Effects of Different Load Magnitudes on Longitudinal Growth of Immature Bones

IN

DEGREE PROJECT MEDICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2018 ,

Effects of Different Load

Magnitudes on Longitudinal Growth of Immature Bones

Olika belastningsamplituder och deras påverkan på den longitudinella tillväxten av ännu inte

utvecklade ben

EMMA DAHLGREN

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ENGINEERING SCIENCES IN CHEMISTRY,

BIOTECHNOLOGY AND HEALTH

Effects of Different Load Magnitudes on Longitudinal Growth of Immature Bones

Olika belastningsamplituder och deras påverkan på den longitudinella tillväxten

av ännu inte utvecklade ben

Emma Dahlgren

Master of Science in Medical Engineering Advanced Level, 30 credits

Scientific Supervisor: Elena Gutierrez-Farewik Examiner: Mats Nilsson

KTH Royal Institute of Technology

School of Engineering Sciences in Chemistry, Biotechnology and Health

Abstract

In vivo studies of mechanical loading on bone have suggested that load magnitude is one of the parameters that play a vital role in bone adaptation. This study examined how longitudinal growth of immature rat metatarsals is affected by different load magnitudes. The main hypotheses were that the longitudinal growth of immature bone would decrease with increased compressive load magnitude, and that the longitudinal growth would be more decelerated the higher the load mag- nitude. The three middle metatarsal bones in the back paws of 19-20 days old Sprague-Dawley rat fetuses were extracted. Metatarsal bones were loaded with 0.05 N, 0.25 N, 1.25 N and 6.25 N. Loading rate and number of cycles were constant at 0.01 mm/sec and 10 cycles respectively.

Length measurements occurred every 2-3 day. Concluded from the study was that a load magni- tude of 0.05 N resulted in an increased longitudinal growth, compared to unloaded bones. For the other load magnitudes the results were insufficient and inconsistent and therefore nothing could be suggested for them. The problem remained as before and further studies are needed.

Keywords: Growth plate, metatarsal bone, longitudinal growth, load magnitude

Sammanfattning

Studier som gjorts in vivo på ben som belastats mekaniskt har visat att belastningsamplituden har en avgörande roll i hur ben anpassar sig till yttre påfrestningar. Denna studie undersökte hur den longitudinella tillväxten av ännu inte utvecklade metatarsalben hos råttor påverkas av oli- ka belastningsamplituder. Huvudhypoteserna var att den longitudinella tillväxten av omogna ben skulle minska med ökad kompressiv belastningsamlitud, och att den longitudinella tillväxten skulle hämmas med högre belastningsamplitud. De tre mittersta metatarsalbenen i baktassarna på 19-20 dagar gamla Sprague-Dawley-råttfoster togs ut. Metatarsalbenen belastades med 0.05 N, 0.25 N, 1.25 N och 6.25 N. Belastningshastighet och antal cykler var konstanta på 0.01 mm/sek respektive 10 cykler. Längdmätningar utfördes med 2-3 dagars mellanrum. Slutsatsen från studien var att en belastningsamplitud på 0.05 N resulterade i en ökad longitudinell tillväxt, jämfört med obelastade ben. För de andra belastningsamplituderna var resultaten otillräckliga och inkonsekventa och där- för kunde ingen slutsats dras för dem. Problemet kvarstod som tidigare och fortsatta studier krävs.

Keywords: Tillväxtplatta, metatarsalben, longitudinell tillväxt, belastningsamplitud

Acknowledgements

I would first like to thank my main supervisor Elena Gutierrez-Farewik, Professor of Biomechanics at KTH, for providing me with this project and for discussing questions that arose. It has been truly valuable.

I would also like to thank my co-supervisor Farasat Zaman, Ph.D, Assistant Professor at KI, for being an excellent support when I needed; for dissecting, photographing and measuring the bones; for staying late one night at KI when the first experiment took a little longer time than expected; and for always answering my questions.

I would also like to thank Lilly Velentza, Medical Doctor, Trainee in Pediatric Endocrinology Lab at KI, for supporting and providing me with measurement data.

Next, I would like to thank Irene Linares Arregui, at KTH Solid Mechanics, for developing a test method and for coming to KI when I was struggling with the machine.

Finally, I would like to thank my project group students Katya Mehyeddine, Philip Wernstedt

and Mofya Mainda for the social support and for helping each others out.

