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bone remodeling


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Trabecular bone strain changes associated with subchondral stiffening of the proximal tibia

 

Abstract

Subchondral stiffening is a hallmark pathologic feature of osteoarthritis but its mechanical and temporal relationship to the initiation or the progression of osteoarthritis is not established. The mechanical effect of subchondral stiffening on the surrounding trabecular bone is poorly understood. This study employs a relatively new application of digital image correlation to measure strain in the trabecular region of the proximal medial tibia in normal specimens and in specimens with simulated subchondral bone stiffening. Coronal sections from eight normal human cadaveric proximal tibiae were loaded in static compression and high resolution contact radiographs were made. Repeat contact radiographs were collected after the subchondral bone near the jointline was stiffened using polymethylmethacrylate. Digital images, made from loaded and unloaded contact radiographs, were compared

using in-house software to measure trabecular displacement and calculate trabecular bone strain. Overall strain was higher in the stiffened specimens suggesting experimental artifiact significantly affected our results. Consistent increases in median maximum shear strain, median maximum principal strain, median minimum principal strain, and peak shear strain were measured near the inner and outer edges of the stiffened segment. Our experiment provides direct experimental measurement of increases in trabecular bone strain caused by subchondral stiffening, however, the clinical and biologic importance of strain increases is unknown

 

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Abstract

It is well admitted that the mechanical loading plays an important role in the growth and maintenance of our skeleton, and that microdamage (i.e.: microcracks) occurs naturally when the bone is overloaded during day-to-day activities. It is also argued, from experimental and theoretical viewpoint, that the cells which built and rebuilt the skeleton are sensitive for both strain and microdamage. The recent damage-bone remodeling theory is employed here to study the mechanical response of the three unit-bone bars that simulate bone trabeculae in the form of truss. It is shown that under constant load, such a structure exhibit inhomogeneous strain and it’s response to external applied load depends strongly upon the manner in which the microdamage is distributed

 

? 2003 Elsevier Ltd. All rights reserved.

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a b s t r a c t

Objectives. Among the current mathematical models for bone remodeling, few can consider bone resorption due to overload. The objective of this paper is to develop a newbone remodeling

model which can simulate both underload and overload resorptions that often occur

in dental implant treatments

Methods. Based on the traditional model, a new mathematical equation relating the density

change rate with mechanical stimulus has been developed. The new equation contains

an additional quadratic term which can produce reduction in bone density at high load

levels. In addition, to fully exploit the characteristics of this model, a range of different bone

remodeling behaviors were studied under the load cases with both constant and varying

stress magnitudes. Finally, the model was applied in conjunction with the finite element

method to a practical case of dental implant treatment.

Results. The FE analysis results showed that bone resorption at the neck of the implant

occurred due to occlusal overload but then resorption stopped after some time before

reaching the coarse threads.

Meanwhile, the density of the bone deeper into the mandible increased slightly due to

the additional mechanical stimulus provided by the occlusal load. This phenomenon is

observable in some clinical situations.

Significance. The new model can describe the bone overload resorption, a feature which is

absent in most of the current models. And by simulating the dental implant treatment using

FE method, the ability of the new mathematical model to simulate overload bone resorption

has been clearly demonstrated.

 

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Abstract

Bone is maintained through a coupled process of bone resorption and bone formation, in a continuous process called bone remodeling. An imbalance in this process caused by disease, abnormal mechanical demands, or fatigue may predis-

 

pose bone to fractu re injuries. The remodeling process is generally viewed as a material response to functional demands Here, we propose a new set of constitutive equations for the bone remodeling proces and contains the specific surface,s .

instead of volume fraction, and the degree of microcracking in the constitutive equations. The rate of remodeling is related to mechanical stimuli, free surface density and a microcrack factor. In this approach, the effect of mechanical stimuli, rate

of mechanical stimuli, and integration of mechanical stimuli on bone remodeling can be evaluated simultaneously in theremodeling equation. Specific examples are given for illustration of the model

.

