Effects of pericapsular soft tissue and realignment exercises for patients with osteoarthritis of the hip and Harris Hip Score below 60 points.

OBJECTIVE: To investigate the effectiveness of pericapsular soft tissue and realignment (PSTR) exercises for patients with osteoarthritis (OA) of the hip and Harris Hip Score (HHS) below 60 points. Most previous studies of hip exercise have not been applied for patients with moderate to severe hip OA, especially those with an HHS below 60 points. Most studies of hip exercise in OA have involved muscle strength training, stretching, functional training and aerobic fitness programs, and have not included pelvic realignment exercise. We investigated the effect of pelvic realignment exercise for patients with hip OA and HHS below 60 points. METHODS: Design: multicenter, prospective, observational, single-arm study. Setting: clinical examination on an outpatient basis. Participants: 193 patients with hip OA and HHS below 60 points. Interventions: patient education and supervised PSTR exercises. Outcome measures: primary outcome: HHS; secondary outcomes: changes in numerical rating scale (NRS) scores, abduction of range of motion, Timed Up and Go (TUG) test within 30 min after PSTR exercises at baseline and other six items, full analysis set (FAS, all participants who performed PSTR exercises) and subgroup analysis (participants with minimal joint space (MJS) of 0 mm at baseline). RESULTS: FAS analysis (N = 193): significant differences in HHS were found between baseline and 3 month follow-up, and between baseline and 6 month follow-up in the Unilateral and Bilateral OA groups (p < .001). All mean differences were within the 95% confidence interval. Significant improvement in NRS scores, abduction of range of motion, and TUG test within 30 min after PSTR exercises were found at baseline (p < .001). Subgroup analysis (N = 130): the results revealed significant differences (p < .001) in HHS and NRS, abduction of range of motion and TUG test within 30 min after PSTR exercises at baseline, as in the FAS analysis. CONCLUSION: Our findings suggested that PSTR exercises were effective for patients with HHS below 60 points, even those with MJS of 0 mm. CLINICAL TRIALS REGISTRY: 20 July 2017 (UMIN000028277).

[Antimicrobial Effects of Iodine-Polyvinyl Alcohol Ophthalmic and Eye Washing Solution (PA * IODO) with Special Reference to its Temperature, Concentration and Time and its Preservation Stability].

PURPOSE: Temperature, concentration and time are the three factors that affect the inactivation capacity of iodine antiseptics. We investigated the effect of these factors on the microbe inactivation of Iodine-Polyvinyl Alcohol ophthalmic and eye washing solution (PA * IODO), and also investigated the preservation conditions on stability of the inactivation activity of the PA * IODO. METHODS: Test microbes were mixed with PA * IODO, varying the three factors. The live microbes were counted after each reaction. The effects of plugging and preservation temperature were investigated to determine the preserving stability. RESULTS: The inactivation capacity of PA * IODO tended to decrease in almost all microbes tested at 4 degrees C. Twenty times or less diluted PA * IODO killed almost all microbes completely. The time effect was more marked in viruses. Plugging and low-temperature made iodine concentration in diluted PA * IODO remain relatively high. CONCLUSIONS: The concentration of PA * IODO affected the inactivation ability more than the temperature and time, although all the three factors correlated positively to the inactivation. For preservation the diluted PA * IODO needed plugging and low temperature.

Influence of standardization on the precision (reproducibility) of dental cast analysis with virtual 3-dimensional models.

INTRODUCTION: Virtual 3-dimensional (3D) models obtained by scanning of physical casts have become an alternative to conventional dental cast analysis in orthodontic treatment. If the precision (reproducibility) of virtual 3D model analysis can be further improved, digital orthodontics could be even more widely accepted. The purpose of this study was to clarify the influence of "standardization" of the target points for dental cast analysis using virtual 3D models. Physical plaster models were also measured to obtain additional information. METHODS: Five sets of dental casts were used. The dental casts were scanned with R700 (3Shape, Copenhagen, Denmark) and REXCAN DS2 3D (Solutionix, Seoul, Korea) scanners. In this study, 3 system and software packages were used: SureSmile (OraMetrix, Richardson, Tex), Rapidform (Inus, Seoul, Korea), and I-DEAS (SDRC, Milford, Conn). RESULTS: Without standardization, the maximum differences were observed between the SureSmile software and the Rapidform software (0.39 mm ± 0.07). With standardization, the maximum differences were observed between the SureSmile software and measurements with a digital caliper (0.099 mm ± 0.01), and this difference was significantly greater (P <0.05) than the 2 other mean difference values. Furthermore, the results of this study showed that the mean differences "WITH" standardization were significantly lower than those "WITHOUT" standardization for all systems, software packages, or methods. CONCLUSIONS: The results showed that elimination of the influence of usability or habituation is important for improving the reproducibility of dental cast analysis.

