Modeling of jaw biomechanics in the reconstructed mandibulectomy patient

Modeling of jaw biomechanics in the reconstructed mandibulectomy patient D. A. Curtis, DMD,a O. Plesh, DDS, MD,a A. G. Hannam, BDS, PhD,b A. Sharma, BDS, MSc,c and T. A. Curtis, DDSd University of California at San Francisco, San Francisco, Calif., and University of British Columbia, Vancouver, British Columbia, Canada Statement of problem. Biomechanics of occlusal force and indirect calculation of temporomandibular joint loading in patients after surgery for head and neck cancer is poorly understood.

Purpose. This study compared occlusal force values of 6 mandibulectomy subjects with reconstructed mandibles to 6 noncancer subjects with intact mandibles and reports occlusal force predictions from a developed computer model simulation of both a mandibulectomy subject with a reconstructed mandible and noncancer subject with an intact mandible. Material and methods. Maximum occlusal force was recorded at the first molar and incisal edge in 6 mandibulectomy subjects who had bony reconstruction of the mandible and 6 noncancer subjects with an intact mandible. Clinical data were then qualitatively compared with occlusal force values generated from an existing computer model simulating an average adult, and a developed model simulating an average mandibulectomy subject who had bony reconstruction of the mandible. The biomechanical parameters modeled also included an estimation of joint force magnitude and direction when biting with maximal force on the first molar. Results. Clinical data revealed no significant differences in occlusal force between the 6 mandibulectomy subjects with bony reconstruction of the mandible and 6 noncancer subjects with an intact mandible; however, average molar and incisal occlusal force values were 22% and 32% less in mandibulectomy subjects with bony reconstruction. Computer simulations of a reconstructed mandibulectomy subject predicted that reconstructed subjects would have 45% less molar occlusal force, 50% less incisal occlusal force, and a higher joint/tooth force ratio compared with a simulated noncancer patient with an intact mandible. Conclusions. There were no significant differences in first molar or incisal occlusal force between reconstructed mandibulectomy subjects and noncancer subjects with intact mandibles. Trends calculated from computer simulations were consistent with clinical findings. (J Prosthet Dent 1999;81:167-73.)

CLINICAL IMPLICATIONS Computer modeling may be used to simulate anatomic deficits to make predictions about the impact of surgery and potential benefits of reconstructive alternatives.

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pproximately 30,000 new patients with head and neck cancer are treated annually in the United States.1 Because the 2 most common sites of oral cancer are the lateral border of the tongue and floor of the mouth, structures vital to mastication are often partially resected, altered, or displaced by surgery. When a segment of the mandible is removed, immediate reconstruction is

Presented to the American Academy of Maxillofacial Prosthetics, Reno, Nev., October 1996. Funded in part by the Tobacco Related Disease Research Program, grant no. 2KT003. aAssociate Professor, Section of Prosthodontics, Department of Restorative Dentistry, University of California at San Francisco bProfessor, Department of Oral Biology, University of British Columbia. cAssociate Clinical Professor, Section of Prosthodontics, Department of Restorative Dentistry, University of California at San Francisco. dProfessor Emeritus, Section of Prosthodontics, Department of Restorative Dentistry, University of California at San Francisco. FEBRUARY 1999

usually recommended to improve both facial symmetry and masticatory function. Although techniques for reconstructive surgery and prosthodontic rehabilitation have advanced, more than 50% of reconstructed head and neck cancer patients still report impaired masticatory function.2,3 Improvement of surgical and prosthetic rehabilitation requires better understanding of how anatomic loss impacts masticatory function. When surgery includes a segmental mandibulectomy, masticatory function is compromised because of muscular imbalance that results from unilateral muscle removal, altered maxillomandibular relationship, and decreased tooth-to-tooth contacts. Although immediate mandibular reconstruction aims to restore facial symmetry, arch alignment, and stable occlusion, masticatory function often remains compromised.2,3 Mandibulectomy subjects with bony reconstruction often complain of limited range of mandibular motion, difficulty in mastication, and exhibit significant THE JOURNAL OF PROSTHETIC DENTISTRY 167

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Table I. Mandibulectomy subjects with reconstructed mandibles Name

Gender/age

Male/71 Male/70 Female/38 Female/28 Female/69 Female/49

Dental status max/mand

Include angle of mandible?

