Basic definitions

A bone can experience four types of loading: tension/compression, shear, torsion, and bending. The first two are linear loads and the last two are angular loads .

The mandible is subjected to forces produced by the muscles of mastication and by reaction forces acting through the teeth and temporomandibular joints. The mandible undergoes deformation as a result of these external loads. Stresses and strains are produced, the distribution of which depends on the nature of the external loads and the material properties and geometry of the mandible. The amount of deformation is quantified by the amount of strain, which is defined as the ratio of the change in length to the original length of the structure under deformation. Strain is specific to a point and a direction in the structure and is dimensionless, although it is sometimes expressed as a percentage . Tensile and compressive loads occur in bone tissue as a result of deformation, and are quantified as the amount of stress in force per unit area in a structure (unit Nm ⁻² or Pa). Depending on how it is applied, a load can be classified as causing tensile, compressive or shear stress. Tensile stress occurs if the bone becomes longer, compressive stress occurs when the bone becomes shorter, and shear stress occurs when one region of the bone moves in parallel relative to an adjacent region.

The stress–strain relationship of a material or tissue (in this case bone) can be described by a stress–strain curve ( Fig. 1 ) that demarcates the regions of elastic and plastic deformation. Within the elastic region, bone will return to its original length when the load is released; in the plastic region, the stress will cause permanent deformation to the bone structure. The Young’s modulus (or elastic modulus) E is defined as E = σ/ε , where σ is the stress and ε the strain, and the unit is the Pascal (Pa). It is also the slope of the elastic region, which is a measure of the ability of bone tissue to resist deformation. The shear modulus G is a measure of the ability of bone to resist shear stress in a particular plane, and tends to be 1/3 to 1/2 of the value of E . The shear modulus is defined as G = τ/γ , where τ is the shear stress and γ the shear strain .

The stress-strain curve.

When bone is deformed, it becomes shorter or longer (primary strain) and thinner or thicker in a direction perpendicular to the direction of the deforming force (secondary strain). The Poisson’s ratio, ν , is a measure of the ability of a structure to resist deformation in a direction perpendicular to the applied load, and is defined as ν = ε _y / ε _x , where ε _y is the secondary strain and ε _x the primary strain. The relationship between a load placed on bone and the resulting deformation within the elastic range is described by the elastic constants of the bone material (the elastic modulus, shear modulus and Poisson’s ratio). A material is termed isotropic if its elastic constants or mechanical properties are the same in all directions. If the mechanical properties of a material are different in different directions, the material is called anisotropic. If there is a difference between these properties in all three perpendicular directions, the material is known as orthotropic. When an orthotropic material has properties that are the same in two of the three directions, it is known as transversely isotropic.

On the stress–strain curve, the yield strength of a material is the stress at the yield point beyond which permanent deformation occurs and the material does not return to its original shape. The ultimate strength is the maximum stress that a material can sustain, and the breaking strength is the stress at which the material breaks. In bone, the value of the breaking strength is usually the same as the value of the ultimate strength, depending on the direction, location, or type of stress. The (absolute) ultimate compressive stress of bone is higher than its tensile stress and shear stress. The biomechanical behavior of a bone structure depends on that structure’s material properties and geometry.

Material properties of mandibular bone

Studies show that mandibular cortical bone is stiffer along the lower border of the body than the alveolus. The direction of maximum stiffness in the body is parallel to the occlusal plane, whereas the maximum stiffness in the ramus is vertical. The longitudinal elastic modulus increases from the molar region to the symphysis and the lingual cortex is stiffer than the buccal cortex in the symphysis and premolar regions. According to V an E ijden , the material properties of mandibular cortical bone were measured by Dechow and Arends and Sigolotto. It was found that the elastic moduli, shear moduli and Poisson’s ratio were different in three directions: longitudinal, radial and tangential. The results of these studies show mandibular cortical bone to be anisotropic.

According to M isch et al. , the anterior mandible has a greater trabecular bone density, which correlates with its greater elastic modulus and compressive strength than other regions. The presence of the cortical plate increases the elastic modulus of the trabecular bone in all regions, with the anterior mandible having the highest values. When cortical bone was present, the elastic modulus ranged from 24.9 to 240 MPa with a mean value of 96.2 MPa . When the cortical bone was absent, the elastic modulus ranged from 3.5 to 125.6 MPa. The ultimate compressive strength of the trabecular bone ranged from 0.22 to 10.44 MPa (mean 3.9 MPa). These data show that the cortical bone plays a major role in dissipating occlusal loads. The trabecular bone of the mandible also has anisotropic properties .