2006 Elsevier Ltd. All rights reserved.

 

Keywords: Bone remodeling; Free surface; Microcracks; Elasticity

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Abstract

In this paper, we introduced a high-order non-linear equation of bone remodeling to combine with FEM by introducing two nonlinearities, i.e. the remodeling coefficient BðtÞ and the order of non-linear remodeling equation. The influence of each non-linearity was tested based on its mechanical and physiological implications discussed. We use two finite element models to investigate the influences of non-linearities in this equation: a plate subjected to a ramp load, and a 2D model of the cross-section of a vertebra. By importing the idea of topology optimization in engineering, their external shapes and internal density distributions were simulated from unfixed configurations. To a certain extent, the high-order non-linear equation of bone remodeling we suggested here can control the remodeling processes of bones in different stages of growth or at different anatomic sites more effectively, and make it that bone’s best morphology is adapted to its mechanical environment. Furthermore, it is likely to describe the process of bone growth and evolution

.

Ltd. All rights reserved.r 2002 Elsevier Science

Keywords: Bone remodeling; Finite element method; High-order non-linear; Bone;

Topology optimization

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After nearly 25 years of work in skeletal anatomy, adaptation, and orthopaedics,Julius Wolff published his seminal 1892 work on bone 'transformation' (known today as bone remodeling and modeling). Wolff's work and his general view of how a limb bone's morphology develops has evolved into a nebulous concept known as "Wolff's law", which is essentially the observation that bone changes its external shape and internal (cancellous) architecture in response to stresses acting on it. Although the rationale for the existence of Wolff's law has been challenged on many fronts (e.g., Bertram and Swartz, 1991; Cowin, 1997; Currey, 1997; Cowin, 2001), many contemporary investigators still ascribe to the idea that there is a "Wolff's law" that states that bone models and remodels in response to the mechanical stresses it experiences so as to produce a minimal-weight structure that is 'adapted' to its applied stresses.

For example, should a fracture of a weight-bearing long bone heal with an angulation, each step that the patient subsequently took would result in a bending stress with compression on the concave side at the angulation and tension on the convex side. Rather than progressively weaken the bone structure at this site, such repeated mechanical stress results in a modeling and remodeling, with new bone growth on the concave side and bone resorption on the convex side. If the patient is young enough, the bone will ultimately grow straight. In control-system terms, the applied mechanical stress causes a growth response that negates the applied stress -- a closed-loop negative-feedback control system.

Many authors have made relevant observations regarding the phenomena of bone modeling and remodeling. An orthopaedic surgeon named Harold Frost made the following salient points:

Remodelling is triggered not by principal stress but by "flexure".

Repetitive dynamic loads on bone trigger remodelling; static loads do not.

Dynamic flexure causes all affected bone surfaces to drift towards the concavity which arises during the act of dynamic flexure.

To define some basic terms of bone growth, we have compiled the following list of characteristics in the formation (osteogenesis), modeling and remodeling of bone.

Osteogenesis

  • Bone formed on soft tissue


  • Occurs during embryonic development, early stages of growth, and during healing


  • Two major subclassifications: intramembranous ossification and endochondral ossification


  • Intramembranous: bone formed on soft fibrous tissue


  • Endochondral: bone formed on cartilage


  • Osteoblasts derived from mesenchymal cells act indepdendent of osteoclasts


  • Potential to create large amounts of bone


Modeling

Bone formed on existing bone tissue

Occurs during growth, and during healing

Osteoblasts and osteoclasts act independently at different sites

Potential to create or resorb large amounts of bone

Remodeling

Bone both resorbed and formed at the same site

Occurs from growth through death.

