Physiological Bone Loading in the Human Head and
Prosthesis Size Estimation
José Eduardo MAY
,
D.Sc. Instituto Nacional de Pesquisas Espaciais, [email protected]Thais de Paula BUSQUIM
,
D.Sc. Biomecanica, [email protected]Carlos Nelson ELIAS*.
D.Sc. Instituto Militar de Engenharia, [email protected]Bruno José Silva de OLIVEIRA
.
B.Sc.Universidade Federal São Carlos, [email protected]Matheus GABOARDI
,
Universidade Federal de São Carlos, [email protected]Celso Roberto RIBEIRO
.
D.Sc. LABMAT,[email protected]*corresponding author. Phone 55-21-2546-7244 E-mail address: [email protected]
Abstract-- Medical device manufacturers are supposed to establish and maintain procedures to control the design of the devices in order to ensure that specific requirements are met. The essential aspects and the regulatory requirements, such as safety, performance, and biocompatibility of a product are established during the design and development phases. Inadequate design can be a major cause of failure of medical devices. Despite a large number of reports on medical device failures, there are no authoritative guidelines for the management of orthopedic fracture fixation. A lack of consensus exists among orthopedic trauma surgeons and manufacturers in the management of these fractures. The design must ensure that devices conform to user needs and intended uses and include testing of production units under actual or simulated conditions of use. For the development of any medical device, the manufacturer needs information about the level of physiological loading. In the case of orthopedic fracture fixation, the values of loading fracture fixation devices not clearly defined in the literature and technical standards. The purpose of this paper is to provide the necessary data of physiological bone loading in the human head (mandible, maxilla, teeth, skull and middle third of the face) for the development of products used in fracture fixation.
Index Term-- Bone loading; physiological loading; prosthesis size estimation.
1. INTRODUCTION
In general, the fracture of a bone produces a situation of complete mechanical instability of the human body. The mechanical effect induced by a fracture consists primarily of a loss of continuity of the bone, resulting in pathological mobility and loss of bone support. This traumatic discontinuity ruptures blood vessels in and around the bone and releases agents that promote bone healing. Thus, although fracture is a purely mechanical process, it initiates important biological reactions [1], such as bone resorption and bone formation. Consequently, untreated fractures may stabilize in a condition that leads to shortening and lack of alignment of the bone and may impair motor function.
In the treatment of fractures, a procedure to restore the alignment and subsequent stabilization of the limb is characterized by absolute or relative stability. Although the rigidity of implants helps to reduce the mobility of the
fracture, the only technique that restricts the motion at the fracture site is interfragmentary compression. The absolute stability lowers the stress at the fracture site to allow direct healing without the formation of visible bone callus.
Flexible surgical fixation of the fracture with plates or rods allows micromotions between the fracture fragments with the application of stresses at the fracture site. The consolidation of a fracture under flexible or unstable condition typically occurs by formation of a callus that mechanically unites bone fragments. Callus healing can be divided into four phases: inflammation, soft callus formation, hard callus formation and. finally. bone remodeling.
The selection of biomaterials for implants, plates and screws is based on biocompatibility. To define the dimensions of these devices one should know the mechanical properties of selected materials and the intensity of the expected load. Typically, the material properties are provided by the manufacturers. As to the intensity of loading, the values are not clearly defined in literature. This paper aims to provide the necessary data for the development of products used in fracture fixation. These values are useful for researchers, engineers and medical device manufacturers. The purpose of the present study is to establish validation criteria for orthopedic prostheses in the human head (middle third of the face, skull, maxilla, mandible and teeth) through biomechanical analysis of forces and stresses.
2. HEAD 2.1 Skull
Figure 1 illustrates the loading of a cranial bone flap. In the present work the physiological loading is calculated for five subregions: middle third of the face, skull, maxilla, mandible and teeth. These subregions differ as to the loads supported and the surgical techniques used in the reconstruction process.
In the skull subregion, it usually involves surgery to have access to the brain. In this type of intervention, the skull is sectioned to extract a block of bone that must be replaced at the end of the surgery; this procedure is called craniotomy. Replacement of the bone fragment usually requires attachment devices, such as plates, screws of bone flaps.
