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14.5: Bone Growth, Remodeling, and Repair - Biology


Break a Leg

Did you ever break a leg or other bone, like the man looking longingly at the water in this swimming pool? Having a broken bone can really restrict your activity. Bones are very hard, but they will break, or fracture if enough force is applied to them. Fortunately, bones are highly active organs that can repair themselves if they break. Bones can also remodel themselves and grow. You’ll learn how bones can do all of these things in this concept.

Bone Growth

Early in the development of a human fetus, the skeleton is made almost entirely of cartilage. The relatively soft cartilage gradually turns into hard bone through ossification. Ossification is a process in which bone tissue is created from cartilage. The steps in which bones of the skeleton form from cartilage are illustrated in Figure (PageIndex{2}). The steps include the following:

  1. Cartilage “model” of bone forms; this model continues to grow as ossification takes place.
  2. Ossification begins at a primary ossification center in the middle of the bone.
  3. Ossification then starts to occur at secondary ossification centers at the ends of the bone.
  4. The medullary cavity forms and will contain red bone marrow.
  5. Areas of ossification meet at epiphyseal plates, and articular cartilage forms. Bone growth ends.

Primary and Secondary Ossification Centers

When bone forms from cartilage, ossification begins with a point in the cartilage called the primary ossification center. This generally appears during fetal development, although a few short bones begin their primary ossification after birth. Ossification occurs toward both ends of the bone from the primary ossification center, and it eventually forms the shaft of the bone in the case of long bones.

Secondary ossification centers form after birth. Ossification from secondary centers eventually forms the ends of the bones. The shaft and ends of the bone are separated by a growing zone of cartilage until the individual reaches skeletal maturity.

Skeletal Maturity

Throughout childhood, the cartilage remaining in the skeleton keeps growing and allows for bones to grow in size. However, once all of the cartilage has been replaced by bone and fusion has taken place at epiphyseal plates, bones can no longer keep growing in length. This is the point at which skeletal maturity has been reached. It generally takes place by age 18 to 25.

The use of anabolic steroids by teens can speed up the process of skeletal maturity, resulting in a shorter period of cartilage growth before fusion takes place. This means that teens who use steroids are likely to end up shorter as adults than they would otherwise have been.

Bone Remodeling

Even after skeletal maturity has been attained, bone is constantly being resorbed and replaced with new bone in a process known as bone remodeling. In this lifelong process, mature bone tissue is continually turned over, with about 10 percent of the skeletal mass of an adult being remodeled each year. Bone remodeling is carried out through the work of osteoclasts, which are bone cells that resorb bone and dissolve its minerals; and osteoblasts, which are bone cells that make the new bone matrix.

Bones remodeling serves several functions. It shapes the bones of the skeleton as a child grows, and it repairs tiny flaws in the bone that result from everyday movements. Remodeling also makes bones thicker at points where muscles place the most stress on them. In addition, remodeling helps regulate mineral homeostasis because it either releases minerals from bones into the blood or absorbs minerals from the blood into bones. The figure below shows how osteoclasts in bones are involved in calcium regulation.

The action of osteoblasts and osteoclasts in bone remodeling and calcium homeostasis is controlled by a number of enzymes, hormones, and other substances that either promote or inhibit the activity of the cells. In this way, these substances control the rate at which bone is made, destroyed, and changed in shape. For example, the rate at which osteoclasts resorb bone and release calcium into the blood is promoted by parathyroid hormone (PTH) and inhibited by calcitonin, which is produced by the thyroid gland (Figure (PageIndex{3})). The rate at which osteoblasts create new bone is stimulated by growth hormone, which is produced by the anterior lobe of the pituitary gland. Thyroid hormone and sex hormones (estrogens and androgens) also stimulate osteoblasts to create new bone.

Bone Repair

Bone repair, or healing, is the process in which a bone repairs itself following a bone fracture. You can see an X-ray of bone fracture in Figure (PageIndex{4}). In this fracture, the humerus in the upper arm has been completely broken through its shaft. Before this fracture heals, a physician must push the displaced bone parts back into their correct positions. Then the bone must be stabilized — for example, with a cast and/or pins surgically inserted into the bone — until the bone’s natural healing process is completed. This process may take several weeks.

The process of bone repair is mainly determined by the periosteum, which is the connective tissue membrane covering the bone. The periosteum is the primary source of precursor cells that develop into osteoblasts, which are essential to the healing process. Bones heal as osteoblasts form new bone tissue.

Although bone repair is a natural physiological process, it may be promoted or inhibited by several factors. For example, fracture repair is likely to be more successful with adequate nutrient intake. Age, bone type, drug therapy, and pre-existing bone disease are additional factors that may affect healing. Bones that are weakened by diseases, such as osteoporosis or bone cancer, are not only likely to heal more slowly but are also more likely to fracture in the first place.

Feature: Myth vs. Reality

Bone fractures are fairly common, and there are many myths about them. Knowing the facts is important because fractures generally require emergency medical treatment.

Myth: A bone fracture is a milder injury than a broken bone.

Reality: A bone fracture is the same thing as a broken bone.

Myth: If you still have a full range of motion in a limb, then it must not be fractured.

Reality: Even if a bone is fractured, the muscles and tendons attached to it may still be able to move the bone normally. This is especially likely if the bone is cracked but not broken into two pieces. Even if a bone is broken all the way through, the range of motion may not be much affected if the bones on either side of the fracture remain properly aligned.

Myth: A fracture always produces a bruise.

Reality: Many but not all fractures produce a bruise. If a fracture does produce a bruise, it may take several hours or even a day or more for the bruise to appear.

Myth: Fractures are so painful that you will immediately know if you break a bone.

Reality: Ligament sprains and muscle strains are also very painful, sometimes more painful than fractures. Additionally, every person has a different pain tolerance. People with high pain tolerance may continue using a broken bone in spite of the pain.

Myth: You can tell when a bone is fractured because there will be very localized pain over the break.