The only normal physiologic mechanism for altering bone structure in adult skeleton

At best leads to maintenance of bone; however as we age leads to net loss of bone (osteoporosis)

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Phenomenology

The relationship between the mass and form of a bone to the forces applied to it was appreciated by Galileo (4.1.1), who is credited with being the first to understand the balance of forces in beam bending and with applying this understanding to the mechanical analysis of bone. Julius Wolff (4.1.2) published his seminal 1892 monograph on bone remodeling; the observation that bone is reshaped in response to the forces acting on it is presently referred to as Wolff's law. Many relevant observations regarding the phenomenology of bone remodeling have been compiled and analyzed by Frost (4.1.3,4.1.4). Salient points are as follows:

1. Remodelling is triggered not by principal stress but by "flexure".

2. Repetitive dynamic loads on bone trigger remodelling; static loads do not.

3. Dynamic flexure causes all affected bone surfaces to drift towards the concavity which arises during the act of dynamic flexure.

These rules are essentially qualitative and they do not deal with underlying causes. A critique of these ideas has been presented by Currey (4). Additional aspects of bone remodeling may be found in the clinical literature. For example, after complete removal of a metacarpal and its replacement with graft consisting of a strut of tibial bone, the graft becomes remodelled to resemble a real metacarpal; the graft continues to function after 52 years (4.1.5). In the standards of the Swiss Association for Internal Fixation it is pointed out that severe osteoporosis can result from the use of two bone plates in the same region as a result of the greatly reduced stress in the bone (4.1.6). Pauwels (4.1.7) suggested that as a result of bending stresses the medial and lateral aspects of the femur should be stiffer and stronger than the anterior and posterior aspects. Such a difference has actually been observed (4.1.8). Large cyclic stress causes more resorption than large static stress (4.1.9). Immobilization of humans causes loss of bone and excretion of calcium and phosphorus (4.1.10). Long spaceflights under zero gravity also cause loss of bone (4.1.11,4.1.12); hypergravity induced by centrifugation strengthens the bones of rats (4.1.13,4.1.14). Studies of stress-induced remodeling of living bone have been performed in vitro (4.1.15). Recently, in vivo studies in pigs (4.1.16) were conducted. In this study, strains were directly measured by strain gages before and after remodelling. Remodelling was induced by removing part of the pigs' ulna so that the radius bore all the load. Initially, the peak strain in the ulna approximately doubled. New bone was added until, after three months, the peak strain was about the same as on the normal leg bones. In vivo experiments conducted in sheep (4.1.17) have disclosed similar results. It is of interest to compare the response time noted in the above experiments with the rate of bone turnover in healthy humans. The life expectancy of an individual osteon in a normal 45 year old man is 15 years and it will have taken 100 days to produce it (4.1.18, 4.1.19).

Remodelling of Haversian bone seems to influence the quantity of bone but not its quality, i.e. Young's modulus, tensile strength, and composition(4.1.20). However the initial remodelling of primary bone to produce Haversian bone results in a reduction in strength (4). As for the influence of the rate of loading on bone remodelling, there is good evidence to suggest that intermittent deformation can produce a marked adaptive response in bone, whereas static deformation has little effect (4.1.16). Experiments (4.1.21) upon rabbit tibiae bear this out. In the dental field, by contrast, it is accepted that static forces of long duration move teeth in the jawbone. In this connection, (4.1.22) the direction (as well as the type) of stresses acting on the bone tissue should also be considered. Currey (4) points out that the response of different bones in the same skeleton to mechanical loads must differ, otherwise lightly loaded bones such as the top of the human skull, or the auditory ossicles, would be resorbed.

Failure of bone remodeling to occur normally in certain disease states is of interest: for example, micropetrotic bone contains few if any viable osteocytes and usually contains a much larger number of microscopic cracks than adjacent living bone (4.1.23). This suggests that the osteocytes play a role in detecting and repairing the damage. In senile osteoporosis, bone tissue is removed by the body, often to such an extent that fractures occur during normal activities. Osteoporosis may be referred to as a remodelling error (4.1.4).

Some theoretical work, notably by Cowin and others (4.1.24), has dealt with the problem of formulating Wolff's law in a quantitative fashion. In this theory, constitutive equations are developed, which predict the remodelling response to a given stress. Stability considerations are invoked to obtain some constraints on the parameters in the constitutive equation.