Partial denture/intact Intact/Partial denture Intact/Intact Intact/partial denture Intact/intact Denture/implant supported

Yes No Yes Yes Yes Yes

Radiation

1st molar

Yes No No No Yes No Mean/SD

142 118 327 220 331 363 250 ± 105

Incisal edge

69 35 167 147 151 136 118 ± 53

Dental implants

Yes No No No No Yes

Occlusal force measured in Newtons (N). Dental status indicated as intact dentition, a fixed partial denture, or as implant supported. Max, Maxillary; Mand, mandibular.

decreases in occlusal force.2,3 Masticatory impairment of patients with mandibular reconstruction are often related to an altered biomechanical relationship that results from muscular imbalance. While the impact of decreased tooth-to-tooth contacts has been evaluated,3,4 assessment of muscular imbalance in patients with mandibular reconstruction has not been reported. The effects of muscular imbalance results in altered temporomandibular joint (TMJ) loading and mandibular rotation, both of which are difficult to assess directly. Therefore an indirect modeling approach becomes helpful. Interactive computer programs based on mechanical and mathematical models have been used to estimate outcomes such as vectors of muscle force or condylar loading when direct measurements are considered invasive or impossible.5,6 Such models should be validated with clinical trials whenever possible. Model estimates have been used to predict outcomes such as expected occlusal force for orthognathic surgical planning. A similar approach could be applied to the patient with head and neck cancer by simulating an anatomic deficit to predict occlusal force, joint loading, or mandibular rotation. With a validated model, predictions of proposed reconstructive surgery or the impact of prosthodontic interventions could be evaluated preoperatively. Therefore the purposes of this study were to (1) compare occlusal force values of 6 mandibulectomy subjects with reconstructed mandibles to 6 noncancer subjects with intact mandibles; (2) qualitatively compare occlusal forces from a developed computer model simulating a reconstructed mandibulectomy subject to clinical data from 6 reconstructed mandibulectomy subjects and 6 noncancer subjects; and (3) calculate TMJ loading magnitude and direction in the reconstructed mandibulectomy model.

MATERIAL AND METHODS Subjects were recruited from the Maxillofacial Clinic at the University of California, San Francisco (UCSF) and at the private practice of the principal author. The clinical phase of this study was completed over a 168

13-month period. The experimental protocol was approved by the UCSF Human Subjects Committee, and all procedures were carefully explained to patients before they signed informed consent forms. The average age of reconstructed patients was 54 years, and for noncancer subjects with intact mandibles it was 57 years. The 6 reconstructed mandibulectomy subjects had mandibular resection for malignant disease; 5 subjects had immediate reconstruction and 1 had delayed reconstruction (Table I). All reconstructed mandibulectomy subjects were over 25 years old, had bony reconstructed mandibles with the rami and condyles intact, ± radiotherapy, ± chemotherapy, at least 6 months after reconstruction, with natural or restored dentition. Subjects were excluded if there was a clinically active tumor, less than 6 months after reconstruction, or with unrestored natural dentition. The surgical defect included the angle of the mandible in all patients and crossed the midline in 3 subjects. All subjects had intact or restored remaining dentition, and exhibited unilateral loss of masseter and medial pterygoid muscles. On the bases of the operation reports, which included a neck dissection, the digastric muscle and aspects of the temporalis were also removed unilaterally. Autogenous mandibular reconstruction included a segment of fibula in 5 patients and iliac crest in 1 patient. All subjects had sensory loss of the inferior alveolar nerve. No subjects had sensory loss of the lingual nerve. One subject received postoperative radiation and 1 subject received preoperative chemotherapy. All subjects were tested at least 6 months after reconstructive surgery. All subjects were at least 25 years old. Noncancer subject with intact mandibles consisted of 6 subjects with intact mandibles, were at least 25 years of age, and had either a full compliment of teeth or dentition restored with a fixed prosthesis (Table II). All subjects had either full compliment of teeth or dentition restored with a fixed prosthesis. Subjects were excluded if they had temporomandibular disorders (TMDs), muscle pain, or unrestored dentition. None of the subjects had TMDs, or was muscle pain or joint VOLUME 81 NUMBER 2

