The cellular transducer in damage-stimulated bone remodelling: a theoretical investigation using fracture mechanics

A mechano-chemo-biological model for bone remodeling with a new mechano-chemo-transduction approach

Bone remodeling is a fundamental biological process that develops in bone tissue along its whole lifetime. It refers to a continuous bone transformation with new bone formation and old bone resorption that changes the internal microstructure and composition of the tissue. The main objectives of bone remodeling are: repair of the internal microcracks; adaptation of the macroscopic stiffness and strength to the actual changing mechanical demands; and control of the calcium homeostasis. Understanding this process and predicting its evolution is critical to reduce the effects of long-term disuse as happens during periods of reduced mobility. It is also important in the design of bone implants to avoid long-term stress shielding. Many mathematical models have been proposed from the earliest purely phenomenological to the latest that include biological knowledge. However, there still exists a lack of connection between the mechanical driving force and the biochemical and cell processes it triggers. Here, and following previous works that model independently the mechanobiological and biochemical processes in bone remodeling, we present a more complete model, useful for both cortical and trabecular bone, that uses a new mechanotransduction approach based on the effect of strains onto the bonding-unbonding rate of RANK/RANKL/OPG receptor-ligand reactions. We compare the results of this model with previous ones, showing a good agreement in similar conditions. We also apply it to realistic situations such as a femoral bone after implantation of a hip prosthesis, getting similar results to the clinical ones in the final bone density distribution. Finally, we extend this approach to the anisotropic case, getting not only the mean density, but also the directional homogenization of the microstructure. This biochemical approach permits, not only to predict the bone evolution under changes in the mechanical loads, but also, to consider anabolic and catabolic drugs to control bone density, such as those used in osteoporosis.

Fatigue exhaustion of the mitral valve tissue

Sudden failure and rupture of the tissue is a rare but serious short-term complication after the mitral valve surgical repair. Excessive cyclic loading on the suture line of the repair can progressively damage the surrounding tissue and finally cause tissue rupture. Moreover, mechanical over-tension, which occurs in a diseased mitral valve, gradually leads to tissue floppiness, mitral annular dilation, and leaflet rupture. In this work, the rupture mechanics of mitral valve is studied by characterizing the fracture toughness exhaustion of healthy tissue. Results of this study show that fracture toughness of the posterior mitral valve is lower than its anterior counterpart, indicating that posterior tissue is more prone to failure. Moreover, the decrease in fracture toughness by increasing the number of fatigue cycles shows that excessive mechanical loading leads to progressive failure and rupture of mitral valve tissue within a damage accumulative process.

Apoptotic osteocytes regulate osteoclast precursor recruitment and differentiation in vitro

Fatigue loading causes a spatial distribution of osteocyte apoptosis co-localized with bone resorption spaces peaking around microdamage sites. Since osteocytes have been shown to regulate osteoclast formation and activity, we hypothesize that osteocyte apoptosis regulates osteoclastogenesis. In this study, we used serum-starvation to mimic reduced nutrient transport in microdamaged bone and induce apoptosis in MLO-Y4 osteocyte-like cells; conditioned medium was used to apply soluble factors released by apoptotic osteocytes (aOCY) to healthy non-apoptotic MLO-Y4 cells. Osteoclast precursor (RAW264.7 monocyte) migration and differentiation were assessed in the presence of conditioned media (CM) from: (A) aOCY, (B) osteocytes treated with apoptosis conditioned medium (i.e., healthy osteocytes in the presence of apoptosis cues; apoptosis CM-treated osteocytes (atOCY)), and (C) osteocytes treated with non-apoptosis conditioned medium (i.e., healthy osteocytes in the absence of apoptosis cues; non-apoptosis CM-treated osteocytes (natOCY)). Receptor activator for nuclear factor-κB ligand (RANKL), macrophage colony stimulating factor (M-CSF), vascular endothelial growth factor (VEGF) and osteoprotegerin (OPG) mRNA, and protein expression were measured. Our findings indicate that soluble factors released by aOCY and atOCY promoted osteoclast precursor migration (up to 64% and 24% increase, respectively) and osteoclast formation (up to 450% and 265% increase, respectively). Osteoclast size increased up to 233% in the presence of aOCY and atOCY CM. Recruitment, formation and size were unaltered by natOCY. RANKL mRNA and protein expression were upregulated only in aOCY, while M-CSF and VEGF increased in atOCY. Addition of RANKL-blocking antibody abolished aOCY-induced osteoclast precursor migration and osteoclast formation. VEGF and M-CSF blocking antibodies abolished atOCY-induced osteoclastogenesis. These findings suggest that aOCY directly and indirectly (through atOCY) initiate targeted bone resorption by regulating osteoclast precursor recruitment and differentiation.