Contents

1 Introduction 1

2 Materials and Methods 2

2.1 Bone Sample Preparation . . . . 2

2.1.1 Ethical Approval . . . . 2

2.2 Measurement . . . . 2

2.3 Loading . . . . 2

2.3.1 Loading Device . . . . 2

2.3.2 Loading Schedule . . . . 3

2.3.3 First Set of Bones . . . . 4

2.3.4 Second Set of Bones . . . . 5

2.3.5 Third Set of Bones . . . . 5

2.4 Result Analysis . . . . 5

3 Result 6 3.1 First Set of Bones . . . . 6

3.2 Second Set of Bones . . . . 8

3.3 Third Set of Bones . . . . 10

4 Discussion 12 5 Conclusion 15 Appendices 18 A Anatomical Structure of Bone 18 A.1 Topography . . . . 18

A.2 Tissue Composition . . . . 18

A.3 Bone Cells . . . . 19

A.4 Growth Plate . . . . 19

B Bone Growth 20 B.1 Laws of Bone Remodeling . . . . 21

B.2 The Role of Bone Cells . . . . 21

B.3 Bone Deformation . . . . 21

C Mathematical Models 22 C.1 Linear Growth of Bone at Steady State . . . . 22

C.2 Bone Growth Due to Multiaxial Loading . . . . 22

C.2.1 Octahedral Shear Stress, σ _S . . . . 23

C.2.2 Hydrostatic Stress, σ H . . . . 23

C.3 Bone Growth Depending on Material Properties . . . . 23

D Previous Studies 23 D.1 Decrease in Daily Load . . . . 23

D.2 Dynamic Compression . . . . 24

D.3 Load Magnitude . . . . 24

D.3.1 Static vs. Dynamic Loading . . . . 24

D.3.2 Number of Cycles and Load Magnitude . . . . 24

D.3.3 Altered Bone Growth and Applied Load Magnitude . . . . 24

List of Figures

1 Rat metatarsal bone . . . . 2

2 ADMET Materials Testing Machine . . . . 3

3 Ramp wave for load magnitude 0.05 N . . . . 4

4 Ramp wave for load magnitude 6.25 N . . . . 4

5 Length of bones loaded with 0.05 N in first trial . . . . 6

6 Length of bones loaded with 0.25 N in first trial . . . . 6

7 Length of bones loaded with 1.25 N in first trial . . . . 7

8 Length of bones loaded with 6.25 N in first trial . . . . 7

9 Bar plot of mean percentage length in first trial . . . . 8

10 Length of bones loaded with 0.05 N in second trial . . . . 8

11 Length of bones loaded with 0.25 N in second trial . . . . 9

12 Length of bones loaded with 1.25 N in second trial . . . . 9

13 Length of bones loaded with 6.25 N in second trial . . . . 9

14 Bar plot of mean percentage length in second trial . . . . 10

15 Length of bones loaded with 0.05 N in third trial . . . . 10

16 Length of bones loaded with 0.25 N in third trial . . . . 11

17 Bar plot of mean percentage length in third trial . . . . 11

18 Topography of long bone . . . . 18

19 Growth plate with different zones . . . . 20

List of Tables

1 Load magnitudes used . . . . 3

1 Introduction

In a long bone, growth plates are located between the epiphyseal head and the metaphysis at each end of the bone. A growth plate consists of an extracellular matrix containing chondrocytes, which are a type of bone cells [1]. The growth plate is divided into different zones [2], where each zone has different properties and characteristics when it comes to biomechanics and histomorphology [3]. Closest to the diaphysis is the calcifying zone where endochondral ossification takes place, i.e.

bone tissue is created. Osseus tissue is thereby added to the diaphysis and longitudinal growth occurs [2]. In most species, the growth plates disappear when skeletal maturity is reached [1].

Throughout life, bone growth is constantly regulated by different factors such as environment, genetics, hormonal balance and nutrition. When skeletal maturity is reached, the body is normally symmetric and bones are of correct length [4]. The majority of the natural loading comes from muscle forces. These forces have to vary in order for the bone to adapt to the loads [5].

Bone deformation may be caused by bending, compression, torque, tension and shear forces [6].

Some skeletal deformations are suspected to be the result from abnormal mechanical loading during the growth of immature bones. Abnormal loading affects the longitudinal bone growth and may result in different clinical conditions (e.g. Blount’s disease or scoliosis) [7]. These afflictions may worsen during adolescence, where bone growth is rapid. To understand the complex relationship between bone growth and mechanical loadings, further investigation is required [3].

When in vivo studies of mechanical loading on bone have been performed it has been suggested that load magnitude, cycle number and frequency play a vital role in bone adaptation [5]. Robling et al. suggested that suppression of growth in immature rat ulnae is independent of type of load (i.e. static or dynamic), and what is crucial is most truly the peak load magnitude to which the growth suppression varies proportionally [8]. Ménard et al. loaded an in vivo rat tail model with different load magnitudes. Suggested from obtained result was that an increase in load magnitude will result in reduction of longitudinal growth [3]. To which extent the load magnitude affects the growth of immature bone will be further examined in this project.

Mathematical models, trying to describe the growth of bone under certain circumstances, have been developed. For example, multiaxial load and its impact on longitudinal growth is a linear sum of two different stresses:

ε m = I O = a ∗ max σ S + b ∗ min σ H (1)

where ε _m is the mechanical growth rate that can be estimated by the osteogenic index, I _O ; σ _S is the octahedral shear stress (always positive); and σ H is the hydrostatic stress (positive: tension, negative: compression). Constants a and b together determine the mechanical growth rate. No clear definitions of the values of a and b exist, but a ratio of 0.3-1 between them is suggested in order to predict how bone formation will occur [2].

The aim of the study was to examine how growth of immature rat metatarsals is affected by different load magnitudes. From that it was hoped to generate suggestions for values of parameters a and b in the mathematical model (1) above. The main hypotheses were that the longitudinal growth of immature bone will decrease with increased compressive load magnitude, and that the longitudinal growth will be more decelerated the higher the load magnitude.

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2 Materials and Methods

2.1 Bone Sample Preparation

Three female Sprague-Dawley rats, 19-20 days pregnant, were sacrificed by CO ₂ . Immediately after sacrifice, the rats were dissected and fetuses were extracted and after that dissected. The three middle metatarsal bones in the back paws were taken out. Dissection media contained 1xPBS (phosphate-buffered saline) with Fungizone (2.5 µg/ml), penicillin (100 U/ml), and streptomycin (100 µg/ml). After dissection, the bones were transferred to a separate plate with 24 well plates of 0.4 ml/well; one bone placed in each well plate. The well plates were filled with a solution of MEM (minimum essential media) with l-glutamine, supplemented with 0.05 mg/ml ascorbic acid, 1 mM sodium glycerophosphate, 0.2% BSA (bovine serum albumin), 100 U/ml penicillin and 100 µg/ml streptomycin.