Surgical techniques recommend that movement of the cranial bone flap be minimized to allow bone healing. Assuming that the fixation system has to support the weight of the bone fragment, a reference value may be taken from the weight of the skull. According to Aerospace Medical Research
Laboratory [2] the head weight is about 4 kg (~40 N). The
weight of the complete skull is approximately 1.2 kg (~12 N). Assuming that at least half of this amount refers to the top of the skull and a craniotomy sections at least half of the skull, a weight of about 3 N must be supported by the fixation system. Figure 1 illustrates the loading of a cranial bone flap. In the skull we do not have any significant physiological loading.
2.2 Middle third of the face
In the region above the superior maxilla or middle third of the face, during reconstructive surgery after trauma or to correct anatomical deformities, the load that must be supported by attachment devices until bone healing takes place is the load due to the supporting bones. This hypothesis is reasonable, since surgical techniques advocate a maxillomandibular blockage after surgery. Since, according to Delille et al [3] the weight of the skull is approximately 1.2 kg (~12 N), the weight of bone for the middle third of the face is about 3 N. Thus, the plates and screws typically used in this subregion of the body must support 3 N. Figure 2 illustrates the loading in this subregion.
Fig. 2. Illustration of loading in the middle third of the face.
2.3 Superior Maxilla and Mandible
In the subregion of the mandible, plates and screws are also used for fixation during bone healing. Figure 3 shows the loading in this subregion.
Farwell et al [4] evaluated 184 patients who underwent 185 reconstructions of mandibular defects using vascularized bone grafts rigidly fixed with a reconstruction plate. The authors concluded that the use of reconstruction plates does not lead to complications such as plate fracture, exposure, infection or nonunion. Because of its lower profile and ease of application, the reconstruction plate is the reference for mandibular reconstruction.
Fig. 3. Illustration of loading in the mandible.
Chritah et al. [5] evaluated the system of rigid fixation plates with locking screws for reconstruction in patients with noncomminuted mandible fractures. The protocol added a 1-week period of maxillomandibular fixation to the three 1-weeks generally used in rigid miniplate fixation. The authors observed a rate of bone healing of 98 %. The application of miniplates with monocortical screws offers good surgical outcomes in most patients with minimal complications. The advantages of using miniplates include easy plate adaptability, small screw diameter, and provision of adequate load-sharing rigid fixation for simple, noncomminuted symphyseal and parasymphyseal mandible fractures.
Gear et al [6] evaluated the rigid plate fixation with locking-screws for reconstruction and treatment of noncomminuted fractures. They concluded that the use of maxillomandibular fixation with the use of locking plates is mandatory.
Doty et al [7] performed comparative tests of reconstruction plates and found values about 100 N for the mechanical yield displacement. Further analysis of the forces involved in cranio-maxillofacial movements was performed by Korioth and Hannam [8], which produced a model of the skull with muscles and bones through the finite element method and simulated the forces acting on mobile structures relevant for five clenching tasks.
Other regions, such as the middle third of the face, orbits, frontal, temple and skull, do not exhibit appreciable loading because they do not perform any active movement or the movements are small. The main loads in these regions involve the structures that are supported by soft structures of skull itself. In general muscle tissues induce low loads with the changes of facial expression during yawns and eye blinks. Therefore, attention should be directed to mandibular movements during chewing [8]. In this work, the intercuspal clenching was analyzed, along with the classical bite tap. After surgery, for about 10 days, the patient ingests only fluids or foods that require little effort. The permitted movements are controlled and involve physiotherapy. The relative amplitude of the movements are small and of low frequency.
Korioth and Hannam [8] suggested a mathematical equation to calculate the perpendicular force to the plane:
[XMI * K] * EMGMI = MIR (Equation 1)
where [XMI * K] is the weight factor and EMGMI is the scale
factor. The product of these factors yields to the components of orthogonal force.
observed that the greatest loading is on the surface of the masseter in intercuspal clenching and so this value (190.4 N) was taken as base value for the calculations that follow to determine the criteria for approval of plates for the above mentioned regions.