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Table II. Noncancer subjects with intact mandibles

Age/gender

1st molar occlusal force Newtons (N)

Incisal edge occlusal force Newtons (N)

62/male 69/male 28/female 56/male 70/female 62/male Mean/SD:

438 351 156 353 286 345 321 ± 94

319 153 66 192 132 180 174 ± 84

pain noted for any subjects. None of the subjects had muscle disorders, arthritis, or known medical conditions that could affect occlusal force.

Data collection Occlusal force for reconstructed mandibulectomy subjects and noncancer subjects with intact mandibles was recorded at the level of the first molar on the nondefect side and between the central incisors (Fig. 1). The instrumentation and methods used to record occlusal force were similar to those described by Marunick et al.7 Occlusal force was recorded with a uniaxial beam consisting of 3 strain gauges to measure torque and indirectly determine occlusal force. The subject’s dentition was separated by approximately 10 mm of the occlusal rim while sitting upright in a dental chair. Subjects were instructed to practice biting twice, and then to bite with maximum force. The highest recordings from 5 trials were calculated for each subject for the molar and incisal edge sites.

Computer modeling The computer modeling program used in this study, developed by Nelson and Hannam,8,9 was based on static equilibrium theory. The model has been described previously and will only be briefly outlined.10 The model assumes that under isometric contraction of the jaw muscles, the generated 3-dimensional forces applied to the TMJ and dentition would be in static balance, and that the sums of all forces would be zero. To simplify the mathematical model, the contact position of teeth and TMJ was assumed to be a single point rather than changing points or a broad area. On the basis of this 3-dimensional computer model, the magnitude and direction of condylar and tooth loading could be calculated during simulated isometric tooth clenching at different positions. Most existing models used to evaluate jaw biomechanics have relied on average data pooled from multiple subjects, and have been considered to represent an “average” human.11 Data from multiple studies of occlusal force, muscle cross-sections, and electomyographic analysis have been compiled to formulate models of varying sophistication levels. FEBRUARY 1999

Fig. 1. Occlusal force was recorded with uniaxial beam consisting of 3 strain gauges to measure torque and indirectly determine occlusal force. Patient’s dentition was separated by approximately 10 mm of occlusal plate while patient sitting upright in dental chair.

Muscles considered in Hannams’s model included the superficial and deep masseter, medial pterygoid, anterior, middle, and posterior temporalis, superior and inferior heads of the lateral pterygoid and digastric muscles. Major muscles were divided into subgroups for which average size, position, and cross-sectional area were derived from computed tomographic scans, dissections, and skeletal measurements. 9,11-13 The prediction of force generated by each muscle was based on the muscle cross-sectional area, and in Hannam’s model the value of 40 N/cm2 was used based on the work of Weijs and Hillen.14 Therefore large muscles were assumed to be capable of producing more isometric force than small muscles. Because different tasks require different levels of muscle activation (for example, clenching at the first molar or incisal edge), a “scaling factor” based on EMG studies was assigned for each of these tasks.15-18 Thus, the magnitude and direction of force resulting from first molar or incisal edge clenching tasks could be calculated at specific points of tooth contact or the condylar level. It was assumed that resistance that occurred at the TMJs were the result of muscular forces not counteracted by the teeth.8 During bilateral clenching, the condylar loading was symmetrical and asymmetrical during unilateral clenching because of the asymmetric muscle contraction. Occlusal forces were found to increase as the bite point moved posteriorly because more muscles become active and the mechanical lever becomes shorter. Joint force/tooth force ratio (JF/TF) was defined as the predicted joint loading with maximum first molar clenching. A lower JF/TF ratio was considered a more efficient biomechanical relation because more force was counteracted by potentially useful tooth contact rather than TMJ loading.8,9 For 169