The metatarsal bones were cultured in 37 ^◦ C for 9 days in a CO 2 -incubator with 5% CO 2 . Cell culture medium was changed every 2-3 day to maintain the quality.

2.1.1 Ethical Approval

Bones were collected from animals that were sacrificed for other projects, approved by ethical committee at Karolinska Institutet (KI).

2.2 Measurement

To measure the metatarsal bones, digital pictures were taken with Infinity digital camera attached to a Nikon SMZ-U microscope with 1x magnification, see Figure 1. Each metatarsal bone was photographed on day 0, 2, 4 or 5, 7 and 9 of culture. Length was measured by using the Infinity- image analysis system; a built in function of the camera.

Figure 1: Picture of a rat metatarsal bone. The calcified zone (dark) is located in the middle, and the two growth plates (light) constitute the rest of the bone.

2.3 Loading

Loading occurred at three different times. Test equipment and procedure are presented below.

2.3.1 Loading Device

Computer programme used for loading was MTESTQuattro [9]. The settings were transferred to ADMET Materials Testing Machine (see Figure 2) driven by a power transformer and a controller.

Rat metatarsals were put in the part of a pencil that is fixating the lead.

2

Figure 2: ADMET Materials Testing Machine. The part of a pencil fixating the lead, where the bone was placed, is shown in the center of the image.

2.3.2 Loading Schedule

The bones were loaded with the magnitudes in Table 1 below. Wave form used was a ramp (see Figure 3 and 4 for highest and lowest load amplitude respectively). Loading rate was constant at 0.01 mm/sec, and number of cycles was constant at 10 cycles. To decide a constant frequency was not possible as an option on the testing machine, which was why rate of applied load was set as a constant instead. This made sure that the strain rate was the same for all different load magnitudes.

Table 1: Different load magnitudes used and number of bones tested for each magnitude. In the first and second loading occasion, all four magnitudes were tested. In the third loading occasion, only the two lowest magnitudes were tested due to lack of bones.

Magnitude [N] Number of Bones Set I Number of Bones Set II Number of Bones Set III

0 (Controls) 4 4 4

0.05 4 3 3

0.25 4 3 3

1.25 4 3 -

6.25 4 3 -

3

Figure 3: Ramp wave for bones loaded with 0.05 N. Only nine whole cycles are shown in the figure due to noise in the first cycle. Time axis starts when loading starts.

Figure 4: Ramp wave for bones loaded with 6.25 N. Only nine whole cycles are shown in the figure due to noise in the first cycle. Time axis starts when loading starts.

2.3.3 First Set of Bones

First loading occasion was located at Royal Institute of Technology (KTH) Campus. The bones were collected at KI in Solna and then transported in their medium to KTH to perform the loading. All bones were brought, including the controls, to make sure that all parameters except load magnitude were the same for all the bones. One bone at a time was loaded, and immediately put back in the medium. Each bone was placed in the holder with a pincette. The instruments used were disinfected with ethanol to lower the risk of contamination. For each load magnitude, there was an unloaded control bone. The control bone was placed in the lead holder but only exposed to air for the same time as the test bone. After loading, the metatarsal bones were transported back to KI for photographing, measuring and incubation. They were kept outside the incubator for a total of five hours.

Loading occurred on day 0 (the day of dissection) and lengths were measured on day 0 (after loading), 2 and 5. Measurement on day 0 was supposed to be executed before loading, but due to lack of time it was done when the bones arrived back to KI. On day 5 the experiment was closed, due to no response from the bones; they were dead.

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2.3.4 Second Set of Bones

For the second trial, the bones that were used were five days older than in the first experiment.

The testing occurred at KI, and the bones were only out in open air while they were loaded and then directly put back in media and incubator again. Load procedure was the same as in the first load occasion, see section 2.3.3. One bone at a time was loaded, meanwhile the bones that were not loaded were held in medium inside the incubator. For each load magnitude, there was an unloaded control bone.

Loading occurred on day 0 (five days after dissection) and lengths were measured on day 0 (before loading), 2, 4, 7 and 9.

2.3.5 Third Set of Bones

For the third trial, the procedure in section 2.3.4 was repeated. Due to lack of bones, all four magnitudes could not be tested. Based on the result from the loading of the second set of bones, the two lower magnitudes were used. For each load magnitude, there were two unloaded control bones.

Loading occurred on day 0 (five days after dissection) and lengths were measured on day 0 (before loading), 2, 4, 7 and 9.

2.4 Result Analysis

Data from measurements were transferred to Matlab (version R2017a), and analysis were made from line plots and bar plots generated by Matlab code. Mean percentage length of each test group, including control bones, was calculated for every trial. The mean percentage lengths were compared to control group and between test groups.

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3 Result

3.1 First Set of Bones

The first experiment was canceled on day 5, because the bones were dead at that time. The controls had not grown the way they were expected and the loaded bones had stopped growing, which is clearly seen in Figure 5-8 below. Bone 1, 2, 5, 9 and 15 were damaged and are therefore not presented in the figures.

Figure 5: Length of bones loaded with magnitude 0.05 N in first trial. Bone 1 and 2 were damaged and are therefore not presented.

Figure 6: Length of bones loaded with magnitude 0.25 N in first trial. Bone 5 was damaged and is therefore not presented.

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Figure 7: Length of bones loaded with magnitude 1.25 N in first trial. Bone 9 was damaged and is therefore not presented.