Mechanobiological regulation of the remodelling cycle in trabecular bone and possible biomechanical pathways for osteoporosis

BACKGROUND

The rapid loss of trabeculae as observed during osteoporosis is attributed to pathological changes in the bone remodelling process. In this study, it is proposed that osteoporosis is due to altered signals resulting from either (i) a decrease in the mechanosensitivity of the sensor cells or (ii) an increase in the bone tissue elastic modulus.

METHODS

To test these hypotheses, a mechanobiological algorithm was developed and applied to simulate the remodelling cycle in a realistic trabecular strut. The model is based on the supposition that bone resorption is initiated either to remove damaged tissue or when strains fall below a lower threshold; bone formation is triggered when strains exceed an upper threshold.

FINDINGS

Applying this algorithm to a realistic trabecula, resorption and subsequent refilling of a cavity was simulated. Results showed that decreases in the mechanosensitivity (simulated by increasing the upper strain threshold) led to under-refilling of cavities. A critical sensitivity was found to exist, above which perforation of the strut due to osteoclastic resorption occurred. It was also found that increases in the bone tissue elastic modulus lead to an increased propensity for trabecular perforation.

INTERPRETATION

It may be concluded that if cells become less mechanosensitive, or if increases in the elastic modulus of trabecular bone tissue occurs, the possibility of trabecular perforation and therefore the rapid loss of bone mass increases. If this is true, the preservation of the bone mineral content or maintenance of bone cell mechanosensitivity are potential therapeutic strategies for the prevention of osteoporosis.

Loss of trabeculae by mechano-biological means may explain rapid bone loss in osteoporosis

Osteoporosis is characterized by rapid and irreversible loss of trabecular bone tissue leading to increased bone fragility. In this study, we hypothesize two causes for rapid loss of bone trabeculae; firstly, the perforation of trabeculae is caused by osteoclasts resorbing a cavity so deep that it cannot be refilled and, secondly, the increases in bone tissue elastic modulus lead to increased propensity for trabecular perforation. These hypotheses were tested using an algorithm that was based on two premises: (i) bone remodelling is a turnover process that repairs damaged bone tissue by resorbing and returning it to a homeostatic strain level and (ii) osteoblast attachment is under biochemical control. It was found that a mechano-biological algorithm based on these premises can simulate the remodelling cycle in a trabecular strut where damaged bone is resorbed to form a pit that is subsequently refilled with new bone. Furthermore, the simulation predicts that there is a depth of resorption cavity deeper than which refilling of the resorption pits is impossible and perforation inevitably occurs. However, perforation does not occur by a single fracture event but by continual removal of microdamage after it forms beneath the resorption pit. The simulation also predicts that perforations would occur more easily in trabeculae that are more highly mineralized (stiffer). Since both increased osteoclast activation rates and increased mineralization have been measured in osteoporotic bone, either or both may contribute to the rapid loss of trabecular bone mass observed in osteoporotic patients.

Theoretical modelling in bioengineering: 12th Haughton Lecture of the Royal Academy of Medicine in Ireland

This paper is concerned with the role of theoretical modelling in bioengineering research. The subject matter was delivered as the 12th annual Haughton Lecture, presented on 28 January 2006 at the Bioengineering in Ireland conference in Galway. The title of the lecture was "Telling Stories About Bone". The paper begins with some general remarks about what constitutes a scientific theory, and it moves on to a discussion about where ideas for theoretical models come from, taking examples from my own work on the mechanical strength and fracture of bone. I conclude with some advice to budding theoreticians.