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B Fig. 2. A, Schematic of computer model represents noncancer subject with intact mandible when biting on right first molar; maximal occlusal force results in bilateral condylar loading, with higher loading on left compared with right side (258 N vs 138N). Length of dotted lines represents magnitude and direction of force. B, During incisal clenching, joint forces were 163 N bilaterally.

example, if at a given level of muscle contraction results in a higher level of joint loading and less occlusal loading, the biomechanical relation would be considered unfavorable because more force was counteracted by TMJ loading than potentially useful tooth contact. Computer modeling for the noncancer subject with an intact mandible was completed as previously described to simulate a subject with average muscle sizes, average anatomic relationships by using norma170

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tive data from literature, and specific muscle activation levels that were task-specific. Molar and incisal occlusal force values were calculated for such an average subject who had intact dentition while clenching with maximum force at the mandibular right first molar with an occlusal contact angle of 90 degrees in the frontal plane (biting straight down with a flat occlusal plane). Similarly, maximum force was calculated at the incisal edge of mandibular right central incisor with an occlusal contact angle of 90 degrees (Table III and Fig. 2, A and B). In addition, the JF/TF ratio, a measure of efficiency, was calculated with a lower number representing a more efficient system.8,9 The computer model for the mandibulectomy subject with a reconstructed mandible was generated by starting with the simulation of an average person and removing structures to represent the anatomic loss most often seen in a reconstructed mandibulectomy patient. Muscles that include the left temporalis, left masseter, left medial and lateral pterygoid, and left digastric muscles were removed so that the anatomic deficit was similar with the 6 reconstructed mandibulectomy patients tested clinically (Fig. 3, A and B). Because the model simulated a leftsided defect and not all clinical patients had a left-sided defect, some data manipulation was necessary. For the 2 mandibulectomy subjects with reconstructed mandibles who had right-sided defects, the absolute numbers for joint loading and tooth force were reversed right for left. On the basis of this model, the following parameters were calculated: 1. maximum occlusal force (Newtons) recorded during clenching at the right first molar and incisal edge of the mandibular right central incisor; 2. JF/TF ratio; and 3. magnitude and direction of mandibular rotation, if present, from the muscular imbalance when biting at the right first molar or incisal edge (Table III). For example, if the rotating force on the nondefect condyle was downward (viewed in the frontal plane), the prediction would be for the mandible to be distracted, and result in occlusal instability. Analysis from clinically generated data included an unpaired t test at the P<.05 level of significance to test differences of first molar and incisal occlusal force between reconstructed mandibulectomy subjects and noncancer subjects with intact mandibles. Comparison of molar and incisal occlusal force between computergenerated data and clinical data was qualitatively evaluated. Analysis of computer-generated data included a qualitative comparison between the first molar and incisal edge occlusal force in modeled normal and reconstructed mandibulectomy patients. In addition, both the counterclockwise force (viewed in the frontal plane) and JF/TF calculated in a modeled noncancer subject with an intact mandible and reconstructed mandibulectomy patient was qualitatively compared. VOLUME 81 NUMBER 2

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Table III. Occlusal force data of left-sided mandibulectomy subjects with reconstructed mandibles and noncancer subjects with intact mandibles Clinical data

Computer model

Noncancer Reconstructed Noncancer Reconstructed N=6 N=6 N=1 N=1

Occlusal force: molar (right) Occlusal force: incical Ratio: joint force/tooth force; left side molar Force on left condyle

321 ± 94

250 ± 105

454

251

174 ± 83

118 ± 53

135

67

1.00

0.30

Seating force

Distracting force

Occlusal force measured in Newtons. A low first molar ratio of joint force/tooth force represents an efficient biomechanical relation. The force on the left condyle is either a seating or distracting force (see Fig. 3).