From the work of Naser-ud-Din [9], it was possible to find the dimensions of the masseter, including the average length of 56.2 mm. One half of this dimension provides the lever arm where the orthogonal force found by Korioth and Hannam [8] induces maximum moment involved in the movement of the intercuspal clenching. Based on this hypothesis, we have:
(Fort*L/2)/1000 = (190.4N*28.1 mm)/1000 = 5.35 Nm
(Equation 2)
where Fort is the orthogonal force and L is the total length of
the masseter muscle. We also have
Z
I
My
(Equation 3)where σ is the stress generated by the movement, M is the moment and Iz is the moment of inertia. The values of y and Iz
depend only on geometric factors related to the mandibular ramus, a bone structure just below the superficial portion of masseter, which is the main object of interest in this work. The value of the moment of inertia (Iz) may be determined using
the equation
12
3bh
I
Z
(Equation 4)where b is the length and h the thickness of the mandibular ramus. In this case, y = h/2. According to Naser-ud-Din [9], the base length b is 29.1 mm. The thickness h was cited by Monazzi et al [10], who determined the average thickness of mandibles of cadavers. According to Monazzi et al [10], h = 12.8 mm and thus y = 6.4 mm.
Using literature data and Equations 3 and 4, the theoretical stress is 6.73 MPa. This value depends on the moment combined with geometric factors of masseter and mandibular insertions. This is the most critical stress to which the bone in this region will be subjected. Likewise, as the plate acts parallel to the bone and also to the muscle, one can assume that the stress on the plate will be of the same order of magnitude (6.73 MPa).
2.4 Teeth - Dental Arch
In the dental arch region, it is known that the application of forces and moments on the teeth in order to induce movement must occur in a controlled manner. Since orthodontic movement depends on a process of resorption and bone growth, the forces imposed should respect the limits of each structure.
Labanauskaite et al [11] analyzed 415 articles published in PubMed between 1978 and 2005 about mini-implants performed for different purposes, including orthodontic treatment.
Lin et al [12] mention that the first commercial system of mini-implants was launched in 1997 by Dentisply. This work
evaluates the raw material (typically Ti-6Al-4V), length (from 4 to 12 mm), diameter (1.0 to 2.3 mm) and shape of the heads (holes for anchoring springs, wires, etc.), among other characteristics.
Mommaerts et al [13] report a study of minimplates for orthodontic anchorage and its advantages, as movements not possible with conventional orthodontic treatment with braces. According to Leung et al [14], the use of mini-implants for orthodontic anchorage does not replace conventional treatment with arches and braces, but significantly improves the mechanical treatment, allowing torques and movements not previously available. It may, in some cases, reduce the treatment time.
According to Choi et al [15], the normal forces applied by orthodontic anchorage plates are about 300 to 400 g or about 3 to 4 N. These same loads were reported by Brettin et al [16], citing loads of 0.3 to 4 N. There are cases of load application from 0.7 to 2 N (70 to 200 g) for teeth translation and 1.5 N for teeth intrusion. According to Von Fraunhofer et al [17], stainless steel springs (SS) can generate forces of 2.5 N either in compression or traction, while nickel titanium (NiTi) coil springs generate up to 1 N in traction or compression. Steel springs require about 1.3 N (130 g), while NiTi needs 0.7 N for each millimeter of distraction. The work of Serra et al [18] shows that the insertion torque of a 1.6 mm mini-screw into rabbit tibial metaphysis reaches values of 10.8 N.cm. The insertion torque into human mandible is of the same order. Based on literature data, the value of 6 N in bending may be used as a standard loading for a product aimed for orthodontic anchorage to correct deformities of the dental arch. As to torque, the value of 33 N.cm can be taken as reference. Figure 4 illustrates the action of loading to correct deformities of the dental arch.
Fig. 4. Loading to correct deformities of the dental arch.
2.5 Mandibular Distraction
Figure 5 shows an example of the loading applied during mandible distraction. In some anatomic correction procedures of the mandible, one needs a controlled distancing of the sectioned parts of the mandibular bone in order to induce distraction osteogenesis, the biological process of new bone formation between bone segments subjected to a stress.
Ilizarov [19] initiated the development of an apparatus for distraction osteogenesis. His external distractor consisted of bearings and wires attached to the bone segments and stretched at a rate of approximately 1 mm/day through four daily increments.
Takahashi et al [20] deal with distraction osteogenesis of the mandible for orthodontic treatment, dental crowding, using a tooth supported device, with excellent cosmetic and functional results.