Allosteric control model of bone remodelling containing periodical modes

To help to understand the modelling process that occurs when a scaffold is implanted it is vital to understand the rather complex bone remodelling process prevalent in native bone. We have formulated a mathematical model that predicts osteoactivity both in scaffolds, as well as in bone in vivo and could set a basis for the more detailed allosteric models. The model is extended towards a bio-cybernetic vision of basic multicellular unit (BMU) action, when some of the regulation loops have been modified to reflect the allosteric control mechanisms, developed by Michaels-Menten, Hill, Koshland-Nemethy-Filmer, Monod-Wyman-Changeux. By implementation of this approach a four-dimensional system was obtained that shows steady cyclic behaviour using a wide range of constants with clear biological meaning. We have observed that a local steady state appears as a limiting cycle in multi-dimensional phase space and this is discussed in this paper. Physiological interpretation of this limiting four-dimension cycle possibly related to a conservative-like value has been proposed. Analysis and simulation of the model has shown an analogy between this conservative value, as a kind of substrate-energy regenerative potential of the bone remodelling system with a molecular nature, and to the classical physical value--energy. This dynamic recovery potential is directed against both mechanical and biomechanical damage to the bone. Furthermore, the current model has credibility when compared to the normal bone remodelling process. In the framework of widely recognised Hill mechanisms of allosteric regulation the cyclic attractor, described formerly for a pure cellular model, prevails for different forms of feedback control. This result indicates the viability of the proposed existence of a conservative value (analogous to energy) that characterises the recovery potential of the bone remodelling cycle. Linear stability analysis has been performed in order to determine the robustness of the basic state, however, additional work is required to study a wider range of constants.

Living with cracks: damage and repair in human bone

Our bones are full of cracks, which form and grow as a result of daily loading activities. Bone is the major structural material in our bodies. Although weaker than many engineering materials, it has one trick that keeps it ahead - it can repair itself. Small cracks, which grow under cyclic stresses by the mechanism of fatigue, can be detected and removed before they become long enough to be dangerous. This article reviews the work that has been done to understand how cracks form and grow in bone, and how they can be detected and repaired in a timely manner. This is truly an interdisciplinary research field, requiring the close cooperation of materials scientists, biologists and engineers.

The role of osteocytes and bone microstructure in preventing osteoporotic fractures

The skeleton alters its geometry following trauma, the introduction of artificial defects and of fatigue-induced microcracks. The precise mechanism by which the skeleton adapts remains unclear. Microcracks might directly affect the cell by damaging the osteocyte cell network or causing apoptosis. Bone microstructure may play an important role in these processes by diverting and arresting propagating microcracks and so prevent fracture failure. This paper discusses the effects of microstructure on propagating cracks, how microdamage may act as a stimulus for bone adaptation and its potential effects on bone biochemistry.

Bone remodelling algorithms incorporating both strain and microdamage stimuli

Biomechanical theories to predict bone remodelling have used either mechanical strain or microdamage as the stimulus driving cellular responses. Even though experimental data have implicated both stimuli in bone cell regulation, a mechano-regulatory system incorporating both stimuli has not yet been proposed. In this paper, we test the hypothesis that bone remodelling may be regulated by signals due to both strain and microdamage. Four mechano-regulation algorithms are studied where the stimulus is: strain, damage, combined strain/damage, and either strain or damage with damage-adaptive remodelling prioritised when damage is above a critical level. Each algorithm is implemented with both bone lining cell (surface) sensors and osteocyte cell (internal) sensors. Each algorithm is applied to prediction of a bone multicellular unit (BMU) remodelling on the surface of a bone trabecula. It is predicted that a regulatory system capable of responding to changes in either strain or microdamage but which prioritises removal of damaged bone when damage is above a critical level, is the only one that provides a plausible prediction of BMU behaviour. A mechanism for this may be that, below a certain damage threshold, osteocyte processes can sense changes in strain and fluid flow but above the threshold damage interferes with the signalling mechanism, or causes osteocyte apoptosis so that a remodelling response occurs to remove the dead osteocytes.