A

RESULTS Mean first molar occlusal force of the reconstructed mandibulectomy patients was 250 ± 105 N with a range of 118 to 363 N. Mean incisal occlusal force for the reconstructed mandibulectomy patients was 118 ± 53 N with a range of 35 to 167 N. Mean value of the first molar occlusal force for the 6 noncancer subjects with intact mandibles was 321 ± 94 N with a range of 156 to 438 N (Table II). Mean incisal occlusal force of the noncancer subjects with intact mandibles was 174 ± 84 N with a range of 66 to 319 N. Thus, the reconstructed mandibulectomy subjects presented 22% less first molar occlusal force and 32% less incisal occlusal force compared with noncancer subjects with intact mandibles, yet statistically this was not significant (P=.245 first molar, P=.195 for incisal edge). First molar occlusal force for the computer-modeled noncancer subject with an intact mandible subject was 454 N and the incisal occlusal force was 135 N (Table III). First molar and incisal occlusal force of the computer-modeled reconstructed mandibulectomy subject was 251 and 67 N, respectively. Thus, the computer model for the reconstructed mandibulectomy subject predicted that first molar and incisal occlusal force was 45% and 50% less, respectively, than the predicted occlusal force of the computer-modeled noncancer subject with an intact mandible. The predicted condyle loading of the right first molar clenching from the computer model of the noncancer subject with intact mandible was 138 N on the right condyle and 258 N on the left condyle (Fig. 2, A and B). As expected, the nonworking condyle is loaded more than the working condyle. During incisal clenching, joint forces were nearly equal at 163 N bilaterally FEBRUARY 1999

B Fig. 3. A, Schematic illustration of computer model represents left-sided reconstructed mandibulectomy subject when biting with maximal force on right first molar (251 N) and results in upward load of 258N on right condyle, but 48 N downward, or clockwise rotation on left condyle. Length of dotted lines represents magnitude and direction of force. B, During incisal biting (67 N), seating force of 184 N on right condyle and 8 N downward or clockwise rotation on left condyle was predicted, and clockwise rotation on mandible for both first molar and incisal clenching.

(Fig. 2, A). The computer model of the reconstructed mandibulectomy patient predicted a clockwise rotation when biting on the right first molar; with an upward load of 258 N on the right condyle, but a downward load of 48 N, or clockwise rotation on the left condyle (Fig. 3, A and B). With incisal edge biting, a seating force of 184 N on the right condyle and 8 N downward or clockwise rotation on the left condyle was predicted (Fig. 3, B). Thus, in the reconstructed mandibulectomy subject, with simulation of right-sided clenching and left-sided defect, higher downward force was pre171

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dicted on the reconstructed condyle with first molar clenching than with incisal edge clenching.

DISCUSSION Occlusal force values measured from our clinical data compared favorably with data from other investigators. In a study of 10 reconstructed mandibulectomy patients, Urken et al4 determined first molar occlusal force to be 182 N. Our finding of a higher level of occlusal force (250 vs 182 N) may be related to 4 of 6 patients having intact remaining dentition versus Urken’s study having 4 of 10 subjects with intact dentition. In addition, the size of the resections in subjects evaluated in Urken’s study appeared to be larger than our subjects. In another study of 4 patients having mandibular reconstruction of the angle of the mandible, Endo19 measured second premolar occlusal force at 363 N. Endo’s higher finding may be because his group was of younger age (34 vs 54 years) or because the smaller size of mandibular reconstruction represented in his subjects. Although occlusal force values of mandibulectomy subjects with reconstructed mandibles were lower than noncancer subjects without cancer, the differences were not statistically significant. This could be because of our small sample size, or because of the between and within subject variability seen with occlusal force measurements.20-22 Previous studies with larger sample sizes have shown significantly less occlusal force in mandibulectomy subjects with reconstructed mandibles compared with noncancer subjects.3,4 Computer simulations predicted that compared with noncancer subjects with intact mandibles, reconstructed mandibulectomy patients would have 45% less molar clenching force and 50% less incisal clenching force. Although the predicted values were close to clinical data with respect to first molar force (251 vs 250 N), predicted occlusal forces predicted (67 N) were less than the clinically determined average of 118 N. These findings could be due to several factors. First, although the angle of the mandible was resected along with the masseter and medial pterygoid muscle insertions, muscles can reinsert into the neomandible and may have provided additional pull. In addition, although the composite resection that included a radical neck dissection removed the digastric, masseter and medial pterygoid muscles and the majority of abduction force, residual temporalis in some patients may have provided additional force. Future model simulations should duplicate exact anatomic deficits of individual patients rather than representing an average, and would ideally be dynamic so that as reconstruction proceeds, the model could be modified for that individual patient. Clinical studies have shown that the incising of a food bolus is difficult in mandibulectomy patients or reconstructed mandibulectomy patients.3,23 This clini172