Reality: A broken bone is often accompanied by injuries to surrounding muscles or ligaments. As a result, the pain may extend far beyond the location of the fracture. The pain may be greater directly over the fracture, but the intensity of the pain may make it difficult to pinpoint exactly where the pain originates.

Review

  1. Outline how bone develops from early in the fetal stage through the age of skeletal maturity.
  2. Describe the process of bone remodeling. When does it occur?
  3. What purposes does bone remodeling serve?
  4. Define bone repair. How long does this process take?
  5. Explain how bone repair occurs.
  6. Identify factors that may affect bone repair.
  7. Parts of bone that have not yet become ossified are made of _________.
  8. If there is a large region between the primary and secondary ossification centers in a bone, is the person young or old? Explain your answer.
  9. The region where the primary and secondary ossification centers meet is called the ________________.
  10. True or False. Most bones are made entirely of cartilage at birth.
  11. True or False. A broken bone is the same as a bone fracture.
  12. If bones can repair themselves, why are casts and pins sometimes needed?
  13. Which bone cell type causes the release of calcium to the bloodstream when calcium levels are low?
  14. Which tissue and bone cell type are mainly involved in bone repair after a fracture?
  15. Describe one way in which hormones are involved in bone remodeling.

Osteogenesis and bone remodeling: A focus on growth factors and bioactive peptides

Javad Behravan, School of Pharmacy, University of Waterloo, Waterloo, ON, Canada.

Biotechnology Research Center, Pharmaceutical Technology Institute, Mashhad University of Medical, Mashhad, Iran

Food and Drug Administration, Mashhad University of Medical Sciences, Mashhad, Iran

Biotechnology Research Center, Pharmaceutical Technology Institute, Mashhad University of Medical, Mashhad, Iran

School of Pharmacy, University of Waterloo, Waterloo, Ontario, Canada

Javad Behravan, School of Pharmacy, University of Waterloo, Waterloo, ON, Canada.

Abstract

Bone is one of the most frequently transplanted tissues. The bone structure and its physiological function and stem cells biology were known to be closely related to each other for many years. Bone is considered a home to the well-known systems of postnatal mesenchymal stem cells (MSCs). These bone resident MSCs provide a range of growth factors (GF) and cytokines to support cell growth following injury. These GFs include a group of proteins and peptides produced by different cells which are regulators of important cell functions such as division, migration, and differentiation. GF signaling controls the formation and development of the MSCs condensation and plays a critical role in regulating osteogenesis, chondrogenesis, and bone/mineral homeostasis. Thus, a combination of both MSCs and GFs receives high expectations in regenerative medicine, particularly in bone repair applications. It is known that the delivery of exogenous GFs to the non-union bone fracture site remarkably improves healing results. Here we present updated information on bone tissue engineering with a specific focus on GF characteristics and their application in cellular functions and tissue healing. Moreover, the interrelation of GFs with the damaged bone microenvironment and their mechanistic functions are discussed.


Introduction

The process of cell differentiation is a widely studied phenomenon which is the basis for all developmental processes. The basic underlying principle of how cell differentiation proceeds is that with each step of the differentiation pathway, cells become programmed to follow a certain specified lineage progression until they are terminally differentiated with an end point of apoptosis or cell death. 1,2,3 Recently, however, many studies have introduced the idea of transdifferentiation, the differentiation of cells (terminally differentiated or not) to a cell type that does not follow the normal, preprogrammed differentiation mechanism. Transdifferentiation refers to a process where one mature cell switches its phenotype and function to that of another mature differentiated cell type. 4,5,6,7,8 This process occurs via two main mechanisms. The first is via direct transdifferentiation of one tissue type to another without undergoing an intermediate pluripotent state or becoming a progenitor cell, which will be denoted as direct transdifferentiation. The second major method occurs via an intermediate step, often manifested by a dedifferentiation and redifferentiation. This mechanism will be denoted as intermediate transdifferentiation.

Cell transdifferentiation has been described in the literature in multiple tissue types and model organisms, and is therefore neither a species- nor tissue-specific phenomenon. There are now many examples of this phenomenon, but for this review, we will only use a small representative population. In the Drosophila intestine, Takashima et al. have shown that ectodermally derived hindgut cells migrate anteriorly to the midgut to form epithelial cells of the endodermally derived midgut, becoming indistinguishable from the surrounding epithelial cells. 9 In zebrafish, during normal myocardial regeneration, Zhang et al. observed that a population of atrial cardiomyocytes can migrate to the ventricle and repair it by direct atrial-to-ventricular transdifferentiation and that this mechanism is regulated by notch signaling. 10 Not surprisingly, tissue regeneration in amphibians and reptiles can also use transdifferentiation mechanisms. Xenopus eye lenses, when removed, can regenerate as the result of transdifferentiation of corneal epithelium to lens cells. 11 Further studies have shown that upregulation of BMP and WNT 12 as well as matrix metalloproteases 13 are required for this direct transdifferentiation.

Furthermore, there are examples of chondrogenic tissues transdifferentiating into cell types of different origins and vice versa. Atherosclerotic lesions in mice have presented what seems to be the transdifferentiation of vascular smooth muscle to chondrogenic tissue. This was confirmed by the reduced expression of α-smooth muscle actin and the increased expression of SOX-9, a marker for immature chondrocytes, in the calcified lesions, 14 as well as a different study that documented this event to occur via increased expression of tissue non-specific alkaline phosphatase and BMP-2 activation. 15 In a reversal of roles, rat chondrocytes have been shown, when stimulated by neurogenic growth factors (FGF-2, Neurobasal-A, EGF, and IGF-1), to transdifferentiate into stellate neuronal cells with ablation of COL2 expression and expression of neuron-specific proteins such as NF-200, MAP-2, and β-III tubulin. 16 Another case of osteogenic transdifferentiation involves the dedifferentiation of myoblasts via BMP-2 induction of SMAD1, which is mediated by osteoactivin. Osteoactivin, in turn, downregulates myogenic markers and upregulates osteogenic markers, such as RUNX2 and ALP. 8,17,18,19,20 Finally, human gingivial fibroblasts have been shown, both in vitro and in vivo to transdifferentiate to osteoblastic lineage cells when treated with 5-aza-2′-deoxycytidine followed by subsequent treatment with BMP2. This was confirmed in vitro by upregulation of Runx2 and Alp expression and in vivo subcutaneous transplantation into mouse, which resulted in increased bone mineral content and bone volume/tissue volume. 21 The issue of whether the transdifferentiation observed in some of these in vitro studies can be attributed to the resident mesenchymal stem cells present in the cultures used remains to be examined.