On allosteric control model of bone turnover cycle containing osteocyte regulation loop

One approach to developing a mathematical model that predicts osteoactivity both in bio-scaffolds, as well as the in bone tissue in vivo, is based on a bio-cybernetic vision of basic multicellular unit (BMU) action. In the case of the model presented in this paper, some of the loops of regulation have been modified to reflect the range of allosteric control mechanisms: Michaelis-Menten, Hill, Adair, Koshland-Nemethy-Filmer (KNF), Monod-Wyman-Changeux (MWC). This approach has resulted in a four-dimensional system that shows steady cyclic behaviour using a range of constants with clear biological meaning. The initial findings suggesting that a steady state appears as a cycle in multidimensional phase space and this is discussed in this paper. The existence of this cycle in the osteoclasts-osteoblasts-osteocytes-bone subspace indicates that there is a conservative value along steady trajectories for this dynamic system. Biophysical interpretation of this conservative value has been proposed as a kind of substrate-energy regenerative potential of the bone remodelling system with a similarity to the classical physical value-energy. Such a recovery "potential" is directed against both mechanical and biomechanical damage to the bone. The current model has credibility when compared to the normal bone remodelling process. In the framework of widely recognised Michaelis-Menten mechanisms of allosteric regulation the cyclic attractor, described formerly for a pure cellular model, prevails for different forms of feedback control. This finding demonstrates the viability of the suggestion of the subsistence of conservative value (analogous to energy) that characterises the recovery potential of the bone remodelling cycle. The results indicate that the robust behaviour of the model is maintained from the simple cellular level to the molecular biochemical level of regulation.

Phenomenological model of bone remodeling cycle containing osteocyte regulation loop

Biological parameters, such as bone resorption and formation constants, are important variables to achieve optimised hard tissue scaffolds design. To help to understand the modelling process that occurs when a scaffold is implanted it is vital to understand the rather complex bone remodeling process prevalent in native bone. One approach to developing a mathematical model that predicts osteoactivity both in scaffolds, as well as in bone in vivo, is based on a bio-cybernetic vision of basic multicellular unit (BMU) action -. In the case of the model presented in this paper, an additional loop of regulation based on osteocyte activity has been added. This approach has resulted in a four-dimensional system, which shows steady-quasi-cyclic behaviour using a particular range of constants with real biological meaning. The initial findings suggesting that the basic steady-state appears as a torus in multidimensional phase space have been discussed. The existence of this surface in the osteoclasts-osteoblasts-osteocytes-bone subspace indicates that there is a first integral for this dynamic system. Biological and physical interpretation of this integral as a conservative value has been proposed. It is possible to draw an analogy between this conservative value, as a kind of substrate-energy regenerative potential of the bone remodeling system with a molecular nature, to the classical physical value (energy). There are clear indications that there is recovering potential within the BMU that results in a steady operating genetically predominated bone remodeling process. This recovering potential is directed against both mechanical and biomechanical damage to the bone. The current model has credibility when compared to the normal bone remodeling process. However, additional work is required to study a wider range of constants.

Re-engineering Colles: form, function and fragility fractures

Of the twenty nine anatomy professors in the Royal College of Surgeons in Ireland, primus inter pares is Abraham Colles. In his 1811 book A Treatise on Surgical Anatomy he revolutionised the subject by teaching it topographically, seeking "to describe the relative position of the parts and to point out the subservience of anatomical knowledge to surgical practice". Today we have extended this to 'clinical practice' and, in the Anatomy Room, students are guided through each region by clinically trained staff, from surface anatomy via three-dimensional dissection to radiological images. This is augmented by online histology and radiology courses and DVDs in which dissection footage, edited by a content analysis engine, is used to preview and review practical classes. In the same book, Colles also wrote that 'the fixed and immutable laws of mathematics are little applicable to the science of medicine'. Computer-aided learning argues against this. So does research which links fatigue microdamage to bone remodelling and the development of algorithms to predict, and thus prevent, osteoporotic fractures. Mechanical principles are being used to develop scaffolds for tissue engineering and to optimise the mechanical environment of seeded mesenchymal stem cells. While Colles' teaching approach holds true, in biomechanics, tissue engineering and computing, mathematical laws are now being successfully applied to medical science.