Methods for studying the mechanics of the mandible

In vivo and in vitro deformation of the mandible and the elastic forces exerted on it have been studied using various methods, including free body analysis, in which simple free body diagrams offer a vectorial depiction of hypothesized external loads that enable a rough approximation of the internal forces; the use of a photoelastic resin as a coating on the mandible or as a replica of the mandible to study the internal stress pattern under various forms of loading; the use of strain gauges, which are glued to the external surface of cadaveric or animal mandibles and used to measure the direction and magnitude of strains under loading; and mathematical modeling using finite element analysis (FEA) to analyze the distribution of stress throughout the mandible and the effects of changes in loading and patterns .

Each of these methods has its disadvantages. Free body diagrams are limited to simple analysis of the force distribution and do not cope well with more detailed analysis. The use of photoelastic resin suffers from the problem that the mechanical properties of plastic are different from those of bone. Much of the information on in vivo forces has come from the use of strain gauges, yet the readings only reflect strains on the superficial surface of the bone. It is not possible to perform strain gauge experiments on humans in vivo, and therefore data gathered from animal studies in vivo have to be extrapolated to humans. The studies of D echow and H ylander and D echow et al., for example, have shown that the elastic properties of the macaque mandible are similar to those of the human mandible. Finite element analysis can provide precise data on stress distributions, but is limited to static situations, and most studies that use this method have tended to assume that the mandible is isotropic, rather than anisotropic, to simplify the calculations. The accuracy of finite element analysis in describing the biomechanical behavior of bony specimens has been shown by many authors . Combining a finite element model with the use of strain gauges applied to the bone surface to validate the accuracy of the calculations has resulted in accurate models .

Forces acting on the mandible during function

According to M eyer et al., Champy and co-workers described a zone of tension in the alveolar part of the mandible and a zone of compression on the lower border. This information allowed ideal lines for mandibular internal fixation to be identified along the physiological tension lines ( Fig. 2 ). When placed along these lines, plates produced stable fixation when function was resumed in accordance with the principle of cross bracing, thus reducing the size of the plate needed .

Mandible and Champy’s ideal lines of internal fixation.

M eyer et al. studied bone deformation in the region of the mandibular condyle during mastication using cadaveric mandibles coated with photoelastic resin. They identified tensile stress patterns along the anterior border of the ramus and in the zone below the sigmoid notch, and compressive stress patterns along the posterior border of the ramus. These findings suggest that the mandible is subjected to sagittal forces that tend to straighten the mandibular angle.

According to V an E ijden when the muscles of mastication contract to bite and clench, the mandible is bent in a sagittal plane ( Fig. 3 ). This bending is produced by the vertical components of the muscle forces, the joint reaction forces and the reaction forces from the chewing action. The magnitude of sagittal bending moments and shear forces depends on the points of application and the moment arms of the muscle and bite forces. The largest shear forces occur between the bite force and the muscle force on the working side, and between the muscle force and the joint force on the balancing side. Sagittal bending results in a zone of tension on the lower border and a zone of compression on the upper border on the working side, with the reverse occurring on the balancing side. The amount of sagittal bending is usually equal bilaterally on both mandibular bodies during incisal biting. When there is unilateral loading, the deformation of the working sides and balancing sides differs.

Distortion of the mandible during unilateral molar loading. The distortion of the mandibular body can be described as a combination of sagittal bending, torsion and lateral transverse bending.

Using a finite element model, K orioth et al. reported the predominant sagittal bending of the balancing side of the mandibular body, as opposed to sagittal bending and torsion on the working side body. They found that this torsion resulted in the narrowing of the mandibular arch (parasagittal and transverse deformation) on clenching and incisal biting. This was caused by torque produced by the elevator muscle force of the mandible acting laterally to the long axis of the mandible and the bite force acting medially to the axis. The bilateral torsion of both the mandibular bodies results in bending at the symphyseal region, which leads to compression at the superior margin of the symphysis and tension at the inferior margin.

H ylander suggested that the mandibular symphysis undergoes three patterns of stress and deformation ( Fig. 4 ): corporal rotation, which is the relative outward rotation of the two halves of the mandible; medial convergence, which describes a change in mandibular width during function; and dorso-ventral shear, which involves the movement of the two halves of the mandible relative to one another in the vertical plane.

Patterns of stress and deformation at the mandibular symphysis. Jaw deformation during function. MC, medial convergence; CR, corporal rotation; DVS, dorso-ventral shear.