Figure 8: Length of bones loaded with magnitude 6.25 N in first trial. Bone 15 was damaged and is therefore not presented.

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Figure 9 below shows a bar plot of mean percentage bone length with standard deviation on day 5.

Figure 9: Bar plot of mean percentage bone length with standard deviation on day 5 in first trial.

3.2 Second Set of Bones

The growth of the second set of bones is presented below in Figure 10-13.

Figure 10: Length of bones loaded with magnitude 0.05 N in second trial.

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Figure 11: Length of bones loaded with magnitude 0.25 N in second trial.

Figure 12: Length of bones loaded with magnitude 1.25 N in second trial.

Figure 13: Length of bones loaded with magnitude 6.25 N in second trial.

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Figure 14 below shows a bar plot of mean percentage bone length with standard deviation on day 9.

Figure 14: Bar plot of mean percentage bone length with standard deviation on day 9 in second trial.

3.3 Third Set of Bones

The growth of the third set of bones is presented below in Figure 15 and 16.

Figure 15: Length of bones loaded with magnitude 0.05 N in third trial.

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Figure 16: Length of bones loaded with magnitude 0.25 N in third trial.

Figure 17 below shows a bar plot of mean percentage bone length with standard deviation on day 9.

Figure 17: Bar plot of mean percentage bone length with standard deviation on day 9 in third trial. The two highest magnitudes were not tested and are therefore not presented.

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4 Discussion

The result from the first trial will be ignored and not discussed. Figure 5-8 show that the growth was leveled out and thus the bones were dead and thereby not responding. Figure 9 shows that the mean lengths for all different magnitudes, including control bones, were similar to the original lengths at 100%. The first trial failed and limitations of the first trial will be discussed in later paragraphs.

The second and third trial generated usable results. Figure 10-13 (second trial) and Figure 15- 16 (third trial) clearly show that the bones were alive and growing. No conclusion about how the bones were affected could be drawn from these figures since the bones were of different lengths from the beginning. Instead, what could be compared was the percentage length on day 9 compared to day 0. Figure 14 (second trial) shows that the groups of the three lower magnitudes (0.05 N, 0.25 N and 1.25 N) had grown more than the control group. The highest magnitude (6.25 N) could not be distinguished from the controls. Figure 17 (third trial) shows that the mean length of the bones for the lowest magnitude (0.05 N) was higher than the mean length of the control bones.

For the second lowest magnitude (0.25 N), the mean length was lower than for the control bones.

In both Figure 14 and 17, the mean length of bones loaded with 0.05 N was higher than the mean length of all the other groups. Since the result for the magnitude of 0.25 N differed between the second and third trial, no conclusion could be drawn for this magnitude. However, observations from Figure 14 and 17 implied that immature bones loaded with 0.05 N responded to the load by growing more longitudinally compared to unloaded bones. Unfortunately, no suggestions could be obtained for the two highest magnitudes (1.25 N and 6.25 N) since they were only tested once and the result was therefore not sufficient. It could yet be speculated about the result; Figure 14 does imply that the mean length of the bones loaded with magnitude 1.25 N was higher than the mean length of the controls, and that the mean length of bones loaded with 6.25 N was not. This raised the question if there is a threshold magnitude in between these magnitudes, where the bones no longer respond to the loading. However, this was only speculation and no valid conclusion.

The generated result contradicted the main hypothesis suggesting that longitudinal bone growth will decrease with increased compressive load magnitude. The bones loaded with 0.05 N were growing more than the control bones. On the other hand, the longitudinal growth seemed to be decreased the higher the applied load, but yet vaguely compared to controls. The hypothesis following the main hypothesis thus agreed with the result; the longitudinal growth seemed to be more decelerated the higher the load magnitude when comparing bones loaded with 0.05 N, 0.25 N and 6.25 N in Figure 14, which was suggested in the hypothesis. As already mentioned, the result was insufficient in order to determine whether this had happened by chance or not, since the two highest magnitudes only were tested once, and the 1.25 N bar was higher than the 0.25 N bar.

The result both contradicted and agreed with previous studies. Ménard et al. suggested that an increase in magnitude will result in reduction of longitudinal growth [3]. Comparing their result to the result of this study, the bones loaded with 0.05 N in this study grew more than unloaded bones, hence contradictory. On the other hand, the bones loaded with 0.05 N grew more than the bones loaded with 0.25 N, hence the results agreed in one way. Robling et al. suggested that inhibition of longitudinal growth is proportional to magnitude of load and that inhibition increases with increased load magnitude [8], which agreed with the result of this study when comparing bones loaded with 0.05 N and 0.25 N respectively. However, the data obtained was too vague to draw a conclusion. The problem remains as before, and further studies are needed.

The facts from previous studies mentioned in the background chapter of this report (see Ap- pendix) is primarily based on studies executed in vivo [3], [8], [6], [10], meaning that animals have been suffering while the experiments were performed. Animal experiments executed in vivo have been one of the most important contributors to biological and biomedical research. In vivo animal

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investigations constitute of both strict ethical considerations and very high economical costs. They are further associated with problems of animal handling [11]. However, the method used in this study possessed the strength of being executed ex vivo. Ex vivo models closely mimics processes that occur in vivo and are therefore powerful tools when investigating bone responses. Important interactions between cell-cell and cell-matrix from the cells’ natural environment are preserved ex vivo, making these techniques advantageous when examining the mechanisms behind bone physiol- ogy and bone diseases. Especially, metatarsal bones can be used for studies of linear bone growth, and to understand the development of bone [12]. Thanks to the remarkable properties of ex vivo biology systems, in vivo and in vitro systems can be replaced in experimental designs. This will both contribute to cost effectiveness and ethically accepted experiments for the sake of animal welfare [11].