Assessment of the accuracy and reliability of new 3-dimensional scanning devices.

INTRODUCTION: The primary objective of this study was to assess the accuracy and the reliability of the SureSmile OraScanner (Orametrix, Richardson, Tex) by comparing it with other desktop 3-dimensional scanners: VIVID910 (Konica Minolta, Tokyo, Japan) and R700 (3Shape, Copenhagen, Denmark). A laser-based scanner, the SLP250 Laser Probe (Laser Design, Detroit, Mich), served as the gold standard. METHODS: Five sets of dental casts were used. First, the accuracy of each scanner was studied by comparing the 3-dimensional models created by OraScanner, VIVID910, and R700 with the gold standard 3-dimensional models of the SLP250. To assess the reliability of the 3-dimensional models, the shell/shell deviation of each model was calculated based on the same surface-based registrations for all 5 sets of dental casts. RESULTS: OraScanner, VIVID910, and R700 were sufficiently accurate when compared with the gold standard. In the assessment of reliability, there were no significant differences between all comparisons. CONCLUSIONS: The results showed that the OraScanner system has a sophisticated algorithm for 3-dimensional surface registration and can be used to generate accurate and reliable 3-dimensional digital models for use by clinicians.

Three-dimensional dental model constructed from an average dental form.

INTRODUCTION: The purposes of this study were (1) to discover a simple method for computing an average dental form, (2) to evaluate the validity of the new computing method, and (3) to build an average digital dental model based on the resulting average dental form. METHODS: Dental casts of 51 adults were scanned, and 3-dimensional virtual models were reconstructed by using specialized software. Fifty-two anatomic landmarks were plotted on each model to obtain a configuration representing that model. The averaging method was a simplified approach of the generalized partial Procrustes analysis (GPPA); called multiple partial Procrustes analysis (MPPA), it was used to superimpose the 51 sample configurations. For the evaluation method, the GPPA was performed to estimate the population mean form. This mean form was compared with the average forms obtained from the proposed method by using the Procrustes distance as the measure of difference. Construction of the average dental model was based on an average form obtained from the proposed method, and a 3-dimensional dental mesh model was reconstructed. RESULTS: The average forms from the proposed method showed no significant differences compared with the one from the GPPA. The Procrustes distances were about 0.01 mm, which can safely be considered insignificant. CONCLUSIONS: The proposed averaging method, which is simpler than the traditional GPPA approach, was found to be feasible for computing average dental forms. The average dental model constructed in this study might serve as a guide for treatment planning in orthodontic and prosthodontic dentistry.

The development of quantitative methods using virtual models for the measurement of tooth wear.

Tooth wear is an unavoidable process associated with aging. Currently, virtual three-dimensional dental models are widely used and provide an advantage for studying tooth wear. However, there are no wear assessment parameters using virtual tooth models for the quantitative analysis of wear. Therefore, the aim of this study is to develop and evaluate quantitative wear measurement parameters. Ninety maxillary and mandibular dental casts were prepared and rendered as virtual three-dimensional models. For qualitative wear scoring, Hooper's new tooth wear index (NTWI) was used. For quantitative wear measurement, virtual vectors and occlusal planes were generated with reference points. Angles, height, and distance parameters were measured from reference points, vectors or planes. Intra- and interobserver reproducibility was determined for NTWI scoring and quantitative measurements. Quantitatively measurements for all parameters were subgrouped according to age groups and NTWI score groups. The mean and standard deviation were calculated for each group. One-way analysis of variance (ANOVA) test and the coefficients test were performed on the groups. Overall, intra- and interobserver reproducibility was good for both qualitative and quantitative measurement. In the ANOVA test, angle and height parameters showed significant differences between groups, whereas distance parameters did not. Similar results were observed in the coefficients test. However, plane heights and lingual side measurement parameters of the mandible are not recommended. In conclusion, this study indicates that all angle or height parameters of the maxilla and angle or vector height parameters of the buccal side of the mandible can be used as meaningful parameters in a quantitative wear study.