4.2 Feedback mechanisms

Bone remodeling appears to be governed by a feedback system in which the bone cells sense the state of strain in the bone matrix around them and either add or remove bone as needed to maintain the strain within normal limits. The process or processes by which the cells are able to sense the strain and the important aspects of the strain field are presently unknown. Bassett and Becker (4.2.1) reported that bone is piezoelectric, i.e. that it generates electric fields in response to mechanical stress; they advanced the hypothesis that the piezoelectric effect is the part of the feedback loop by which the cells sense the strain field. This hypothesis obtained support from observations of osteogenesis in response to externally applied electric fields of the same order of magnitude as those generated naturally by stress via the piezoelectric effect. The study of bone bioelectricity has received impetus from observations that externally applied electric or electromagnetic fields stimulate bone growth (4.2.2). The electrical hypothesis, while favored by many, has not been proven. Indeed, other investigators have advanced competing hypotheses which involve other mechanisms by which the cells are informed of the state of stress around them.

For example, inhomogeneous deformation at the lamellae may impinge on osteocyte processes and thus trigger the osteocytes to initiate bone formation or remodelling (4.2.3). Motion at the cement lines was observed and it was suggested that such motion could act as a passive mechanism by which bone's symmetry axes may become aligned to the direction of time averaged principal stresses (2.9.9). Stress on bone may induce flow of fluid in channels, e.g. canaliculi, and such flow could play a role in the nutrition and waste elimination of osteocytes, which may be significant in bone remodeling (4.2.4). In a related vein, theoretical arguments have been presented in support of the hypothesis that bone cells are directly sensitive to hydrostatic pressure transmitted to them from the bone matrix via the tissue fluid (4.2.5). Although no experimental test of this direct pressure hypothesis has been published, we observe with interest that direct hydrostatic pressure has recently been observed to alter the swimming behavior of paramecia, possibly by means of action upon the cell membrane (4.2.6). Otter and Salman found that a hydrostatic pressure of 68 atm abolishes the reversing of direction of swimming, 170 atm stops swimming, and 400-500 atm irreversibly damages the cell. We observe that 100 atm corresponds to 1400 psi stress, or in bone, a strain of 0.07% which is in the normal range of bone strain. 500 atm corresponds to 7000 psi or a strain of 0.35%, well above the normal range of bone strain. Stress in bone also results in temperature differences between osteons (4.2.7); the cells may be sensitive to sudden temperature changes during human activity. A mechanochemical hypothesis has been advanced, in which the solubility of calcium may be affected by stress in the bone matrix (4.2.8). Strain energy in bone might also influence the energetics of bone mineral nucleation (4.2.9). It has also been suggested that remodelling may be initiated in response to microcracks generated by mechanical fatigue of bone (4.2.10). In summary, many hypotheses have been proposed for the mechanism by which appropriate cells sense the state of strain in bone, but little or no experimental evidence is available to discriminate among them.

4.3 Cellular and biochemical aspects of bone remodelling

The adaptive response of bone to mechanical stimuli is mediated by living cells. A great deal is known concerning bone cell function and its control by ionic and hormonal factors, but little is known concerning the effect of mechanical strain in bone upon the biochemistry of its cells. Rasmussen and Bordier (4.3.1) have presented an extensive review of studies of bone cell physiology. Recently, the biochemical consequences of electrical stimulation of bone have been reported (4.3.2). Biochemical steps associated with cell activation are as yet poorly understood, but ion fluxes appear to play a role (4.3.3). Cyclic nucleotides mediate the effects of extracellular signals(4.3.4) and prostaglandins modulate them (4.3.4). Prostaglandin E 2 has been hypothesized to mediate bone resorption in trauma, malignancy, and periodontal disease. This prostaglandin, as well as the cellular constituents cyclic AMP and cyclic GMP, has been found in association with regions of bone stimulated electrically (4.3.2).

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