Beyond these examples, it is important to note that any process of developing induced pluripotent stem cells from somatic cells is a form of intermediate transdifferentiation. For example, in the famous study by Takahashi and Yamanaka, mouse embryonic fibroblasts were transduced to express what are now known as the Yamanaka factors (Oct3/4, Sox2, c-Myc, Klf4) to induce a pluripotent cell intermediate. These cells were then able to form teratomas in cell culture settings and when introduced into an undifferentiated blastocyst, were able to follow normal differentiation programming indistinguishable from the natural pluripotent stem cells. 22 Transdifferentiation is, therefore, not limited to artificial cell culture settings, but a natural phenomenon.

While there are many examples of transdifferentiation in the literature, this review will focus mainly on recent examples of transdifferentiation relating to the transformation of chondrogenic tissue into osteogenic tissue and the underlying mechanisms.


As soon as one of your bones break, your body springs into action to fix the injury. The time it takes for a bone to heal depends on a lot of things, such as the person's age and location of the break.

Within a couple hours, a blood clot forms around the break. Inside the blood clot, special cells called phagocytes begin cleaning bone fragments and killing any germs which might have gotten in around the break. Phagocytes are part of the immune system. The word phagocyte means 'cells that eat' in Greek, so these cells are named after the way they surround and destroy unwanted bacteria and material.

Next, a soft callus made mostly of collagen is created around the fracture by another special group of cells called chondroblasts. This stage can last anywhere from 4 days to 3 weeks.

A hard callus forms next as osteoblast cells create new bone, adding minerals to make it hard. This stage typically begins 2 weeks after the break, and ends somewhere between the 6th and 12th week.

Lastly, the bone is remodeled. Special cells called osteoclasts break down extra bone around the fracture until it's completely healed and returned to its original shape. Bone remodeling is a very slow process which can take anywhere from 3 to 9 years to complete!


Models

The role of molecular signaling in bone remodeling

To date, a considerable number of signals involved in BMU operation have been identified in the literature [10, 14, 20, 21]. Osteocytes are key players in the regulation of bone. They produce many signaling molecules including sclerostin, a secreted glycoprotein that inhibits both osteoblast activation and osteoclast recruitment [10, 22]. This inhibitory effect prevents the activation of BMUs in regions where bone remodeling is not needed. In a given area, the inhibitory effect of sclerostin is significantly depleted only if an appropriate number of osteocytes undergo apoptosis due, for instance, to microfractures. Decreased sclerostin levels invoke the activation of a BMU and the subsequent initiation of a bone remodeling event.

On the other hand, a set of signals known under the generic name of Bone Morphogenetic Proteins (BMPs) have also been shown to play a key role during the early stages of bone remodeling. Some members of this family, such as TGF-β and TGF-α, are known to foster the differentiation of mesenchymal stem cells to osteoblasts [23, 24]. TGF-β can also induce migration of osteoblasts to the sites of bone formation during remodeling [25, 26] and inhibit osteoblast apoptosis [5]. TGF-β is mainly produced by osteocytes [22, 27], but it is also present in the bone matrix [23] and in platelets [28]. This latter factor, together with other signals such as HMGB-1 [29] provides a link with inflammatory processes occurring in early stages of large fractures repair. Cytokines such as IGF-1, released from bone matrix, seem to play a similar role in activating osteoblast differentiation [30] and are necessary for their survival in vitro [31].

The next stage in the process of bone remodeling consists in the recruitment of osteoclasts. The main signals involved in this step are M-CSF and RANKL [21, 32, 33]. They promote the differentiation of osteoclast precursors and the survival of activated osteoclasts. Since RANKL is mostly produced by activated osteoblasts [10, 32], osteoclasts will only be recruited to sites were bone remodeling has already been triggered. Sclerostin both inhibits osteoblast activation and induces apoptosis of active osteoclasts [10, 22]. It may thus act as a signal to stop bone resorption when the cutting edge has reached the required depth in each remodeling event. Moreover, osteoid matrix production by active osteoblasts, as well as differentiation of osteoblasts into osteocytes seem to be cell-density dependent [34], and have been suggested to be mediated by connexin, a molecule that circulates through gap junction communications between osteoblasts, as well as by sclerostin [20, 35]. Finally, various chemoattractants/chemorepulsors that drive osteoclasts away from the region where their precursors are recruited have been described in the literature (see for instance [36]). We shall use one such generic signal as part of our algorithm below.

Concerning signaling effects, one must bear in mind that: i) different signals can have redundant effects for example both TGF-β and IGF-1 induce osteoblast differentiation [37], ii) a given signal can have different effects on different cell types. For instance TGF-β, FGF and PDGF activate osteoblast and inhibit osteoclast action [28] whereas G-CSF is known to induce apoptosis and inhibit differentiation in osteoblasts [33], and iii) signals are not always provided by chemicals. In this context we have already remarked that osteocytes act as sensors responsive to changes in mechanical stress of bone [38, 39].