Late in the power stroke of biting and clenching, lateral transverse bending occurs and the bending moment increases from back to front to reach its maximum magnitude near the symphysis. This lateral bending produces compressive stress at the buccal cortex and tensile stress at the lingual surface. Using a finite element model, K orioth et al. calculated the maximal deformation of the mandible to be approximately 0.6 mm in a simulated unilateral molar bite of 526 N. They observed the helical deformation of the mandible upward and toward the working side during this simulated bite, with regions experiencing high magnitudes of tensile stress (15–25 MPa) running down and forward buccally and lingually from the anterior aspect of the coronoid processes and rami to meet at the lingual surface of the symphysis. The highest values of compressive stress (15–25 MPa) were found at the bite point and both sigmoid notches, at the working side mandibular angle, and in an area running from the posterior aspect of the balancing side ramus along the lower border of the body to the lower symphysis and up along the buccal aspect of the alveolar bone to the bite point. The shear stresses were generally larger on the working side, although the peak shear stress value of 25 MPa was found on the condyle of the balancing side. The lingual cortical surface at the symphysis experienced higher magnitudes of tensile strain than the buccal cortex. The strains at the posterior molar regions were smaller than those at the symphysis. In general, the levels of strain during chewing are smaller than those during static biting, and bone strain values are generally larger on the working side than on the balancing side.

A l -S ukhun and K elleway calculated the maximum stress values as predicted by a finite element model in the human mandible during maximum jaw opening, right and left lateral excursions and protrusion. The predicted medial convergence ranged between 14.4 and 58.4 μm, with the maximum value occurring during for protrusion. The corporal rotation and dorso-ventral shear ranged between 0.4 and 2.7 degrees. The areas of maximum stress occurred in the region of the condylar neck, mandibular angle, sigmoid notch and symphysis.

Fracture behavior of the human mandible

U nnewehr et al. determined the fracture threshold (breaking strength) of the human mandible to be 2.4–3.1 kN for frontal impacts to the chin and 0.6–0.7 kN for lateral impacts to the body of the mandible. According to the finite element model of Gallas T orreira and F ernandez , the maximum stress areas following a simulated blow (10 MPa) to the symphyseal region are located at the symphysis and in the bilateral retromolar and condylar regions. Conversely, following a blow to the mandibular body, the maximum stress areas occur at the contralateral angle and the ipsilateral body and in the ipsilateral condylar neck region.

Methods of reconstruction

Any attempt to reconstruct a mandible following a continuity defect would ideally need to reconstruct the height and shape of the missing part anatomically, to allow the replacement of missing dentition, to withstand the forces that act on the mandible in normal functioning, to have a similar fracture threshold to the intact mandible or preferably exceed it, to allow early or immediate masticatory function, to allow normal sensation to the lips and tongue, to be simple, flexible, and cost effective and to be able to sustain repeated loading.

The chief methods proposed for mandibular reconstruction include the use of free bone grafts, pedicled bone grafts, particulate cancellous marrow grafts, vascularized free bone flaps or tissue engineered bone, the use of reconstruction plates for bridging recent defects either temporarily or indefinitely, and recently, the TL (Tideman-Lee) modular endoprosthesis .

Few of these methods allow for immediate or early function. This is mainly due to the use of bone plates and screws, which requires time for the bone to heal before loading can occur and normal mastication can resume. Consequently, patients may be put on a prolonged soft diet and may have to wait for months before dental rehabilitation is completed.

Change in bite forces

Occlusal forces are generally classified as swallowing, chewing or maximum bite forces. The maximum bite force in the mandibular body region for healthy dentate patients ranges from 15.7 to 4341.4 N, depending on age, gender, and the method of measurement. The mean body swallowing force for dentate patients ranges between 1.7 and 296 N, and the mean body chewing force ranges from 15.7 to 261.7 N. Among edentulous patients, the maximum bite force ranges from 28 to 190 N, and the chewing force ranges from 8.8 to 49.9 N. The bite force of patients is reduced following partial or composite resection of the mandible . M aurer et al. measured the chewing force of patients who had undergone mandibular reconstruction, and found a reduction of 76% in the bite force in the molar region and 59% in the incisor region.

