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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); hyper gravity 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). By contrast, 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: orthodontic wires and appliances apply such forces. Dynamic forces due to chewing are superposed on such static force. Chewing forces may be modified by the presence of an orthodontic device. 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). By contrast, exercise stimulates bone growth. Athletes have stronger bones in the body regions most affected by exercise.
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 micro cracks 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 areas 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 E2has 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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