The preceding list of molecular mediators and their effects on BMU cell types is presented in Table 1 below as a concise summary of a more complex scenario. A limited knowledge of the identity of such mediators or describing their effects in qualitative terms is not enough to explain BMU operation during bone remodeling. In order to understand how a coherent collective plan of action emerges at a multicellular scale, quantitative aspects of the process need to be taken into account. Indeed, for any given set of signals involved, the amount of bone to be resorbed and produced in different remodeling events can be highly variable [10]. This implies in turn that the number and activity of cells recruited in a BMU should change to suit the needs of each particular remodeling process [27, 28, 40, 41].

Abbreviations for cell types are as follows. OCY: Osteocytes, aOCY: apoptotic osteocytes, OBL: osteoblasts, OBA: activated osteoblasts, OCL: osteoclasts. Each entry in a row contains (from left to right) the name of one (or several) signals, its main source, and its effect on the cell types sequentially listed. For instance, the third line in the table asserts that sclerostin is produced by Osteocytes, prevents Osteoclasts recruitment and inhibits proliferation and differentiation and induces apoptosis in both Osteoblasts and activated Osteoblasts.

Signal integration by individual cells. Inhibitory proteins

We now formulate our basic modeling assumptions, which can be summarized as follows. Cells within a BMU integrate signals from their immediate surroundings and the outcome determines a very limited set of actions, namely differentiation, cell division, migration and/or apoptosis. In addition, we propose that inhibitory proteins that impede the progression of these actions within each cell type, mediate cell decisions in any bone-remodeling event.

To clarify this last assumption, it is worth recalling the well-known behavior of two inhibitory proteins, Rb and Bcl-2. The retinoblastoma protein (Rb) arrests progression into the cell cycle, whereas the B-cell lymphome-2 protein (Bcl-2) precludes the initiation of the apoptosis program in most cell types, including osteocytes and other stromal cells [38]. More precisely, Rb binds to transcription factors of the E2F family, preventing the progression of the cell cycle to the synthesis stage [42]. When the amount of active Rb falls below a critical threshold, a point of no-return is reached (the Restriction Point of the cell cycle) that irreversibly leads to cell division. Analogously, Bcl-2 precludes the release of cytochrome c through the mitochondrial outer membrane, thus avoiding the initiation of the apoptosis program. If Bcl-2 is depleted beneath a suitable level, its inhibitory action is lost and the cell is committed to death [28, 43]. Hence a competition between inhibitory molecules results in a mechanism of cell fate control: the first of these inhibitors (Rb or Bcl-2) that falls below its corresponding threshold value determines the decision of the cell between dividing or dying and, importantly, the timing of this decision (see Fig 2A). This mechanism also provides an explicit link between external signals and cell decisions, since membrane receptors are known to modulate the evolution of inhibitory molecules within the cell [43]. As a matter of fact, it has been recently shown that the interplay between receptor/signal interaction and the internal dynamics of Rb and Bcl-2 suffices to explain the onset of emergent population properties (as clonal expansion and contraction) in the case of immune response to acute infections [44], see also Fig 2.

A) Inhibitory proteins Rb and Bcl-2 provide a fate decision mechanism in several cell types. The first of these molecules to reach its critical threshold determines if the cell will divide or undergo apoptosis. For convenience all inhibitory thresholds are set equal to zero. B) The presence of inhibitors blocking alternative differentiation programs allows an increase in the complexity of this cell fate-decision mechanism. B Left) If differentiation is assumed to be blocked by Inhibitor 1, and this inhibitor vanishes before Rb and Bcl-2 do, then the cell will not divide or die, but will instead undergo the differentiation program 1. B Right) Two alternative differentiation programs can be controlled by two different inhibitors (1 and 2). If one of them (inhibitor 2 in this case) disappears faster than the remaining molecules, the corresponding differentiation program is selected.

In our case, the occurrence of inhibitory proteins controlling cellular processes during bone remodeling is well documented in the literature. For instance, the roles of Rb, Bcl-2 and the transcription factor Runx2 have been described in [45–47] respectively. Moreover, different restriction points are known to occur for the various cell commitment alternatives involved in bone remodeling. In particular, the onset of two restriction points in the differentiation program of osteoblasts (marking respectively the transition to activated osteoblast and osteocyte types) has been pointed out in [28].

The increased complexity derived from the presence of more than one cell type, together with the existence of several cell fates (division, apoptosis or alternative differentiation programs) introduces new possibilities with respect to the basic dichotomy between cell division vs. cell death [44]. However, the underlying logic can be extended to account for these new alternatives. For instance, several inhibitory molecules can simultaneously block the progression of alternative differentiation programs. In this case, the first inhibitor to reach its critical threshold will determine the fate of the cell (see Fig 2B). We propose that cell choices thus determined are mutually exclusive. This seems to be the case for BMU cells. For instance, osteoblasts that start the differentiation program or decide to secrete osteoid matrix do not complete the cell cycle, and therefore do not proliferate [28]. We also remark that this mechanism allows for one signal to trigger alternative cell decisions depending on its concentration.

Bearing in mind the multiplicity of signals collected in Table 1, as well as the redundancy often observed in their functioning, we propose that the effective operation of a BMU can be modeled by means of a reduced version of the complex signaling network previously sketched. Specifically, we propose that three cell-released signals, denoted by R, S and T (with analog roles to those of RANK, sclerostin and TBF-β respectively see Table 1) plus one osteoclast cue (see [36]), that keeps such cells moving towards intact bone, acting on three types of internal inhibitors suffice for that purpose. The effect induced by such signals in the cell types involved is described in Table 2.