Changes in the ageing population

An older patient is more likely to have a poorer blood supply in the oro-facial tissues and also more likely to have other co-morbidities that might increase the risk of anaesthesia and exacerbate other risks. The current ideal standard of a free vascularized flap might not be feasible in all cases. There might be a corresponding loss of bone mineral density due to osteoporosis. Such patients might also have impaired dentition or edentulous regions, which are atrophic. Considerations for mandibular reconstruction may range from free vascularized flap in relatively healthy patients to using a load-bearing reconstruction plate to bridge any defects.

Reconstruction plates for bridging mandibular defects

The use of reconstruction plates to maintain the space and contours of the mandible without bone grafting is sometimes necessary for patients with poor health or advanced cancer, but there are frequent reports of complications with this procedure, such as screws loosening, plate exposure and plate fractures. The size and location of the defect and the crossing of the mandibular midline are the main causes of these complications . The masticatory loads on the plates cause vertical discrepancies that can lead to bone resorption and screw loosening. A rden et al. reported that extirpative losses of more than 5 cm of bone are associated with unacceptably high complication rates of 81% when plates alone are used to repair lateral defects .

According to M artola et al., a principal reason for plate fractures is the residual stresses generated through plate bending during surgery, which may affect the mean stress in fatigue loading. Y i et al. studied the stress distribution of mandibles reconstructed only with reconstruction plates using photoelastic models and conducted a retrospective follow-up of 68 patients. They found that most of the plate fractures occurred 1–2 years after operation, and that all occurred at the mandibular angle. The regularity of the stress distribution was similar when 2, 3 and 4 screws were used for fixation on each side of the plate, but the maximum stress value at the edge of the screw holes was inversely proportional to the number of screws used. Screw loosening occurred more frequently in the proximal fragment, at areas with high stress concentrations (the chin and angle), and in the screws nearest and farthest from the resection margins. The bony trabeculae of the mandible are arranged to cushion the forces transmitted from the teeth to the bone, but the forces applied to the bone via screws, which can be described as bending moments and shear forces, will not be so cushioned, as their trajectories are different to those transmitted by dentition. This means that bone resorption occurs around the screw threads when the external forces exceed the limits that bone can withstand. According to K imura et al., there is a potential for plate bowing on loading in large defects of the mandible, and thus a third intermediate screw should be placed close to the crucial screw, which is the screw at the distal end of the mandibular stumps.

K noll et al. found that the stresses in angle defects bridged by standard 2.7-mm reconstruction plates with a linear screw configuration were far in excess of the material strength of titanium and cortical bone. This leads to the fatigue fracture of the plate, loss of bone and the gradual loosening of the screws. As a solution, they recommended the redesign of the plate to maximize the interface between bone and plate by allowing a triangular or square screw configuration.

The early reconstruction plates were non-locking and necessitated good plate adaptation, which was difficult due to the thick and stiff nature of the plate. Failure to get good adaptation created a translation of pressure through the plate into the underlying bone when the screws were tightened. This led to bone resorption over a long period and loosening of the plate. By locking the screw to the plate, as in locking reconstruction plates, a single functional unit is created which minimizes pressure transmission to the bone; thus combining the benefits of an external fixator with an internal plate. S chupp et al. compared the performance of 2.4-mm locking plates with 2.4-mm and 2.7-mm reconstruction plates for bridging small segmental defects, and found that the locking plates and screws had greater long-term stability than the 2.4-mm reconstruction plates. A 1-mm gap between the bone and locking plate had no effect on stability. The 2.7-mm reconstruction plates were more stable, but were difficult to contour and were more susceptible to complications if they were not well adapted. The effect of plate adaptation was investigated by H aug et al., who found that the degree of plate adaptation had an effect on the mechanical behavior of non-locking plates but did not affect the locking system. The failure strength of 2.0 locking plates was compared with that of conventional 2.0 mm plates by C hiodo et al. The force of failure for the non-locking plates was 599.9 N compared with 637.8 N for the locking plates, although the difference was not statistically significant.

Vascularized free bone flaps

Mandibular reconstruction with vascularized osteocutaneous, osteofasciocutaneous or osteomyocutaneous free flaps has the best success rates because of the rapid bone healing and revascularization that occurs due to the lack of requirement for the creeping substitution of free bone grafts. The procedure involves a prolonged operating time and significant morbidity for the patient.