Basa et al [21] used a bi-directional external distractor for the correction of a mandibular defect of major proportions. After one year of distraction consolidation it was observed that although the correct dimension was reconstituted, the volume of formed bone was not sufficient to restore the patient's anatomy. Thus, an auxiliary technique was used to ensure aesthetics.
Swennen et al [22] reported the use of a load of 9 N for maxillary distraction, uni- and bilaterally, with young people 12 to 16 years old, through the use of an external distractor. According to Robinson et al [23], the average torque for distracting the human mandible 0.5 mm twice a day was 4.2 N.cm. The measurements were correlated with in vivo torque readings in an attempt to better understand the force required to distract the osteogenic bone callus of the human mandible during osteogenesis. In vitro data showed that the forces for distraction used in similar equipments are of the order of 36 N. Additionally, this paper mentions that the average force of device failure was 235.8 N.
2.6 Maxillary Distraction
Figure 6 shows the loading that occurs during maxillary distraction.
Fig. 6. Example of loading during maxillary distraction
As mentioned, distraction osteogenesis is a procedure that relies on biomechanics. The application of progressive traction forces leads to bone lengthening by new bone formation. Although the process is widely discussed in the literature, few published studies address the involved forces during maxillary distraction because of the difficulty in measuring the biomechanical demands in the recovery process.
The distractions in use still follow the same standards set by Ilizarov [19]. Kahn et al [24] show the distraction of the upper maxilla through internal distractors for a Le Fort I osteotomy. According to Wiltfang et al [25] the determination the loads required to promote maxillary distraction is complicated by monitoring difficulties. In 2009, Suzuki and Suzuki [26] determined the forces of distraction in the craniofacial region. They concluded that 42.5 N is the average force to promote maxillary distraction, varying in their studies between 16.4 N
to 65.3 N. The average force increase was 10.5 N after activation and adaptation.
Since a load of the order of 65 N is considered uncomfortable and painful for the patients, the distractor should not exhibit any changes when subjected to forces below this value; thus, the value of 65 N serves as a reference for the validation of a mandibular distraction device.
2.7 Tendons
Tendons differ in shape and orientation, depending on their union to muscle fibers. Suture anchors are common implants used to attach tendons and other soft tissues. According to Kato et al [27] anchors have been successfully used to repair ligaments and muscle lesions. Several authors discuss and describe an analysis of the mechanical forces that involve the several tendons of human body.
Among temporomandibular disorders the most common is the dislocation of the temporomandibular joint (TMJ). The anchors used for restoring the functionality of the TMJ must withstand forces greater than 71.17N.
REFERENCES
[1] F. Shapiro, Bone development and its relation to fracture repair. The role of mesenchymal osteoblasts and surface osteoblasts. Eur Cell Mater 15 (2008) 53-76.
[2] Aerospace Medical Research Laboratory, Investigation of inertial properties of the human body. U.S. Department of Commerce, AD-A016 485, Publication 92; p. 68, 1975.
[3] R. Delille, C. Delille, P. Drazetic, C. Masson, E. Markiewicz, Mechanical Characteristics of the Human Skull Bone. Biomechanics. Benidorm, Spain, September 7-9, 2005.
[4] D.G. Farwell, E.J. Keririan, J.L. Heydt, B. Yueh, N.D. Futran, Efficacy of Small Reconstruction Plates in Vascularized Bone Graft Mandibular Reconstruction, Head & Neck 28 (2006) 573-579.
[5] A. Chritah, S.K. Lazow, J.R. Berger, Transoral 2.0 mm Locking Miniplate Fixation of Mandibular Fractures Plus 1 Week of Maxillomandibular Fixation: A Propective Study, J Oral Maxillofac Surg 63 (2005) 1737-1741.
[6] A.J.L. Gear, E. Apasova, J.P. Schmitz, W. Schubert, Treatment Modalities for Mandibular Angle Fractures. J Oral Maxillofac Surg 63 (2005) 655-663.
[7] J.M. Doty, D. Pienkowski, M. Goltz, R.H. Haug, J. Valentino, O.A. Arosarena, Biomechanical evaluation of fixation techniques for bridging segmental mandibular defects, Arch Otolaryngol Head Neck Surg 130 (2004) 1388-1392.