A model for BMU operation

We next describe the cellular algorithms that constitute our proposed model. For simplicity, we will consider a two-dimensional cross section of bone adjacent to a section of bone marrow. The bone section considered will be thought of as a lattice with coordinates x, y, divided in boxes of equal size. Any such box can either remain empty or be occupied by only a single cell. On such a region we define a cellular automaton (CA) to describe the dynamics of the remodeling process. To that end, we implement cellular algorithms based on the biological assumptions stated below. A first assumption is that progression within the cell cycle, apoptosis and the initiation of differentiation programs are initially blocked by specific inhibitory molecules as described above. This would allow for newly formed cells to remain in the first stage of the cell cycle (G1) before choosing a given cell fate. During this stage, membrane receptors interacting with external signals govern the dynamics of inhibitors, thus controlling the eventual decision of the cell. The effect of the complexes formed by membrane receptors and external cues in the inhibition (activation) of any cell fate choice takes place through an increase (decrease) in the amount of the inhibitory molecule controlling this choice. Cell fate is decided when the concentration of the first of the inhibitors considered attains its threshold value, which we set equal to zero for simplicity.

In our case, the inhibitor dynamics will be assumed to be of the following form: (1) where c(t), a(t) and d(t) respectively denote the concentrations of division, apoptosis and differentiation inhibitors at time t and fc, (here and henceforth, prime denotes time derivative) fa, and fd are functions of three external signals S, R and T (see Fig 3). For simplicity, we shall assume in the sequel that such functions will be piecewise linear. We next describe the main details of the decision algorithm proposed to describe BMU operation.

Signals R, S and T (in small circles) are produced by the cell types listed. They may inhibit (-) or induce activation (+) on the actions considered. Activation results from double inhibition, that is by lowering the concentration of an inhibitor. Within any cell type, possible decision choices are indicated by thin arrows. Dashed arrows correspond to a starting decision stage in a newly formed cell. Extracellular release of signals by any cell type (for instance, R and T in the case of active osteoblasts) is denoted by thick, white arrows.

Osteoblasts (OBL).

Osteoblasts (OBL) are initially located at the interface between bone matrix and bone marrow. In normal conditions, osteoblast homeostasis is maintained by a continuous cell turnover, involving both division and apoptosis [48]. When a remodeling process starts, OBLs can choose among three alternative programs: division, apoptosis and differentiation into active osteoblasts (OBAs). We shall assume that OBL division and apoptosis just balance each other, and therefore focus on the third choice above. Activation is known to be mainly blocked by the release of sclerostin by osteocytes [6, 10]. This will be modeled by assuming that signal S, produced by osteocytes, increases the amount of a differentiation inhibitor in OBLs, denoted by dB, according to the following dynamics: (2) where (x, y) denotes the position of the OBL, DB is the maximum amount of inhibitor that can accumulate within a OBL, S(x, y t) is the amount of signal S at location (x, y) at time t and and are positive structural parameters. During a bone remodeling process, osteoblasts remain in their original positions, delimiting the BRC [11]. Accordingly, OBLs do not move in our model. We recall that differentiation of a particular OBL is blocked while dB > 0, and that the process of differentiation is triggered by the condition dB = 0.

Active osteoblasts (OBA).

Once differentiated, OBLs become active osteoblasts (OBA). OBAs have three possible choices: cell division, cell death and differentiation into osteocytes (OCY). Cell division proceeds according to the following rules: (3) where (x, y) denotes the position of the OBA, T(x, y t) is the amount of signal T at location (x, y) at time t and is a positive parameter. Cell division only occurs when the condition c(A) = 0 is verified. Notice that, in our model, the movement of active osteoblasts front is just a consequence of cell division.

When OBAs are attached to the bone surface, cell division is no longer possible for lack of space. In that case OBAs secrete osteoid matrix this is represented by an order parameter b(x, y t) which ranges from 0, corresponding to eroded bone, to value 1 for fully functional bone. Apoptosis, differentiation into OCY and osteoid production can take place, according to these equations: (4) where S(x, y t) is the amount of signal S at location (x, y) at time t, (for i = 1, 2, 3) are positive structural parameters, the rate of bone production, and δA is a positive constant that represents a threshold in cell-to-cell contact inhibition by OCYs on OBA differentiation, resulting from gap junction communications between cells [10, 13, 49].

Osteoclast precursors (OCP).

OBA can recruit OCP to the bone remodeling zone by secreting signal R, while signal S inhibits OCP recruitment. For simplicity, we will not consider in the model OCP division and apoptosis, and assume instead that enough OCP are available in the bone marrow (in particular, in the locations adjacent to those occupied by OBAs). OCPs attach to the bone surface upon their recruitment by OBAs, after which they become active osteoclasts (OCL). We assume that OCP activation is blocked by inhibitor dP, whose dynamics is modeled as follows: (5) where R(x, y t) and S(x, y t) are respectively the amounts of signal R and S at location (x, y) at time t and and are positive parameters.

Osteoclasts (OCL).

Once recruited to the BRC, OCPs become active osteoclasts (OCL) and start eroding the bone matrix, thus leading to the formation of a cutting cone [36]. OCLs are assumed to be endowed with one apoptosis pathway controlled by signal S, produced by OCYs. This signal is instrumental in determining the depth that will be reached by the cutting cone. In particular, OCLs in locations with high concentrations of S will stop digging into the bone matrix and die. We model the apoptosis pathway controlled by signal S by assuming that cell death is blocked by inhibitor aC, whose dynamics are given by the following equations: (6) where S(x, y t) is the amount of signal S at location (x, y) at time t and and are positive parameters.

We next describe the movement of osteoclasts during a bone remodeling event. We will assume that osteoclasts remove bone at a rate that depends on the amount of signal S and move to an adjacent box, along the normal to the ossification front, once they have removed bone in their current position. Bone resorption will be modeled by means of the following equation: (7) where b measures the presence of bone, so that b = 1 corresponds to functional bone, and b = 0 to degraded bone. S(x, y t) is the amount of signal S at location (x, y) at time t and and are positive parameters.

Signal diffusion and decay.

The dynamics of signals R, S and T in our cellular automaton (CA) model is now described. At any given time, they are produced by the corresponding cell types at constant rates. Signals are also assumed to undergo Arrhenius-type decay (meaning that their decay rate is proportional to their concentration). Signal transport through the bone matrix is conveniently represented as a diffusion process. We assume that such diffusion occurs faster than internal cell processes. In order to account for these two time scales simultaneously, we model diffusion by calculating, at each box and each iteration step of the model, a weighted average of the amount of signals in neighboring positions (see Fig 4A). Cells decisions are made upon comparing the amount of different signals in their adjacent boxes.