A three-dimensional analysis of the perceived proportions of maxillary anterior teeth.

OBJECTIVE: The proportions of the anterior dentition, which is important for excellent esthetics, have been extensively studied, but there have been no 3-dimensional interpretations. This study was conducted to compare real tooth sizes and perceived tooth sizes between different genders and populations and to analyze the effects of 3-dimensional tooth position and alignment. MATERIALS AND METHODS: Complete dental stone casts were prepared for a total of 139 subjects (50 males and 44 females from Korea and 46 females from Japan). Using 3-dimensional scanning and reconstructions, virtual models were constructed and the widths, lengths and rotations of maxillary anterior teeth were measured. Parameters related to the arch form were measured orthographically. Descriptive statistics and ANOVA were performed to determine the differences among the three groups. A regression model was created to interpret the values of 2-dimensional perceived widths with 3-dimensional measurements and other parameters. RESULTS: This study observed differences in the average mesiodistal perceived and real dimensions of the maxillary central incisors between Japanese and Korean females, as well as differences in lateral incisor/central incisor ratios and canine/lateral incisor ratios in the perceived 2-dimensional measurements. There were no differences in individual tooth rotations between groups. The r(2) values of the regression model decreased from the central incisors to the canine. CONCLUSIONS: Several differences were found between Japanese and Korean females and the regression models that used real dimensions, rotations and arch form parameters as independent factors were not sufficient to explain the perceived widths of anterior teeth in the study samples.

Morphological analysis of the skeletal remains of Japanese females from the Ikenohata-Shichikencho site.

The aim of this study was to assess morphological differences between early-modern (Edo) Japanese and contemporary Japanese using recently uncovered human female remains at the Ikenohata-Shichikencho site in the Tokyo urban area. In this study, 30 female skeletal remains that still retained the upper and lower first molars and central incisors were selected [early-modern (Edo) Japanese group]. Forty contemporary female Japanese were selected as a control. Analyses by standard methods of geometric morphometrics revealed some morphological differences between the early-modern (Edo) Japanese group and the contemporary Japanese group. For example, the early-modern (Edo) Japanese group exhibited bimaxillary dentoalveolar protrusion, a flat occlusal plane, and a large S-N length. On the other hand, the contemporary Japanese group exhibited slight protrusion of the anterior nasal spine. These findings may be of interest to orthodontists who are studying age variation or temporal differences and could lead to a better understanding of morphological diversity and variability.

Development of a novel statistical model for mandibular kinematics.

The purpose of this study was to establish a new statistical method for the analysis of masticatory function. The subjects were patients with anterior crossbite who had received orthognathic surgery. Chewing movement was measured by means of an opto-electronic motion-analysis system. This movement was compared with similar movement in control patients. We sought to develop a statistical model to predict the population average curves of the chewing cycles. In this study, the mandibular incisor point was used as a target point of jaw movement. The combination of a spline function with random coefficients and self-modeling regression (SEMOR) extended to three dimensions was used to predict population average curves for each group. Unquestionably, significant differences were present in some areas. The present modeling method that uses the combination of a spline function and SEMOR is one of the best ways to eliminate subjective estimation with regard to predicting representative chewing cycles.

Effect of combined treatment with alendronate and calcitriol on femoral neck strength in osteopenic rats.

BACKGROUND: Hip fracture is associated with pronounced morbidity and excess mortality in elderly women with postmenopausal osteoporosis. Many drugs have been developed to treat osteoporosis and to reduce the risk of osteoporotic fractures. We investigated the effects of combined alendronate and vitamin D3 treatment on bone mass and fracture load at the femoral neck in ovariectomized (OVX) rats, and evaluated the relationship between bone mass parameters and femoral neck strength. METHODS: Thirty 12-week-old female rats underwent either a sham-operation (n = 6) or OVX (n = 24). Twenty weeks later, OVX rats were further divided into four groups and received daily doses of either saline alone, 0.1 mg/kg alendronate, 0.1 microg/kg calcitriol, or a combination of both two drugs by continuous infusion via Alzet mini-osmotic pumps. The sham-control group received saline alone. After 12 weeks of treatment, femoral necks were examined using peripheral quantitative computed tomography (pQCT) densitometry and mechanical testing. RESULTS: Saline-treated OVX rats showed significant decreases in total bone mineral content (BMC) (by 28.1%), total bone mineral density (BMD) (by 9.5%), cortical BMC (by 26.3%), cancellous BMC (by 66.3%), cancellous BMD (by 29.0%) and total cross-sectional bone area (by 30.4%) compared with the sham-control group. The combined alendronate and calcitriol treatments improved bone loss owing to estrogen deficiency. On mechanical testing, although OVX significantly reduced bone strength of the femoral neck (by 29.3%) compared with the sham-control group, only the combined treatment significantly improved the fracture load at the femoral neck in OVX rats to the level of the sham-controls. The correlation of total BMC to fracture load was significant, but that of total BMD was not. CONCLUSION: Our results showed that the combined treatment with alendronate and calcitriol significantly improved bone fragility of the femoral neck in OVX osteopenic rats.