Prenatal bones are highly responsive and grow faster than postnatal bones [13], therefore it was assumed to be possible to see an effect of the loading within two days in immature bones of such low age as zero days. Thus, the results obtained from a standardized method may be important and work as a support for further research. The method in this study was strongly dependent on human handling, with no guarantees that it would be repeated identically for each bone. Hence, if the method could work in a systematic way, free from errors and limitations, it may contribute to future studies of the mechanisms behind bone growth.

From the first experiment it was easily concluded that all conditions were wrong. The bones were very sensitive to all other environments that were not similar to their original environment.

Time outside the incubator would most probably affect the outcome of the experiment, since the bones were kept away from their optimal conditions. The longer the time away from optimal conditions, the larger the negative impact on the growth; which was clearly seen in the different results between the first and the two following trials. The bones were recommended not to stay outside of the incubator for more than a maximum of 30 minutes, and in the first experiment they were out for at least five hours. The actual loading was estimated to take less time than it did, and added to that was the time of transportation between KI and KTH and then back to KI again. The time of transportation was known before, and the bones were expected to be in an acceptable condition if they were outside the incubator for two hours. Unfortunately, two hours were exceeded. Furthermore, all three groups in this project tested their bones at the same occasion, which further extended the time. What was also noticed was how fragile the bones of this specific age were. They were easily damaged and thereby unusable due to the difficulty in handling them sensitively. Because of their small size and their stickiness, it was complicated to grab them with the pincette exactly at the calcified zone. The first experiment failed and the learning outcome was seen as a foundation for the next experiment; a few days older, hence less fragile, bones were needed; and the test equipment had to be stationed at KI to remarkably minimize the time out of incubation.

Another problem with this method was the risk of bending. The bone should be aligned with the load rod in order for the load rod to compress the bone. The bending risk was dependent on how the bone was placed and directed in the fixture. These angles were small and hard to see with the naked eye, which means that the final placing of the bone was more or less correct by chance than skill in performance. Along with the bending, the loaded bone was in some cases pushed into the fixture, since there was no natural stop for the bone inside the fixture. Due to this, it was hard do conclude whether the bone or the fixture was loaded in these occasions.

Ethical approval in this specific project, hence for publication, only existed for the metatarsals.

Bigger bones were easier to handle than small bones, and therefore it would be an advantage to use larger long bones instead, i.e. femur, tibia or ulna. Ethical approval for using one of these bones would probably facilitate the performance of the experiment.

The mathematical model (1) presented in the Introduction describes multiaxial loading of the

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bone. One part of the aim of the study was to suggest probable values for constants a and b in the model. The bones in this specific study were loaded on only one axis, hence it was not possible to suggest values for the two constants. Neither it was possible to calculate the octahedral shear stress and the hydrostatic stresses from the loading setup, which is another constraint for the purpose.

Therefore, no suggestions for the constants a and b can be presented in this report.

Preferably, a statistical analysis of the results should be performed. However, it was not relevant for this specific project because of insufficient data. A statistical analysis in this case would therefore not be statistically valid. Number of trials and bones limited the project and the ability to draw a valid conclusion. To be able to either accept or reject the hypothesis, a lot more bones and trials were needed. Furthermore, the number of control bones were few and thus there had to be common control bones for all bone groups, which limited the result analysis even more.

Future research should involve a better developed method for loading of the bones. The method used in this specific project was not optimal for prenatal bones. Since they were suggested to be very responsive to loading, it would be advantageous to develop a test equipment that can easily load them without destroying or bending them, and that there is a natural stop for the bone inside the fixture. Also, exclusion criteria should be stated in advance. For example, bones that are bended when loaded should be rejected. Furthermore, more bones and more loading occasions are needed to obtain a valid result.

For the methodology of this experiment, it should be evaluated in advance how the bones grow in the medium in which they are held without doing anything to them. Thus, it is possible to know what to expect for the control bones after a certain amount of days. Also, it has to be shown that the bones can take the loads and respond to them, before the actual experiment is performed.

What furthermore would be of advantage is to build an experimental design where the bones can be loaded in the medium they are held and thus never be out in open air. This would prevent contamination and make sure that the bones never leave an environment of correct humidity. Such a design could mimic what would happen in vivo, and the outcome will most probably be similar, if not identical, to in vivo experimental results.

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5 Conclusion

Metatarsal bones loaded with 0.05 N grew more than unloaded control bones. For the other load magnitudes (0.25 N, 1.25 N and 6.25 N) the problem remains as before. The method was too weak to draw a conclusion and the result was thus not sufficient to suggest how different compressive load magnitudes will affect the longitudinal growth of immature bones.

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“Deformation regimes of collagen fibrils in cortical bone revealed by in situ morphology and elastic modulus observations under mechanical loading,” Journal of the Mechanical Behavior of Biomedical Materials, vol. 79, no. September 2017, pp. 115–121, 2018.

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State of Art

A Anatomical Structure of Bone

Knowledge of anatomy is of great importance in understanding the function of the bones. It is es- sential in understanding structural and functional modifications caused by abnormal circumstances such as disease [14]. A description of the anatomical structure of the bone, from topography down to cell level, follows below.