A) Signal diffusion takes place at a different scale than cell decisions. Let Δt be the characteristic time step for cell processes. In order to model how signals spread out, we calculate the diffusion profile created by the signal release from each cell during this time interval. Diffusion can then be modeled at this characteristic time by applying the corresponding profile to any source of signals in the CA. B) Snapshots of a signal diffusion from the source shown in A. Time increases from left to right and from top to bottom. C) Spatial arrangement of the main elements of the model. Bone matrix is locally represented by means of a lattice consisting of equal-size boxes, each able to accommodate one cell. The lower boundary of the box considered in C) is represented as lined with an osteoblast layer, lying upon a layer of osteoclast precursors. D) Initial configuration of the model. At selected sites within the bone matrix, osteocytes (blue dots) may undergo apoptosis, thus triggering BMU operation in the corresponding region (blank). The lattice element considered in C) is represented here for comparison purposes (red square in the lower left corner). Shades of blue represent different concentrations of signals in each box.

BMU initialization.

As a starting point we consider a population of osteocytes (OCY), regularly distributed within the bone matrix, and a layer of osteoblasts lining the bone section (see Fig 4C). Simulations of the model are started after apoptosis of a group of osteocytes has occurred (see Fig 4D).


Osteoblasts: differentiation and function

Osteoblast differentiation is achieved by the concerted expression of a number of key transcription factors (see Poster panel “Osteoblast lineage”), and bone formation by osteoblasts is controlled both locally and systemically during bone modelling in development (Box 1) and throughout life. Studies of diseases associated with defects in bone formation, such as developmental limb disorders and high bone mass conditions, have demonstrated the crucial importance of local bone formation control by bone morphogenetic protein (BMP) (Cao and Chen, 2005) and wingless (Wnt) (Day et al., 2005) signalling pathways for osteoblast differentiation and function. In the adult, BMP2 can act as a potent stimulator of ectopic bone formation (Chen et al., 1997) and it is used clinically to enhance bone formation, for example, during fracture repair (Govender et al., 2002). BMP signalling through the recruitment and activation of

Box 1. Bone formation and function

During embryogenesis, long bones are formed initially as cartilage that becomes gradually replaced by bone, a process known as endochondral bone formation. By contrast, flat bones, such as the skull, are formed directly from mesenchymal condensation through a process called intramembranous ossification. During early childhood, both bone modelling (formation and shaping) and bone remodelling (replacing or renewing) occurs, whereas in adulthood bone remodelling is the predominant process to maintain skeletal integrity, with the exception of massive increases in bone formation that occur after a fracture. Most bones consist of a mixture of dense outer cortical bone and inner trabecular (spongy) bone, enabling the optimal compromise between strength and weight. In addition to providing support, attachment sites for muscles and protection for vulnerable internal organs, bone also provides a home for bone marrow and acts as a reservoir for minerals.

Osteoblasts produce bone by synthesis and directional secretion of type I collagen, which makes up over 90% of bone matrix protein. This, together with some minor types of collagen, proteoglycans, fibronectin and specific bone proteins, such as osteopontin, bone sialoprotein and osteocalcin, becomes the unmineralised flexible osteoid on which the osteoblasts reside. Rigidity of bone, which distinguishes it from other collagenous matrices, is provided by the bone mineral. Mineralisation is achieved by the local release of phosphate, which is generated by phosphatases present in osteoblast-derived, membrane-bound matrix vesicles within the osteoid. Together with the abundant calcium in the extracellular fluid, this results in nucleation and growth of crystals of hydroxyapatite [Ca10(PO4)6(OH)2]. The proportion of organic matrix to mineral (in adult human cortical bone approximately 60% mineral, 20% organic material, 20% water) is crucial to ensure the correct balance between stiffness and flexibility of the skeleton.

heterodimeric Smad proteins controls the expression of Runt-related transcription factor 2 (Runx2), also known as core binding factor alpha1 (cbfa1), a transcription factor indispensable for osteoblast differentiation (Ducy et al., 1997). The canonical Wnt signalling pathway is indispensable for osteoblast differentiation during skeletogenesis and continues to have important roles in mature osteoblasts (Box 2). Although the major function of circulating parathyroid hormone (PTH) is to regulate plasma calcium (see below), it also has an important role in bone formation and prevents osteoblast and osteocyte apoptosis. Intermittent administration of low levels of PTH increases osteoblast number, bone formation and bone mass, and is an established anabolic treatment for osteoporosis.

The exact mechanisms involved in the anabolic effects of PTH on bone formation are not fully understood, but might involve Wnt signalling (Box 2) as well as insulin-like growth factor 1 (IGF-1). IGF-1, which is released by the liver in response to growth hormone, has a role in the commitment of mesenchymal stem cells to osteoprogenitor cells. IGF-1 also regulates osteoclastogenesis both directly, through the IGF receptor (IGFR) present on osteoclasts, and by upregulating the crucial osteoclast differentiation factor receptor activator of nuclear factor κB ligand (RANKL).

Another pathway by which osteoblast function is regulated is the sympathetic nervous system (Elefteriou et al., 2005). Sympathetic stimulation through the β2 adrenergic receptor located on osteoblasts inhibits bone formation and increases bone resorption, thereby resulting in a reduction in bone mass.