Microdamage: A cell transducing mechanism based on ruptured osteocyte processes

As a result of underlying pathological diseases, such as osteoporosis, osteopenia, or due to altered loading after joint replacements, bones become more susceptible to microdamage accumulation than those of normal human beings, as are those of athletes who undertake strenuous exercise [Stromsoe, 2004. Fracture fixation problems in osteoporosis. Injury 35, 107-113]. Experimental evidence has linked bone adaptation to microdamage, and to increased cell activity. In this work, we investigated whether microcrack detection is related to rupturing of the cellular material itself due to crack face displacements. Using specific cell staining techniques, it was confirmed that relative crack displacements are capable of tearing cell processes between neighbouring osteocytes. No ruptured cell processes were found near the crack tip where the displacements are less. Rupturing of cell processes due to crack opening and shear displacement is a feasible new mechanism by which bone can detect and estimate the size of a microcrack. Ruptured cell processes may directly secrete passive and active components in the extracellular matrix, triggering a repair response.

Osteocyte lacunae tissue strain in cortical bone

Current theories suggest that bone modeling and remodeling are controlled at the cellular level through signals mediated by osteocytes. However, the specific signals to which bone cells respond are still unknown. Two primary theories are: (1) osteocytes are stimulated via the mechanical deformation of the perilacunar bone matrix and (2) osteocytes are stimulated via fluid flow generated shear stresses acting on osteocyte cell processes within canaliculi. Recently, much focus has been placed on fluid flow theories since in vitro experiments have shown that bone cells are more responsive to analytically estimated levels of fluid shear stress than to direct mechanical stretching using macroscopic strain levels measured on bone in vivo. However, due to the complex microstructural organization of bone, local perilacunar bone tissue strains potentially acting on osteocytes cannot be reliably estimated from macroscopic bone strain measurements. Thus, the objective of this study was to quantify local perilacunar bone matrix strains due to macroscopically applied bone strains similar in magnitude to those that occur in vivo. Using a digital image correlation strain measurement technique, experimentally measured bone matrix strains around osteocyte lacunae resulting from macroscopic strains of approximately 2000 microstrain are significantly greater than macroscopic strain on average and can reach peak levels of over 30,000 microstrain locally. Average strain concentration factors ranged from 1.1 to 3.8, which is consistent with analytical and numerical estimates. This information should lead to a better understanding of how bone cells are affected by whole bone functional loading.

A bone remodelling model coupling microdamage growth and repair by 3D BMU-activity

Bone as most of living tissues is able, during its entire lifetime, to adapt its internal microstructure and subsequently its associated mechanical properties to its specific mechanical and physiological environment in a process commonly known as bone remodelling. Bone is therefore continuously renewed and micro-damage, accumulated by fatigue or creep, is removed minimizing the risk of fracture. Nevertheless, bone is not always able to repair itself completely. Actually, if bone repairing function is slower than micro-damage accumulation, a type of bone fracture, usually known as "stress fracture", can finally evolve. In this paper, we propose a bone remodelling continuous model able to simulate micro-damage growth and repair in a coupled way and able therefore to predict the occurrence of "stress fractures". The biological bone remodelling process is modelled in terms of equations that describe the activity of basic multicellular units. The predicted results show a good correspondence with experimental and clinical data. For example, in disuse, bone porosity increases until an equilibrium situation is achieved. In overloading, bone porosity decreases unless the damage rate is so high that causes resorption or "stress fracture".