A.1 Topography

There are four main topographic parts in long bones. These are the epiphysis, the growth plate (epiphyseal plate), the metaphysis and the diaphysis, see Figure 18. The epiphysis, or epiphyseal head, is the end of a long bone. It is located between the growth plate and the articular cartilage.

The growth plate lies between the epiphysis and the metaphysis, and is the section of the bone where growth occurs in children (described in more detail in section A.4). The metaphysis is the region of the bone between the growth plate and the diaphysis. The diaphysis is also referred to as the bone shaft, i.e. the middle of the long bone [15].

Figure 18: Topography of long bone.

A.2 Tissue Composition

The tissue composition of bone is unique; it possesses mechanical properties whereas it adapts to the loads placed on it. Thanks to these remarkable advantages it has the capability to resist fractures. Bone consists of two different osseus tissues: cortical (compact) bone and trabecular (cancellous or spongy) bone. Together they build up a hierarchical structure contributing to the

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quality of the bone and its mechanical properties. Cortical bone and trabecular bone consist of bundles of fibers of mineralized collagen fibrils [16]. There are remarkable differences between the two types of osseus tissues; cortical bone is solid and trabecular bone contains large spaces [17]. The outer layer of the bone consists of cortical bone. Due to its densely packed structure, the resorption and replacement of cortical bone takes much longer time than that of trabecular bone. As much as 80% of bone consists of cortical bone whereas the last 20% consist of trabecular bone [15]. The porosity (i.e. proportion of total volume not consisting of bone tissue) varies for trabecular bone. The structures of the two tissues result in different mechanical responses [17].

A.3 Bone Cells

There exist several types of bone cells. These are bone-lining cells, osteoblasts, osteocytes and osteoclasts; all cells having different purposes and functions [17], such as bone repair, bone main- tenance and bone adaptation [18]. The bone cells play a significant role in bone remodeling [19], and therefore it is of importance to know what the different cells’ main purposes are.

Bone-lining cells are formed into a thin sheet and cover all bone surfaces. They are in charge of the ion transport between body and bone. Bone-lining cells on the outside of the bone form the layer called the periosteum; as well as on the inside of the bone, where the layer is called endosteum.

Osteoblasts control bone formation [17]. They are responsible for bone matrix synthesizing [18]

(where bone matrix refers to the bone tissue; i.e. the water, the organic material, and the mineral.) Osteocytes are cells within the hard bone [17] and constitute the largest quantity of bone cells.

Osteocytes are sensitive to mechanical stimuli, which make them able to decide whether there is a need for increase or decrease of bone. Osteoclasts destroy and resorb bone [18].

The role of osteoblasts, osteocytes and osteoclasts in the growth of bone is further discussed in section B.2.

A.4 Growth Plate

In long bones the growth plates are located between the epiphyseal head and the metaphysis at both ends of the bones. Long bones (e.g. femur and tibia) contain one growth plate at each end; they can grow longitudinally at two locations. All bone growth is directed away from the proliferative zones (see Figure 19). Small bones (e.g. in hands and feet) contain only one growth plate and therefore grow longer at only one end. The growth plates disappear in most species when skeletal maturity is reached.

A growth plate consists of an extracellular matrix containing a type of bone cells called chon- drocytes. Chondrocytes are organized in columns throughout the growth plate. Size and shape of the chondrocytes change gradually from the epiphyseal end towards the metaphysis; at the epi- physeal end the chondrocytes are smaller and flatter than at the metaphysis where they are larger and rounder [1].

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Figure 19: Growth plate with different zones. Adapted from [25].

The growth plate is divided into four zones: reserve zone, proliferative zone, hypertrophic zone and calcifying zone [2], see Figure 19. Every zone has different properties and characteristics when it comes to biomechanics and histomorphology [3].

The zone closest to the epiphyseal head is the reserve zone containing resting chondrocytes (stem cells) [1]. Below the reserve zone is the proliferative zone, where larger chondrocytes are located.

Proliferative chondrocytes divide and form columns in the longitudinal growth direction [2]. The proliferative zone answers for two out of three main factors for bone growth: the matrix synthesis and cell duplication contributing to bone growth by 35-45% and 10% respectively [3]. Next zone towards the diaphysis is the hypertrophic zone, where the chondrocyte division ceases. Instead, hypertrophic chondrocytes increase in volume; height increase is larger than width increase, thus the chondrocyte enlargement is anisotropic [2]. In the hypertrophic zone, cellular enlargement is one of the main factors contributing to 40-50% of the bone growth [3]. The last zone, closest to the diaphysis, is the calcifying zone. This is where the mineralization on collagen fibrils and matrix calcification take place, i.e. endochondral ossification. Chondrocytes experience apoptosis and bone tissue is secreted on calcified cartilage by osteoblasts, resulting in addition of osseus tissue to the diaphysis – longitudinal growth occurs [2].

B Bone Growth

Similar to the body’s other tissues and organs, bones are also growing to an adult size and undergo remodeling throughout life. Remodeling is the process of removal and replacement of bone tissue.

It serves several purposes such as adaptation to loads and repair of damaged bone [18].

During a lifetime, the bone growth is constantly regulated by different factors such as environ- ment, genetics, hormonal balance and nutrition. When skeletal maturity is reached, the body is normally symmetric and bones are of correct length. Mechanical factors hardly affect the regu- lating factors of the bone growth since the regulating factors are strictly controlling the growth process in order to ensure typical development of the bones [4]. Muscle forces are responsible for the majority of the natural loading. Variations in these forces are required in order for the bone to adapt to the loading. Adaptation may be local, which is for example shown in the tennis player’s playing arm. When studying mechanical loading of bone in vivo it has been suggested that load magnitude, cycle number and frequency play a vital role in the bone adaptation [5].