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Stages of Indirect Healing [ edit | edit source ]

Acute Inflammatory Response [ edit | edit source ]

The acute inflammatory response peaks within 24 hours and ends after 7 days and is essential for healing to occur. [2] A haematoma forms immediately after trauma. This consists of cells from the peripheral and intramedullary blood and bone marrow cells. The inflammatory response causes the haematoma to coagulate around the fracture ends and within the medulla, which creates a model for callus formation. [2]

Recruitment of Mesenchymal Stem Cells [ edit | edit source ]

Bone is unable to regenerate unless specific mesenchymal stem cells are recruited, proliferated and differentiated into osteogenic cells. It is not currently understood exactly where these cells come from. [2]

Generation of Cartilaginous and Periosteal Bony Callus [ edit | edit source ]

After the haematoma has formed, a fibrin-rich granulation tissue forms. Endochondral formation occurs between the fracture ends and beyond the periosteal sites in this tissue. These areas are less stable, so the cartilaginous tissue forms a soft callus, giving the fracture more stability. [2]

In animal studies, soft callus formation peaks at 7 to 9 days when type II procollagen and proteoglycan core protein extracellular markers are at their highest levels. [2] Concurrently, an intramembranous ossification response occurs subperiostally immediately by the fracture ends. This creates a hard callus. The bridging of this central hard callus provides the fracture with a semi-rigid structure which enables weight bearing. [2]

Revascularization and Neoangiogenesis [ edit | edit source ]

Adequate blood supply is necessary for bone repair to occur. Angiogenic pathways, chondrocyte apoptosis and cartilaginous degradation are essential to this process because cells and extracellular matrices must be removed in order to ensure that blood vessels can move into the repair site. [2]

Mineralization and Resorption of the Cartilaginous Callus [ edit | edit source ]

The primary soft cartilaginous callus must be resorbed and replaced by a hard bony callus for bone regeneration to continue. [2] In some ways, this stage repeats embryological bone development and involves cellular proliferation and differentiation, as well as an increase in cellular volume and matrix deposition. [2]

Bone Remodeling [ edit | edit source ]

While the hard callus is rigid and provides stability, it does not mean that the fracture site has all the properties of normal bone. A second restorative stage is necessary. This stage results in the remodelling of the hard callus into a lamellar bone structure with a central medullary cavity. [2]

Remodelling occurs when the hard callus is resorbed by osteoclasts and lamellar bone is deposited by osteoblasts. This starts at 3–4 weeks, but the whole process may take years. Remodelling may be faster in younger patients (and other animals). [2]

Bone remodelling results from the production of electrical polarity. This occurs when pressure is applied in a crystalline environment. [2]

  • When axial loading of long bones occurs, an electropositive convex surface and an electronegative concave surface are created
  • This activates osteoclastic and osteoblastic activity.
  • As a result, the external callus is slowly replaced by a lamellar bone structure. As well as this, the internal callus remodels which re-creates a medullar cavity, similar to diaphyseal bone. [2]

Bone remodelling will only be successful if there is adequate blood supply and a gradual increase in mechanical stability. If not, complications such as non-union may occur. [2]


Materials and Methods

Mathematical Modeling

In developing a new mathematical model for bone remodeling we have chosen to employ the biochemical systems analysis formalism used in e.g. [1], [15], [20]–[22], [30], but extended to incorporate further biological detail as summarized in Figure 1. We chose this approach in anticipation of the type of data to which we may eventually have access, and the types of questions which are of concern to us. For example, explicit chemical data are not obtained in current clinical practice. Our approach does represent many of the mechanisms contained in [17], [23], [28], [29], albeit implicitly. In particular, we incorporate the actions of an important signaling pathway based on the specific molecules: receptor activator of nuclear factor -B (RANK) and osteoprotegerin (OPG) [2], [3], [39]–[42]. These cytokines, plus the RANK ligand, form a pathway commonly known as the RANK/RANKL/OPG pathway. We also incorporate the actions of growth factors such as transforming growth factor (TGF- ) [43], [44], and other cytokines on bone remodeling cells. It is well known that RANKL is a key cytokine in the differentiation process of osteoclast cells, while OPG, which is produced by differentiated osteoblastic cells, has been shown to function as an inhibitory factor for osteoclastogenesis [38].

We have developed a cell population model for osteocyte-induced targeted bone remodeling. This model consists of the osteocyte, pre-osteoblast, osteoblast, and osteoclast cell populations the interactions of these cells with one another, and through the power law formalism the autocrine and paracrine signaling among these cells. Figure 2 shows the equations that make up the model, these are described in detail below. In this model we explicitly include the population of pre-osteoblasts to emphasize the switch of cells in the osteoblast lineage from being osteoclastogenic, i.e., osteoclast generating, to being osteogenic, i.e., bone forming, see e.g., [45], [46]. Specifically, there is a clear distinction between the signaling behaviors of pre-osteoblasts and osteoblasts that is important for the considerations taken up in this work. On the other hand, for the purposes we have in mind there is no similar a priori reason to explicitly represent a population of pre-osteoclasts.

A general assumption is that there is a large pool of mesenchymal stem cells available to differentiate into pre-osteoblasts [28]. Similarly, we assume there is a large pool of osteoclast progenitor cells which are available to differentiate to fully committed mature osteoclasts [28]. Such cell differentiation is determined by autocrine and paracrine signaling discussed in more detail below, see also [8]. We assume that some percentage of pre-osteoblasts differentiate under the influence of autocrine and paracrine signaling while some percentage undergo apoptosis. We also assume that some percentage of mature osteoblasts will undergo apoptosis, and some percentage of osteoblasts will become embedded in the bone matrix as osteocytes. Figure 1 outlines the assumptions that we make to construct the mathematical model. The details of the assumptions and how they influence the development of a mathematical model is described in detail below.