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cal finding is consistent with our model predictions, which determined that without bilateral muscle abduction, unilateral joint loading results in mandibular rotation. In a dynamic 6-degrees of freedom mathematical model, Koolstra6 demonstrated that different parts of the masseter and the medial pterygoid muscle, despite their orientation, to be involved in protrusive movement of the mandible. Therefore patients with muscular imbalance created by unilateral removal of the masseter and temporalis may still have difficulty in incising, even if the lateral pterygoid muscles are intact. Downward movement of the left condyle with rightsided molar clenching (Fig. 3, A and B) is consistent with investigators who have described frontal plane rotation in mandibulectomy subjects who are not reconstructed.24 The downward rotation occurs less in reconstructed mandibulectomy subjects for reasons that may include bilateral bony articulation and increased soft tissue resistance to rotation. Predictions from computer modeling of an “average reconstructed mandibulectomy patient” is difficult because of the heterogeneous patient population. Variability in the remaining anatomic structure makes creating an “average model” difficult. In our reconstructed mandibulectomy subjects population, the lateral pterygoid muscle was probably functioning in most subjects, yet was not represented in the computer model. In addition, the calculations of muscle force and muscle vectors in our model were static, yet we know muscle vectors within a group of muscles shorten during clenching, or lengthen during opening. Not accounting for the dynamic change in muscle vectors introduces error and may have influenced our results.25,26 Throckmorton25,26 determined, if each of the 5 muscles in his model were known to the nearest 1% of total force magnitude, 1% of muscle direction, and 1 mm of movement arm length, TMJ force could be calculated to the nearest 4 kg and joint force direction to the nearest 7%. The accuracy of future models will be enhanced with dynamic muscle vector calculations.

CONCLUSIONS Computer modeling of jaw biomechanics has potential application in many areas of preprosthetic surgery and mandibular reconstruction. For example, clinical experience has shown that patients who have had unilateral resection and subsequent reconstruction of the mandible, ramus, and condyle tend not to have joint pain associated with their reconstructed condyle. Computer modeling simulation of the reconstructed patient may predict that joint loading of the reconstructed condyle would be minimal, even when clenching maximally at the mandibular incisors (Fig. 2, A and B). The lack of symptoms observed clinically may be related to the minimal joint loading occurring. Other applications of computer modeling of jaw biomechanics include VOLUME 81 NUMBER 2