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To which extent the different loading parameters affect the bone growth is to be further inves- tigated in this specific study. Especially the role of load magnitude is to be examined.

B.1 Laws of Bone Remodeling

The remodeling process is regulated by Wolff’s law which is based on how bone responds to applied mechanical loadings. Wolff’s law states that the bone will adapt to the load under which it is placed;

if the loading on the bone increases, the bone remodels in order to resist the specific loading and thereby it becomes stronger and vice versa. The process of bone remodeling is thus sensitive to the mechanical loadings in its environment [20].

Mechanical influence on longitudinal growth of bone can be described by the Hueter-Volkmann law. Especially, it describes the growth of immature bone [21]; it proposes that the longitudinal bone growth is retarded when compressive loading is increased and accelerated when compressive loading is decreased. Both loadings compared to normal values [3], [22].

The two laws are describing complex mechanisms which still are not fully understood [23].

B.2 The Role of Bone Cells

Osteocytes are bone cells which play a significant role in bone remodeling. They stimulate bone formation when exposed to mechanical stimuli, but they also stimulate bone degradation when there is a lack of these stimuli. How osteocytes are able to sense mechanical stimuli is still being investigated. What is known today is only a fraction of the total. Bone consists of over 90% of osteocytes, which thus makes them most likely of being the cells sensing stimuli from mechanical forces. Osteocytes are embedded within the bone matrix and build up a large network of direct contact between cells, giving rise to a possibility of fast signal transduction. Compared to the other bone cells, osteocytes are highly sensitive to mechanical stimuli. Triggering of osteocytes make them produce a large amount of signaling molecules, which theoretically make them qualified of arranging bone adaptation when a mechanical stimulus is applied. Further, osteocytes are vital conciliators in the bone resorption by the osteoclasts. The activity of the osteoclasts are stimulated by the osteocytes when continuous mechanical loading is abscent, which has been validated in studies in vitro [19].

The remodeling of bone is a coordinated action between osteoclasts and osteoblasts. They are structured in basic multicellular units where osteoclasts have the bone-resorbing role and osteoblasts have the bone-forming role. Micro-damage leading to fatigue is removed thanks to the bone cells’ continuous remodeling. Adjustment of bone mass and structure is an always on going process where the net result either leads to stronger or weaker bones due to bone mass gain or loss respectively [19]. The growth rate of bone longitudinally is depending on cell parameters in the different growth plate zones, whereas the growth plate height is corresponding to growth rate.

Cells in the proliferative zone contribute to growth according to in which rate cell division occurs.

In the hypertrophic zone, the growth rate is dependent on how rapid the cell enlargement is and the rate at which matrix synthesizing and degrading occur [10].

B.3 Bone Deformation

Bone deformation is defined by strain, which is the fraction between change in length and original length. The deformation is caused by bending, compression, torque, tension and shear forces.

Triggering of bone response may be affected by different characteristics of strain; such as strain magnitude, frequency and strain rate [6].

Bones consist of both large and small interconnected pores filled with fluid. The permeability of the small pores is low; several orders lower than the permeability of the large pores. This will

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cause strains that put pressure on the interstitial fluid around the osteocytes when mechanical load is applied in a fast manner. The strains will lead to fluid flow giving rise to a hydraulic pressure.

In vivo studies have shown that the osteocytes experience a pressure magnitude of up to 5 MPa.

The fluid shear stress is caused by a release of nitric oxide (NO) when stimulated mechanically, and the rate at which the shear stress is applied correlates linearly to the amount of released NO.

Since applied stimulus rate is the product of load magnitude and frequency, it can be concluded that a stimulus of high frequency and low magnitude is as likely as a stimulus of low frequency and high magnitude to cause a reaction of the bone cells; if the mechanical stimulus is applied fast enough, even a very small one can induce a cellular response [19].

Some skeletal deformations are suspected to be the result from abnormal mechanical loading during the growth of immature bones. The abnormal loading affects the longitudinal bone growth and are expressed in clinical conditions such as Blount’s disease (tibia vara), scoliosis [7], kyphosis and other deformities. During adolescence, where bone growth is rapid, these afflictions may worsen. On the other hand, the deformities can be stalled (or even corrected) by mechanical growth modulation where growing bones are put under specific loads. Today, treatment devices based on these modulations in order to correct skeletal deformities are desired to be designed.

To completely understand relationships between bone growth and mechanical loadings, and thus contribute to the development of treatment devices, further investigation is required [3].

C Mathematical Models

Mathematical models are valuable when predicting bone growth. The ones that exist today are simplified to different extent and are based on different parameters [2].

C.1 Linear Growth of Bone at Steady State

Linear growth of bone at a steady state can be described mathematically by Growth = N ∗ h max

where Growth is the 24 hour growth in µm; N is the number of new chondrocytes per day in the proliferative zone; and h _max is average height in µm in the hypertrophic zone.

The above model is simplified, and takes into account the increase in bone length in growth direction when a compressive force is applied. Several assumptions exist behind this model in order to simplify it to this extent. Assumed is that no matrix space exists between the chondrocytes and that all new cells differentiate to mature chondrocytes [7].

C.2 Bone Growth Due to Multiaxial Loading

Multiaxial load and its impact on longitudinal growth is a linear sum of two different stresses. It can be described by

ε m = I O = a ∗ max σ S + b ∗ min σ H

where ε m is the mechanical growth rate that can be estimated by the osteogenic index, I O ; σ S is the octahedral shear stress (always positive); and σ _H is the hydrostatic stress (positive: tension, negative: compression). Constants a and b together determine the mechanical growth rate.