Relationship between the curve of Spee and dentofacial morphology evaluated with a 3-dimensional reconstruction method in Korean adults.

INTRODUCTION: The purposes of this study were to examine the curve of Spee of the maxillary and mandibular arches by using a 3-dimensional reconstruction method and to determine the relationship between the curve of Spee and dentofacial morphology with multiple regression analysis. METHODS: Lateral cephalograms and dental models were evaluated from 18 Korean men and 31 Korean women. The depth of the curve of Spee was measured on the virtual dental models with computer software. Seventeen cephalometric variables related to the lateral cephalograms were analyzed to determine differences in dentofacial morphology. The Pearson correlation analysis and a multiple linear regression analysis were performed to determine the relationship between the curve of Spee as the dependent variable and other cephalometric and dental variables as the independent variables. RESULTS: The depth of the curve of Spee in the mandibular arch was significantly related to overbite, overjet, and the sagittal position of the mandible with respect to the anterior cranial base. The curve of Spee was not affected by sex. CONCLUSIONS: These results will assist in the determination of the sagittal organization of the teeth as a reference for prosthetic restoration and orthodontic treatment.

Effect of preoperative combined treatment with alendronate and calcitriol on fixation of hydroxyapatite-coated implants in ovariectomized rats.

BACKGROUND: Osteoporosis is a potential risk factor affecting implant stability following total joint arthroplasty. Bisphosphonates are potent inhibitors of osteoblastic bone resorption, and vitamin D is an important hormone involved in the regulation of calcium metabolism. We investigated the benefit of preoperative treatment with alendronate, vitamin D (calcitriol), or a combination of these substances on fixation of hydroxyapatite-coated implants in an ovariectomized rat model of osteoporosis. METHODS: Of sixty-four female rats in the study, fifty-six underwent ovariectomy and eight, a sham operation. A hydroxyapatite-coated femoral implant and an uncoated implant were implanted in all rats seven months after the ovariectomy or the sham operation. Of the fifty-six rats that underwent ovariectomy, eight served as the control group. The remaining forty-eight were treated with alendronate, calcitriol, or a combination of these agents either starting eight weeks before implantation of the rod or starting immediately after implantation. The treatment was continued until four weeks after the implantation. Four weeks after the implantation, the total and cancellous bone mineral density at the proximal part of the tibia and the shear strength of the bone-implant interface were measured in all rats. RESULTS: Although total bone mineral density increased in all of the alendronate-treated groups, compared with that in the ovariectomized control group, cancellous bone mineral density increased only in the group pretreated with both alendronate and calcitriol. The implant stability in the ovariectomized control rats was significantly decreased compared with that in the sham-operation rats. While treatment with alendronate only or calcitriol only did not improve the stability of the implants, treatment with a combination of alendronate and calcitriol, starting preoperatively, significantly improved the stability of the hydroxyapatite-coated implants. CONCLUSIONS: Treatment with a combination of alendronate and calcitriol, starting preoperatively, can improve cancellous bone mineral density and the stability of hydroxyapatite-coated implants in an osteoporotic rat.

Predicting first molar width using virtual models of dental arches.