Various types of free-flaps have been proposed, including the fibula, scapular and iliac crest free-flaps. With the exception of the iliac crest free-flap, most free-flaps lack sufficient bone height and width to support dental implant placement in order to satisfy requirements for implant length–crown height ratio without needing additional bone grafting or distraction osteogenesis procedures. The fibula free-flap and iliac crest free-flap remain the flaps of choice if dental implant placement is planned, depending on the size and length of the defect. S eikaly et al. compared the dimensions and biomechanical properties of bones commonly used in oro-mandibular reconstruction, measuring the dimensions of mandibles, fibulae, iliac crests, scapulae, clavicles, second metatarsals, radii and anterior ribs from cadavers and performing three-point breaking strength and screw pulling force tests on all of the bones. They concluded that the fibula best matches the material properties of the mandible.

T ie et al. compared the biomechanical effects of using fibula and iliac crest free-flaps using a three-dimensional finite element model. The stress distribution for mandibles reconstructed with iliac crest free-flaps was similar to that of the normal mandible, whereas mandibles reconstructed with fibula free-flaps experienced greater stresses on the grafted bone, with the maximum stress at the graft/mandibular bone interface. The principal stresses in the grafted bone were tensile or compressive. The iliac crest free-flap displays better biomechanical performance because the iliac crest has a more similar structure to the mandible than the fibula, which is mainly cortical bone, and because of the greater binding area between the residual mandible and the iliac crest, a property that favors better bite force transmission. T ie et al. concluded that the iliac crest free-flap is a better option for mandibular reconstruction for smaller defects, whereas the fibula free-flap may be more appropriate for larger defects due to the greater quantity of available bone.

Tissue-engineered bone transplant and growth factors

Tissue-engineered bone is a relatively new method that uses a scaffold of usually resorbable material seeded with engineered bone marrow stromal cells and osteogenic factors. This is implanted into the defect to reconstruct the mandible. This method can potentially eliminate the morbidity associated with the harvesting of free-flaps, but it entails microvascular anastomosis and a period of immobilization to allow healing before full function is resumed. The use of osteogenic growth factors to enhance bone healing and formation also raises concerns about their oncogenic potential and unknown long-terms effects. The use of tissue-engineered bone for routine clinical applications is still far from being realized.

Several authors have studied the material properties of tissue-engineered bone. T oriumi et al. studied the effects of placing human recombinant bone morphogenetic protein-2 (BMP-2) in the mandibular defects of dogs and noted good bone growth in defects where BMP-2 was placed. Three-point bending tests of the newly formed bone were 27% that of the normal mandible 6 months after operation, compared with 0% in defects in which nothing had been placed. The effects of osteogenic factors on bone formation in mandibular defects were investigated by K ontaxis et al. and A bu -S erriah et al., who found that there were wide variations in the quality and mechanical properties of the newly formed bone and variable degrees of healing.

W illiams et al. showed that it is possible to design and accurately fabricate a polycaprolactone scaffold with porous architecture that has suitable mechanical properties using selective laser sintering. The scaffolds that they designed had compressive modulus values of 52–67 MPa and yield strength values of 2–3.2 MPa, which are within the lower limits for trabecular bone.

According to W arnke et al., tissue-engineered bone transplants have a similar stability to natural bone when subject to mechanical compression. H e et al. reported that autogenous cultivated bone marrow stromal cells seeded into a three-dimensional tricalcium phosphate scaffold yielded better results than the insertion of just the scaffold itself (control) into small segmental defects of the mandible. The engineered bone had a greater compressive strength and stress of 102.7 N and 3.504 N/mm, respectively, compared with 42.9 N and 1.930 N/mm in the control.

Modular endoprosthesis

T ideman and L ee introduced the concept of modular endoprosthesis as an effective replacement for the lost part of the mandible. This method, which has been used with great success in orthopedic surgery, entails the cementation of stems into the remnant stumps of the mandible with acrylic bone cement, and the connection of the stems with modules via locking systems. The technique allows immediate accurate three-dimensional replacement of the lost part of the mandible, and once the bone cement has set immediate function is possible because no screws are involved. The acrylic bone cement acts as a grout and transfers load from the prosthesis to the bone as uniformly as possible. The biomechanical performance of this new method merits further investigation.

In conclusion, the biomechanical behavior of the mandible has been studied and described by many authors using a combination of animal testing, photoelastic experiment and mechanical modeling. There is no ideal solution for mandibular reconstruction. The mechanical strength of, and forces exerted on, reconstructed mandibles are complex and not fully understood. Excessive stress on traditional bone grafts and metal plates causes plate fracture, loosening of the screws and bone resorption, which leads to potential fracture of the mandible. Newer methods of mandibular reconstruction have been explored with varying degrees of success, but it remains to be seen whether these methods can withstand the mechanical forces acting on the mandible in the long term.