes of either, favors fibrous tissue, and only when both stimuli are low enough, can ossification occur The spatial and temporal comparison of the fluid velocity and solid shear strain, with tissue type indicated a pattern of increasing tissue stiffness (maturity)

as these mechanical variables decreased in magnitude (Figure 2-11)

Figure 2-11: The tissue differentiation scheme proposed by Prendergast et al (1997) and

Huiskes et al (1997) Mesenchymal stem cells differentiate depending on the magnitudes of fluid velocity and tissue shear strain Reprinted from Lacroix and Prendergast (2002), Copyright (2002), with permission from Elsevier

Based on work by Prendergast et al (1997), Lacroix et al applied the same algorithm to investigate tissue differentiation during fracture healing (Lacroix and Prendergast, 2002; Lacroix et al., 2002) They used a 2D axisymmetric finite element model with a poroelastic material description The dynamic model created by Lacroix was able to simulate direct periosteal bone formation, endochondral ossification in the external callus, stabilisation when bridging of the external callus occurs, and resorption of the external callus (Lacroix et al., 2002) The model was able to predict slower healing with increasing gap size and increased connective tissue production with increased interfragmentary strain These studies introduced some biological representations by prescribing stem cell concentrations initially at the external boundaries and using a diffusive mechanism to collectively simulate migration, proliferation and differentiation of cells Actual tissue differentiation depended on resulting cell concentration and stimulus

This model has later been used for successful predictions of tissue differentiation in a rabbit bone chamber (Geris et al., 2003; 2004), and during osteochondral defect healing (Kelly and Prendergast, 2005)

2.8.4 Models based on biochemical factors

vascularity and growth factors implicitly However, since the isolation and clinical use of growth factors such as TGF-β and BMPs, it has become necessary to incorporate them into models of bone healing for some research questions

Framework by Bailon Plaza and van der Meulen

Bailon-Plaza and van der Meulen (2001) developed a mathematical framework to study the effects of growth factors during fracture healing They used finite difference methods to simulate sequential tissue regulation and cellular events, studying the evolution of chondrocytes and osteoblasts existing in the callus In their model, cell differentiation was

controlled by the presence of osteogenic and chondrogenic growth factors The rate of change

of cell density, matrix density and growth factor concentrations, as well as matrix synthesis and degradation and growth factor diffusion, were included into their model The model was further refined in an attempt to include the influences of the mechanical environment (Bailon-Plaza and van der Meulen, 2003)

This model was recently adopted by Geris et al (2006a) They developed the model further by including key aspects of healing, such as angiogenesis, and comparing the results with experimental data of normal fracture healing (Geris et al., 2006b; Geris, 2007) This study also evaluated the models’ ability to predict certain pathological cases of fracture healing, and took

a first step towards attempts to test therapeutic strategies

2.8.5 Other computational models of tissue differentiation

Recently, the focus has been shifted towards incorporating a more accurate description of cellular processes Two models with different approaches are described below

Models of callus growth

Garcia et al (2006) developed a continuum mathematical model that simulated the process of tissue regulation and callus growth, taking different cellular events into account The model attempts to mimic events such as mesenchymal-cell migration, and mesenchymal stem cell, chondrocyte, fibroblast, and osteoblast proliferation, differentiation and cell death, and matrix synthesis, degradation, tissue damage, calcification and remodeling over time They aimed to analyze the main components that form the matrix of the different tissues, such as collagen types, proteoglycans, mineral and water, and used that composition to determine mechanical properties and permeability of the tissue They chose the second invariant of the deviatoric strain tensor as the stimulus guiding the tissue differentiation process

This model was the first to include tissue growth in adaptive simulation of fracture healing (Garcia-Aznar et al., 2006) Even though the predicted callus geometries in their growth model are not completely physiological, it is able to predict increased callus size for increased interfragmentary movements (Garcia-Aznar et al., 2006), as well as realistic variations when gap size, and fixator stiffness were varied (Gomez-Benito et al., 2005; 2006)

Stochastic cell modelling

Recently, a study by Perez and Prendergast (2006) developed a new model for cell dispersal in the callus A ’random walk’ model was included to represent cell migration both with and without a preferred direction The study simulated an implant-bone interface, using the stochastic cell model and the mechano-regulatory model by Prendergast et al (1997), and compared the results with those using the diffusion model for cell migration (Lacroix et al., 2002) The predictions of both models are similar, although the ‘random walk’ model was able

to predict a more irregular tissue distribution than the diffusion model

2.8.6 Summary of computational models of tissue differentiation

The models proposed and the mechanobiological processes included, discussed in the previous sections, are summarized in Table 2-1