[8] T.W.P. Korioth, A.G. Hannam, Mandibular forces during simulated tooth clenching, J Orofac Pain 8 (1994)178-189. [9] S. Naser-ud-Din, Analysis and correlation study of human
masseter muscle with EMG, ultrasonography & 3D imaging, PhD thesis, The University of Adelaide, Australia, 2009.
[10] M.S. Monazzi, L.A. Passeri, M.F.Gabrielli, P. D.A. Bolini, E.H. Vieira, Avaliação da espessura da mandíbula com relação à fixação interna rígida em osteotomia sagital. Estudo anatômico, Rev Bras Cir. Buco-Maxilo-Fac 10 (2010) 43-48.
[11] B. Labanauskaite, G. Jankauskas, A. Vasiliauskas, N. Haffar, Implants for orthodontic anchorage, Meta-analysis, Stomatologija 7 (2005) 128-132.
[12] J.C.Lin, E.J.Liou, C.L. Yeh, C.A. Evans, A comparative evaluation of current orthodontic miniscrew systems, World J Orthod 8 (2007) 136-144
[13] M.Y. Mommaerts, M.L. Michiels, G.A. De Pauw, A 2-year outcome audit of a versatile orthodontic bone anchor, J Orthod 32 (2005) 175-181.
[15] B.H. Choi, S.J. Zhu, Y.H. Kim, A clinical evaluation of titanium miniplates as anchors for orthodontic treatment, Am J Orthod Dentofacial Orthop 128 (2005) 382-384.
[16] B.T. Brettin, N.M. Grosland, F. Qian, K.A. Southard, T.D. Stuntz, T.A. Morgan, S.D. Marshall, T.E. Southard, Bicortical vs monocortical orthodontic skeletal anchorage. Am J Orthod Dentofacial Orthop 134 (2008) 625-635.
[17] J.A. von Fraunhofer, P.W. Bonds, B.E. Johnson, BE. (1993) Force generation by Orthodontic coil springs. Angle Orthod 63 (1993) 145-148.
[18] G. Serra, L.S. Morais, C.N. Elias, M.A. Meyers, C.A. Muller, Sequential bone healing of immediately loaded mini-implants: histomorphometric and fluorescence analysis, Am J Orthod Dentofacial Orthop 137 (2010) 80-90.
[19] G. Ilizarov, Treatment of fractures, Transosseous Osteosynthesis, Springer-Verlag New York Inc, Berlin, Heidelberg. pp. 406–444, 1992.
[20] I. Takahashi, H. Kawamura, T. Takano-Yamamoto. Combined maxillary and mandibular midline and mandibular ramus distraction osteogenesis for treatment of a Class II patient with implants as orthodontic anchorage. Am J Orthod Dentofacial Orthop 137 (2010) 412-23.
[21] S. Basa, E. Uner, M. Citir, K. Aras, Reconstruction of a Large Mandibular Defect by Distraction Osteogenesis: A case report, J Oral Maxillo Surg. 58 (2000) 1425-1428.
[22] G. Swennen, F. Colle, A. De May, C. Malevez, Maxillary Distraction in Cleft Lip Palate Patients: A Review of Six Cases, J Craniofac Surg. 10 (1999) 117-122.
[23] R.C. Robinson, P.J. O'Neal, G.H. Robinson, Mandibular Distraction Force: Laboratory Data and Clinical Correlation, J Oral Maxillofac Surg. 59 (2001) 539-544.
[24] D.M. Kahn, S.A. Schendel, Distraction Osteogenesis of Maxilla at Le Fort I Level Using an Internal Distractor. Distraction Osteogenesis of the Facial Skeleton, B.C. Decker Inc. Hamilton, ON, L8N 3K7, Canada. pp. 267-71, 2007.
[25] J. Wiltfang, P. Kessler, H.A. Merten, F.W. Neukam, Continuous and intermittent bone distraction using a microhydraulic cylinder. An experimental study in minipigs, Br J Oral Maxillofac Surg. 39 (2001) 2-7.
[26] E.Y. Suzuki, B. Suzuki, A Simple Mechanism for Measuring and Adjusting Distraction Forces During Maxillary Advancement, J Oral Maxillofac Surg. 67 (2009) 2245-2253.