In the following we denote by S(t), or simply , the osteocyte cell population at given time t. Sclerostin is produced by osteocytes and inhibits the Wnt/β-catenin pathway, [6], [8]. Wnt is known to promote osteoblastic proliferation and differentiation [7]. We incorporate the effects of sclerostin and the Wnt/β-catenin pathway into the mathematical model through a term of the form where and Ks is a parameter that describes the relation between osteocyte apoptosis and decrease in sclerostin inhibition. The idea is that, for a threshold level Ks of osteocytes, there is sufficient sclerostin production to inhibit local Wnt signaling. When osteocytes die, the sclerostin level decreases, [6], [8]. This releases osteoblast precursor cells from Wnt inhibition, thereby initiating a cycle of targeted bone remodeling. We note that the term is a dimensionless quantity that is used to modify the standard biochemical systems analysis formalism in order to accurately capture the action of sclerostin signaling as previously described. It is also important to note that in the biochemical systems analysis formalism the basic relations used to represent signaling are nonlinear. However, it may be the case that the exponents used take on numerical values equal or close to unity. This should not be misconstrued as an a priori assumption of linearity within the model.

Equation (1) in Figure 2 describes the dynamics of the osteocyte cell population. This equation simply states that osteocytes are mature osteoblasts that become embedded in extra cellular matrix at a given rate . We further note that there is no death term for osteocytes in equation (1). This is due to our assumption that, over the time scale of a single event of targeted remodeling considered here, the most significant influence on osteocyte apoptosis is the initial biomechanical action that begins remodeling [9], [47]. This appears in the mathematical model as an initial condition.

The pre-osteoblast cell population at a time t is denoted by P(t), or simply P. Pre-osteoblasts are differentiated mesenchymal stem cells. We assume that this differentiation is controlled by osteocytes through the sclerostin, Wnt/β-catenin pathways, and various growth factors. The effectiveness of sclerostin regulations of the differentiation of mesenchymal stem cells to become pre-osteolbasts is represented mathematically by Where g22 is a dimensionless parameter. Thus when osteocytes undergo apoptosis due to microdamage, local mesenchymal stem cells differentiate to pre-osteoblasts due to the resulting signaling. Moreover, the pre-osteoblasts are free to proliferate and differentiate to mature osteoblasts since they have been released from Wnt inhibition. Equation (2) in Figure 2 describes the dynamics of the pre-osteoblast cell population. This equation states that pre-osteoblasts are differentiated from a large pool of stem cells at a rate in response to signaling molecules produced by osteocytes, that pre-osteoblasts proliferate at a rate under the influence of autocrine signaling provided this is not inhibited by sclerostin. Furthermore, pre-osteoblasts differentiate to become mature osteoblasts at a rate . This is under the influence of autocrine and osteoclast regulated paracrine signaling. Finally, pre-osteoblasts undergo apoptosis at a rate .

The osteoblast cell population at a time is denoted by , or simply . Equation (3) in Figure 2 describes the dynamics of the mature osteoblast cell population. This equation states that osteoblasts are differentiated pre-osteoblasts, that osteoblasts undergo apoptosis, and that some osteoblasts are embedded in the extra cellular matrix during formation to become osteocytes. Notice that the term also appears in equation (1) of Figure 2, representing the embedding of osteoblasts that become osteocytes, and the term , also appears in equation (2) of Figure 2, which corresponds to the differentiation of pre-osteoblasts to become mature osteoblasts. Here the parameter describes the pre-osteoblast autocrine signaling. The parameter represents the effects of osteoclast derived paracrine signaling on pre-osteoblasts. This could represent, for example, the effects of TGF- on pre-osteoblasts as described for example in [28].

The osteoclast cell population at a time is denoted by , or simply . The equation (4) in Figure 2 describes the dynamics of the osteoclast cell population. This equation states that mature osteoclasts come from the differentiation of a large pool pre-osteoclasts at a rate . This differentiation is influenced essentially by the RANK/RANKL/OPG pathway. Thus the term , describes the effects of this pathway. The dimensionless parameter models the effectiveness of sclerostin regulation of osteoclastogensis. One novel feature of this model is that we have included osteocytes as a source of RANKL as discussed in recent literature [6]–[9], [48]. The parameter represents the effect of osteocyte derived RANKL signaling on osteoclastogenesis. We also retain pre-osteoblast derived RANKL signaling via the parameter . While we have explicitly included the pre-osteoblast cell population dynamics, we have neglected to explicitly include a dynamic cell population for pre-osteoclasts. This is based on a simplifying assumption that, over the relevant time span, there is a steady pool of circulating pre-osteocalsts that may be recruited for differentiation to active osteoclasts. This simplifying assumption is common the literature on mathematical modeling of bone remodeling, e.g., [15]–[18], [21]–[23].

We note that either of these, or , could take on the value . Thus advances in the understanding of the relative role of osteoblasts and osteocytes in RANKL production would result in parameter changes in our model, but not a change in the model structure itself.

The term represents the effect of OPG acting as a decoy receptor for RANKL. Typically the parameter takes on negative values, and since has as a steady state value, we add a sufficiently small number to avoid dividing by zero. This represents the factor of production when . We also have a term for the osteoclast cell death at a rate .

We denote by , or simply , the bone mass at a given time . We follow [22], [28] to develop an equation for the change of bone mass (or bone volume depending on the scaling) over time. The rate of change of bone mass has the form

As in e.g., [28], we assume that the amount of bone being resorbed is proportional to the osteoclast population, while the amount of bone being formed is proportional to the osteoblast population.

We can summarize the mathematical model with the following verbal description:

  1. change in osteocytes = increase due to embedded osteoblasts
  2. change in pre-osteoblasts = increase due to differentiation of stromal cells (released from sclerostin or exposure to growth factors) + proliferation of pre-osteoblasts (autocrine signaling of Wnt and growth factors) – differentiation to osteoblasts (growth factors) - apoptosis
  3. change in osteoblasts = increase due to differentiation of pre-osteoblasts (growth factors) – apoptosis – embedding as osteocytes
  4. change in osteoclasts = increase due to differentiation of pre-osteoclasts (due to RANKL and limited by OPG) – apoptosis
  5. change in bone mass = increase due to activity of osteoblasts – activity of osteoclasts

The corresponding full mathematical model is the set of equations shown in Figure 2. The definitions of the variables and parameters appearing in the model equations of Figure 2 is summarized in table 1.


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