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force vector changes after orthognathic surgery, evaluating the influence occlusal splints may have on TMJ loading, and in altered biomechanics seen with skeletal growth. REFERENCES 1. Silverman S. Oral cancer. 3rd ed. Atlanta (GA): American Cancer Society; 1990. p. 1. 2. Olson ML, Shedd DP. Disability and rehabilitation in head and neck cancer patients after treatment. Head Neck Surg 1978;1:52-8. 3. Curtis DA, Plesh O, Miller AJ, Curtis TA, Sharma A, Schweitzer R, et al. A comparison of masticatory function in patients with or without reconstruction of the mandible. Head Neck 1997;19:287-96. 4. Urken ML, Buchbinder D, Weinberg H, Vickery C, Sheiner A, Parker R, et al. Functional evaluation following microvascular oromandibular reconstruction of the oral cancer patient: a comparative study of reconstructed and nonreconstructed patients. Laryngoscope 1991;101:935-50. 5. Hatcher DC, Faulkner MG, Hay A. Development of mechanical and mathematic models to study temporomandibular joint loading. J Prosthet Dent 1986;55:377-84. 6. Koolstra JH, van Eijden TM. Biomechanical analysis of jaw-closing movements. J Dent Res 1995;74:1564-70. 7. Marunick MT, Mathoj RH. Mastication in patients treated for head and neck cancer: a pilot study. J Prosthet Dent 1990;63:566-73. 8. Nelson GJ. Three dimensional computer modeling of human mandibular biomechanics. [MSc thesis.] Vancouver: The University of British Columbia, 1986. 9. Nelson GJ, Hannam AG. A biomechanical simulation of the craniomandibular apparatus during tooth clenching. J Dent Res 1982;61: 813(abstract). 10. Korioth TW, Hannam AG. Effect of bilateral asymmetric tooth clenching on load distribution at the mandibular condyles. J Prosthet Dent 1990; 64:62-73. 11. Hannam AG, Langenbach GE, Peck CC. Computer simulations of jaw biomechanics. In: McMeil C, editor. Science and practice of occlusion. Chicago: Quintessence; 1977. 12. Nelson GJ, Hannam AG. The simulation of muscle, tooth, and joint biomechanics during isometric tooth clenching in man. J Dent Res 1983; 62:687(abstract). 13. Baron P, Debussy T. A biomechanical functional analysis of the masticatory muscles in man. Arch Oral Biol 1979;24:547-53.

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14. Weijs WA, Hillen B. Relationship between the physiological cross-section of the human jaw muscles and their cross-sectional area in computer tomograms. Acta Anat (Basel) 1984;118:129-38. 15. Pruim GJ, de Jongh HJ, ten Bosch JJ. Forces acting on the mandible during bilateral static bite at different bite force levels. J Biomech 1980;13: 755-63. 16. MacDonald JW, Hannam AG. Relationship between occlusal contacts and jaw-closing muscle activity during tooth clenching: part I. J Prosthet Dent 1984;52:718-29. 17. Moller E. An electromyographic study of the action of the muscles of mastication and its correlation to facial morphology. Acta Physiol Scand 1965;69:1-229. 18. Pruim GJ, ten Bosch JJ, de Jongh HJ. Jaw muscle EMG-activity and static loading of the mandible. J Biomech 1978;11:389-95. 19. Endo N. Studies on masticatory functions in patients with surgical mandibular reconstruction. Oral Surg 1972;34:390-406. 20. Hagberg C. Assessments of bite force: a review. J Craniomand Disord 1987;1:162-9. 21. Helhimo E, Carlsson G, Carmeli Y. Bite force in patients with functional disturbances of the masticatory system. J Oral Rehab 1975;2:397-406. 22. Carlsson GE. Bite force and chewing efficiency. Front Oral Physiol 1974;1:265-92. 23. Atkinson HF, Shepherd RW. The masticatory movements of patients after major oral surgery. 1969;21:86-91. 24. Beumer J, Curtis T. Acquired defects of the mandible. In: Beumer J, Curtis T, Firtell D, editors. Maxillofacial rehabilitation prosthodontic and surgical considerations. St Louis: CV Mosby; 1979. 25. Throckmorton GS, Throckmorton LS. Quantitative calculations of temporomandibular joint reaction forces—I. The importance of the magnitude of the jaw muscle forces. J Biomech 1985;18:445-52. 26. Throckmorton GS. Quantitative calculations of temporomandibular joint reaction forces—II. The importance of the direction of the jaw muscle forces. J Biomech 1985;18:453-61.

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