In dentistry, large regions of dentition often are restored with minimal information about the original anatomy. The ability to predict missing anatomy from existing anatomy would aid such restorations. This study investigated the relationship between first molar mesial-distal width and arch shape using newly defined reference points and three-dimensional (3D) digital methods. Full-mouth dental stone casts from 167 dental students were scanned and rendered as 3D virtual models. Maxillary and mandibular arch lengths and widths and first molar mesial-distal widths were measured on the virtual models using new definitions incorporating virtual planes. A linear mixed model of the first molar width regressed on the other measurements was done. Intraobserver reproducibility was evaluated by means of intraclass correlation (ICC) and standard deviation of measurement error (SDME). All measured distances were averaged as a combined group and as gender groups. The correlation coefficients between the maxillary and mandibular first molar widths were over 0.70 (P < 0.01). Intraobserver error was small. ICCs were over 0.92 and SDMEs were from 0.11 to 0.21 mm. Arch dimensions and first molar widths were defined and measured. Regression equations were calculated for predicting first molar width. The prediction of first molar width using arch dimension is essential for virtual designing of missing first molars. This approach also provides reliable reference point definitions for the virtual dental model which was impossible with traditional measurement methods. Therefore, this study would be helpful for understanding the 3D anatomy of dental arch and fabrication of automatic prosthodontic restorations.

Three-dimensional analysis of orthodontic tooth movement based on XYZ and finite helical axis systems.

The purpose of this study was to demonstrate the advantage of the finite helical axis (FHA) system in the biomechanical analysis of orthodontic tooth movement by comparing it with the rectangular coordinate (XYZ) system. Ten patients (6 females and 4 males, mean age 23 years 7 months) were selected. Maxillary canine retraction using light continuous forces of two different magnitudes (0.5 and 1 N) was used to retract the right and left maxillary canines in subjects who required maximum posterior anchorage. The findings were compared based on midpalatal implants that provided a fixed reference for measurement. The significance of the difference between the results with the two different force magnitudes was determined using Wilcoxon's signed-rank test. With both the XYZ and the FHA system, no significant differences in the amount of distal movement of the canines over 2 months were found between the two force magnitudes. However, the results showed that the canine was likely to incline distally during tooth retraction with a force of 1 N compared with a force of 0.5 N (P < 0.05). With the FHA system, the result indicated that the canine was likely to incline palatally during tooth retraction with a force of 0.5 N compared with a force of 1 N (P < 0.05). In this study, the combination of these two different approaches for describing tooth movement clearly showed a difference between light continuous forces of 0.5 and 1 N.

Airflow produced by dielectric barrier discharge between asymmetric parallel rod electrodes.

We observed a novel type of airflow produced by an atmospheric rf discharge between asymmetric parallel rod electrodes. The electrodes were a bare metal rod 1 mm in diameter and a glass-coated metal rod 3.2 mm in diameter. The thrust, measured by a pendulum, increased with discharge input power.

A novel method for the 3-dimensional simulation of orthognathic surgery by using a multimodal image-fusion technique.

INTRODUCTION: The aim of this study was to establish a novel method for simulating orthognathic surgery in 3-dimensional (3D) space. METHODS: This system mainly consists of 6 procedures: (1) reconstruction of a virtual skull model (VS) from presurgical computed tomography scans; (2) reconstruction of virtual dentition models from 3D surface scanning of dental casts occluded at presurgical and postsurgical intercuspal positions (VD1 and VD2, respectively); (3) reconstruction of a preliminary fusion model of VS and VD1 by an initial intermodality registration; (4) reconstruction of another preliminary fusion model of VS, VD1, and VD2 by a second intramodality registration; (5) repositioning of bony segments by a third intramodality registration and reconstruction of final fusion models at presurgery and postsurgery; and (6) 3D analysis of the movement of bony segments. To test this system, 2 patients with severe skeletal deformities, who had undergone presurgical orthodontic treatment, were used as models. Registration accuracy was determined by the root mean squared distance between the corresponding fiducial markers in a set of 2 images. RESULTS AND CONCLUSIONS: The sum of the root mean squared error of the 3 registration processes was less than 0.4 mm in both patients. This simulation system could be used to precisely realize the presurgical and postsurgical occlusal relationships and craniofacial morphology of a patient with severe skeletal deformities, and to quantitatively describe the movement of a given anatomical point of bony segments. It is assumed that there could be significant benefits in sharing visual and quantitative 3D information from this simulation system among orthodontists and surgeons.

Galvanic corrosion behavior of orthodontic archwire alloys coupled to bracket alloys.