Microcracks in cortical bone: how do they affect bone biology?

Microcrack accumulation in cortical bone has been implicated in skeletal fragility and stress fractures. These cracks have also been shown to affect the mechanical and material properties of cortical bone. Their growth has been linked to osteocyte apoptosis and the initiation of the remodeling process, which also has a role in their repair. Clinically, osteoporosis is diagnosed using dual energy x-ray absorptiometry. However, evidence now indicates that bone mass alone is insufficient to satisfactorily explain the skeletal fragility of osteoporosis and consideration needs to be given to bone quality in the diagnosis and treatment of the disease. Bone quality includes parameters such as trabecular and cortical microarchitecture, morphology, bone turnover, degree of mineralization of the bone matrix, and significantly, the amount of microdamage present in the bone. Current clinical treatments concentrate on the inhibition of osteoclast activity to maintain bone mass in osteoporotic patients. However, these cells have a major role in removing existing microcracks from the bone matrix, and hence the use of bone resorption- inhibiting drugs may lead to insufficient bone repair and therefore an increase in microdamage accumulation and loss of bone quality.

Bone architecture and fracture

Bones are designed to carry out their requirements effectively. One of these requirements is to resist fracture. Two other important requirements are to be stiff and to be light. Few theories of adaptive modeling distinguish modeling for adequate stiffness from modeling for adequate strength. Bones achieve their architecture partially through genetics, the rough form of the bone being laid down in the genes, and partially through response to normal loading. Normal loading rarely includes traumatic loading and bones are not usually well adapted to resist trauma, though they are probably well adapted to fatigue loading. Some aspects of architectural function, such as hollowness, are well understood. Some aspects, such as the need for uniform loading in impact, are less understood, and some, such as size effects, are only now beginning to be investigated.

Perforation of cancellous bone trabeculae by damage-stimulated remodelling at resorption pits: A computational analysis

Loss of trabeculae in cancellous bone is often attributed to a general decline in the bone mass leading to fracture of the thin trabeculae. It has never been investigated whether trabecular perforation may have any other biomechanical mechanism. In this paper, an alternative hypothesis is proposed and tested using a computational model. Taking it as given that osteoclastic resorption is targeted to microdamage, it is hypothesised that the creation of a resorption cavity during normal bone remodelling could cause a stress-concentration in the bone tissue. If the resorption cavities were excessively deep, as is seen during osteoporosis, then this stress concentration may be sufficient to generate more microdamage so that osteoclasts "chase" newly formed damage leading to perforation. If this were true then we should find that, for a given trabecular thickness, there is a critical depth of resorption cavity such that smaller cavities refill whereas deeper cavities cause microdamage accumulation, continued osteoclast activity, and eventual trabecular perforation. Computer simulation is used to test this hypothesis. Using a remodelling stimulus calculated from both strain and damage and a simplified finite element model of a trabeculum with cavities of different sizes, it is predicted that such a critical depth of resorption cavity does indeed exist. Therefore we suggest that an increase in resorption depth relative to the thickness of trabeculae may be responsible for trabecular perforation during osteoporosis, rather than simply trabecular fracture due to insufficient strength.

A Novel Application of the Principles of Linear Elastic Fracture Mechanics (LEFM) to the Fatigue Behavior of Tendon Tissue

Background: Experiments on the fatigue of tendons have shown that cyclic loading induces failure at stresses lower than the ultimate tensile strength (UTS) of the tendons. The number of cycles to failure Nf has been shown to be dependent upon the magnitude of the applied cyclic stress. Method of approach: Utilizing data collected by Schechtman (1995), we demonstrate that the principles of Linear Elastic Fracture Mechanics (LEFM) can be used to predict the fatigue behavior of tendons under cyclic loading for maximum stress levels that are higher than 10% of the ultimate tensile strength (UTS) of the tendon (the experimental results at 10% UTS did not fit with our equations). Conclusions: LEFM and other FM approaches may prove to be very valuable in advancing our understanding of damage accumulation in soft connective tissues.