Material description

Biophysical stimuli

Cell modeling

Growth factors

Tissue growth Carter et al., 1988 fracture healing single linear elastic

octahedral shear stress and dilatational stress

Carter and Wong,

1988

joint development single linear elastic

octahedral shear stress and dilatational stress

Blenman et al, 1989 fracture healing single linear elastic

octahedral shear stress and dilatational stress

Carter et al., 1998 fracture healing single linear elastic

principal tensile strain and hydrostatic stress

Loboa et al., 2001 oblique fracture

healing single linear elastic

principal tensile strain and hydrostatic stress

Claes and Heigele,

1999 fracture healing single hyper elastic

principal strain and hydrostatic pressure

Prendergast et al.,

and Huiskes et al.,

1997

implant osseointegration adaptively poroelastic

shear strain and fluid flow

Bailon Plaza and

van der Meulen,

2001

fracture healing adaptively MSC, CC, OB osteogenenic, chondrogenic

Bailon Plaza and

van der Meulen,

2003

fracture healing adaptively linear elastic

deviatoric strain and dilatational strain

MSC, CC, OB

osteogenenic, chondrogenic

Lacroix and

Prendergast, 2002 fracture healing adaptively poroelastic

shear strain and fluid flow

MSC diffusion

Geris et al., 2003 bone chamber adaptively poroelastic shear strain and

fluid flow

MSC diffusion bone chamber adaptively linear elastic

principal strain and hydrostatic pressure

Kelly and

Prendergast, 2005

osteochondral defects adaptively poroelastic

shear strain and fluid flow

MSC diffusion

Shefelbine et al.,

2005

trabecular bone healing adaptively linear elastic

ostahedral shear strain, hydrostatic strain, fuzzy logic

OB

osteogenenic, chondrogenic

Garcia et al., 2006 fracture healing adaptively poroelastic shear strain invariant MSC, FB, CC, OB volume growth

Mechanical Biological Bone

regeneration process

Time point evaluation

Table 2-1: Summary of computational models of tissue differentiation

Over the last two decades, the computational models employed for studies of bone healing have progressed a great deal As described in previous sections, it has gone from single phase linear elastic models which were evaluated at only one time point (Carter et al., 1988; 1998) via hyperelastic (Claes and Heigele, 1999) to poroelastic material descriptions implemented in models that adapt tissue distributions over time (Huiskes et al., 1997; Prendergast et al., 1997) Poroelastic material description is especially important when describing the soft tissues involved in the early stages of healing, and has become the standard Unfortunately, the material properties of these soft tissues are not yet well characterized

Over the last couple of years, the focus has shifted from pure mechanical analyses, towards implementing more mechanobiological aspects, initially only including stem cell concentrations (Lacroix and Prendergast, 2002), as well as solely biological models (Bailon-Plaza and van der Meulen, 2001) including effects of growth factors and directed cell movement The models are becoming more complex as the knowledge about the detailed processes during bone healing increases The work in this thesis contributes to the development in this area Many of the above discussed models and methods are recent developments, and were not available when this thesis work was initiated This development is still progressing focusing on describing cells and their activities (Garcia et al., 2002; Geris, 2007) In this work, a slightly different approach is taken, which is described in Chapter 6-7 of this thesis

3 Comparison of biophysical

stimuli for mechano-regulation

of tissue differentiation during

It was concluded that all the previously published regulation algorithms simulated the course of normal fracture healing correctly, including intramembranous bone formation along the periosteum and callus tip, endochondral ossification within the external callus and cortical gap, and creeping substitution of bone towards the gap from the initial lateral osseous bridge Furthermore, simulation as a function of only deviatoric strain accurately predicted the course of normal fracture healing

mechano-The content of this chapter is based on publication I

Journal of Biomechanics, 2006

3.1 Introduction

Most fractures heal through indirect or secondary healing Indirect fracture healing starts from the injury-induced haematoma, and involves the sequential differentiation from one connective tissue type to another (Chapter 2.2) Cartilage forms within the fracture gap, which

is calcified and replaced by immature bone, which is later remodeled into mature bone This sequence of tissue differentiation is known to be sensitive to the local mechanical environment within the tissue However, the mechano-transduction mechanisms are not well understood

Many scientists have tried to determine the mechanical and biological parameters influencing the process of tissue differentiation, either by using experimental or computational models Experimentally, the ovine tibia model is a common well characterized model often used in fracture healing studies It was shown that the amount of callus formed is related to the interfragmentary movement in the fracture gap (Goodship and Kenwright, 1985; Claes et al., 1995) If the interfragmentary movement is too high, the healing process might be delayed or lead to nonunion (Kenwright and Goodship, 1989) Several mechano-regulation algorithms for investigating the influence of mechanical stimuli on tissue differentiation during fracture healing with finite element analysis (FEA) were proposed They are described in Chapter 2.8

Three mechano-regulation proposals, although different in theory, have shown consistent with the actual tissues formed during fracture healing (Carter et al., 1988; Claes and Heigele, 1999; Prendergast et al., 1997) It has so far been difficult to compare these theories since they were investigated in FE models with different geometrical and material parameters The algorithms

of Carter and Claes both predicted changes in tissue phenotype at specific time points, but their simulations were not continued over the complete healing period Their material properties were linear elastic, whereas those used by Lacroix et al (2002), with the algorithm

by Prendergast et al (1997), were poroelastic Until recently, no studies were performed to compare these mechano-regulation algorithms or to investigate the individual contributions of the stimuli in the mechano-regulation algorithms Two of the algorithms’ ability to predict bone formation inside a rabbit bone chamber was compared (Geris et al., 2003) Although this study introduced both algorithms in one geometrical model, different material descriptions for each algorithm were used The aim of this study was to compare the existing mechano-regulation algorithms with regards to their ability to predict the normal fracture healing processes For this purpose they were implemented in the same computational FEA model Additionally, we studied the hypothesis that tissue differentiation could equally well be regulated by the individual mechanical stimuli, e.g deviatoric strain, pore pressure or fluid velocity alone

3.2 Methods

3.2.1 Finite element model

For the computational model, a mechano-regulatory adaptive, axisymmetric finite element model of an ovine tibia was created The geometry involved a 3 mm transverse fracture gap and an external callus (Figure 3-1) The external surface of the callus, the ends of the cortical