The purpose of this study was to provide a quantitative assessment of galvanic corrosion behavior of orthodontic archwire alloys coupled to orthodontic bracket alloys in 0.9% NaCl solution and to study the effect of surface area ratios. Two common bracket alloys, stainless steels and titanium, and four common wire alloys, nickel-titanium (NiTi) alloy, beta-titanium (beta-Ti) alloy, stainless steel, and cobalt-chromium-nickel alloy, were used. Three different area ratios, 1:1, 1:2.35, and 1:3.64, were used; two of them assumed that the multibracket appliances consists of 14 brackets and 0.016 inch of round archwire or 0.016 x 0.022 inch of rectangular archwire. The galvanic current was measured for 3 successive days using zero-impedance ammeter. When the NiTi alloy was coupled with Ti (1:1, 1:2.35, and 1:3.64 of the surface area ratio) or beta-Ti alloy was coupled with Ti (1:2.35 and 1:3.64 of the surface area ratio), Ti initially was the anode and corroded. However, the polarity reversed in 1 hour, resulting in corrosion of the NiTi or beta-Ti. The NiTi alloy coupled with SUS 304 or Ti exhibited a relatively large galvanic current density even after 72 hours. It is suggested that coupling SUS 304-NiTi and Ti-NiTi may remarkably accelerate the corrosion of NiTi alloy, which serves as the anode. The different anode-cathode area ratios used in this study had little effect on galvanic corrosion behavior.

Comparison of the finite helical axis and the rectangular coordinate system in representing orthodontic tooth movement.

In orthodontics, tooth movement is typically described using the rectangular coordinate system (XYZ); however, this system has several disadvantages when performing biomechanical analyses. An alternative method is the finite helical axis (FHA) system, which describes movement as a rotation about and a translation along a single axis located in space. The purpose of this study was to examine differences between the FHA and the XYZ systems in analyzing orthodontic tooth movement. Maxillary canine retraction was done using sliding mechanics or a retraction spring with midpalatal orthodontic implants used as measuring references. Tooth movement calculated with the FHA was compared with the corresponding movement in the rectangular coordinate system weekly over a 2-month interval in eight patients. The FHA showed that sliding mechanics controlled rotation of the canine better than the retraction spring (Ricketts retractor), and that the Ricketts retractor controlled tipping better. Changes in the FHA direction and position vectors with time showed that the biomechanical forces are not uniform during the treatment period. In both mechanics, the FHA provided a simple biomechanical model for canine retraction.

Simulation study for a finite helical axis analysis of tooth movement.

The description of motion using a finite helical axis (FHA) is independent of the chosen coordinate system because the values of the helical axis parameters do not change with coordinate transformations. However, an intuitive understanding of tooth movement expressed by the FHA can be slightly difficult for orthodontists who have never used it. The purpose of this study was to clarify the basic behavior of the FHA to increase our understanding of the FHA during tooth movement. Parameters of the FHA were calculated in two different simulations of canine retraction. In simulation 1, as the tipping angle of the canine was increased from 5 degrees to 30 degrees, the direction vector of the FHA v approached the x-axis (tipping axis), thus increasing the rotation angle about the FHA theta. These results demonstrated that the direction vector of the FHA can indicate the axis of rotation that is most affected in three-dimensional transformation. In simulation 2, bodily tooth movement of the canine was increased from one to five mm, and the shortest distance from the origin to the FHA d increased in a linear manner. In this case, the percent increase in bodily tooth movement could be determined by the d value. This study showed that the use of FHA makes it possible to determine the torques applied to the tooth and the true bodily tooth movement during orthodontic treatment, and this may lead to a better understanding of how to move teeth.

Basic behavior of the finite helical axis in a simple tooth movement simulation.

A finite helical axis (FHA) analysis can provide precise three-dimensional information on orthodontic tooth movement compared to an analysis based on a rectangular coordinate system. The FHA has already been applied in an analysis of orthodontic tooth movement. Interestingly, the position of the FHA changes dramatically in different stages of treatment; however, no previous report has provided detailed information of its basic behavior for clinicians. The purpose of this study was to clarify the basic behavior of the FHA in simple tooth movement, which could promote a better understanding of the 3-D orientation of and rotation about the FHA during tooth movement. Parameters of the FHA were calculated from a simulation of canine retraction. As the tipping angle of the canine was increased from 5 degrees to 30 degrees , the orientation vector of the FHA approached the most affected axis of rotation (on a rectangular coordinate system) in a non-linear manner. The angle of rotation about the FHA also increased in a non-linear manner. This non-linear problem was solved analytically. The basic behavior of the orientation vector of the FHA and the non-linear characteristics of the FHA parameters clarified in this study should be important for the future analysis of actual tooth movement based on the FHA. However, we must be aware that the non-linearity of the FHA itself may affect the analysis of the mechanical properties of the periodontal tissue.