There are no clear definitions of the values of a and b rather than a suggested ratio between them. The ratio is said to lie between 0.3 and 1 in order to predict how bone formation will occur.

The model is based on the theory that periodic hydrostatic compressive stress impedes growth and periodic octahedral shear stress accelerates growth; positive stresses promote growth and negative stresses inhibit growth [2].

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Hopefully, this study on how load magnitudes affect the bone growth according to this model will help to generate suggestions for values of parameters a and b.

C.2.1 Octahedral Shear Stress, σ S

The octahedral shear stress is defined as σ S = ^{√ 1}

3 [(σ 1 − σ m ) ² + (σ 2 − σ m ) ² + (σ 3 − σ m ) ² ] ^1/2 where σ ₁ , σ ₂ , σ ₃ are the principal stresses and σ _m is the mean stress [24].

C.2.2 Hydrostatic Stress, σ H

The hydrostatic stress is defined as

σ _H = ^σ

^+σ ₃

^+σ

where σ 1 , σ 2 , σ 3 are the principal stresses [24].

C.3 Bone Growth Depending on Material Properties

The osteogenic index might differ depending on whether the material is linear elastic or poroelastic.

When a poroelastic material is exposed to an external load, the fluid filled pores in the material matrix will change in volume due to increased pressure. The pressure change gives rise to a flow of fluid through the matrix. Taking this in account, the following mechanobiological model can describe the stage of bone formation:

f _S = ^γ _a + ^ϑ _b

where f S is the stimulus factor; γ is the octahedral shear strain; ϑ is the fluid flow velocity; and a and b are empirically derived constants depending on tissue type [2].

D Previous Studies

Relevant for this specific project are previous studies focusing on bone growth, especially bone deformation, when external loads are applied. Furthermore, load magnitude and the effects that come with it are of interest. As for the experimental setup, i.e. loading schedule and choice of load magnitude(s), previous studies will give ideas of how this specific study will be performed.

D.1 Decrease in Daily Load

Hichijo et al. studied how the mandibular bone in male rats reacted to a decrease in daily load.

The rats were immature at arrival and thus still growing. They were randomly separated into different groups of hard (ordinary pellet) diet and soft (powder) diet. Both diets having the same constituents. Food consistency was decreased for thirteen weeks followed by an investigation of the mandibular bone. The hard-diet group had overall larger mandible than the soft-diet group at the end of the experiment. Suggested from the test results was that a decrease in continuous loading will lead to significant changes in bone characteristics. Also, when food consistency is decreased the closer activity of the jaw becomes weaker, meaning that the soft-diet seems to lead to a lower muscle activity [5].

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D.2 Dynamic Compression

Ménard et al. investigated how dynamic compression parameters affected the growth rate of bone and the histomorphometry of the growth plate. The hypothesis was that average compressive stress is the controlling factor of growth modulation. Secondly, they also hypothesized that frequency was responsible for more of the effects than magnitude on bone growth. To accomplish this an in vivo rat tail model was used and three similar time-averaged dynamic compression stresses were tested.

The magnitude and frequency were varied. The conclusions from the study suggested that either an increase in magnitude or frequency will result in reduction in growth, while histomorphometry will remain the same. Furthermore, an increment in both magnitude and frequency seems to lead to drastic consequences in the growth plate [3].

D.3 Load Magnitude

Load magnitude has been studied in different ways, with different experimental setup and circum- stances.

D.3.1 Static vs. Dynamic Loading

Robling et al. investigated in a deeper manner the already known fact that mechanical stimuli has an impact on bone growth. Three groups of immature male rat ulnae were exposed to different load magnitudes. The first group received a static loading at 17 N, the second group received a static loading at 8.5 N and the third group received a dynamic loading at 17 N. All loading occasions lasted for 10 minutes. In the groups where the ulnae was loaded with 17 N (both static and dynamic) the length was 4% shorter compared to the ulnae in the contralateral control group.

For the 8.5 N static group the same number was 2%. In the loaded ulnae the hypertrophic zones in distal growth plates became thicker. In the proximal growth plates there were no significant changes. Suggested from the result was that suppression of growth is independent of type of load (i.e. static or dynamic). What is crucial for growth suppression is most truly the peak load magnitude, to which the growth suppression varies proportionally. Inhibition of longitudinal growth is furthermore proposed to be proportional to the magnitude of the load and not the average load [8].

D.3.2 Number of Cycles and Load Magnitude

Cullen et al. tested how number of cycles and load magnitude affected bone response to external loading. Loadings were put on mature rat tibia with a constant frequency of 2 Hz and variation in the other parameters (i.e. number of cycles and magnitude). Applied external force were either a sinusoidal of 25 or 30 N for 3 days/week for 3 weeks. The study suggested that mechanical loading increases bone response when either number of cycles or load magnitude increases [6].

D.3.3 Altered Bone Growth and Applied Load Magnitude

Stokes et al. studied the relationship between altered bone growth and applied load magnitudes. In three different species of immature animals of two different ages, growth plates in caudal vertebra and proximal tibia were exposed to three different stress levels. Stress and percentage growth (according to controls) seemed to be linearly dependent. Growth was accelerated by distraction and decelerated by compression. For the different growth plates, the sensitivity to stress varied.

Differences between species were small, but differences between the two different anatomical growth plates were more remarkable. Stokes et al. suggested that the results, to a specific stress level, could be generalized to human growth plates as well [10].

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