JP2005304601A - Method for calculating side deviation amount of hyoid bone median line to mandible median line in panoramic tomogram - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a judgement reference for the diagnosis of influence on the whole body by occlusion treatment and the treatment effect by calculating a hyoid bone deviation amount to a mandible median from a hyoid bone image projected on a panoramic tomogram clinically. <P>SOLUTION: In the panoramic tomogram of a certain patient, from the deviation amount α of a mandible rear part and the deviation amount (a) of a mandible front part, it is assumed that the hyoid bone is present in the median to the mandible and the deviation amount C of the hyoid bone is calculated. Further, an actual hyoid bone deviation amount β is computed from the same panoramic tomogram and the left and right deviation amounts of the hyoid bone are calculated by observing a difference between the deviation amount B and the deviation amount C obtained from an assumption expression. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a method for calculating the lateral deviation of the hyoid midline with respect to the mandibular midline from projection images of the mandible and hyoid bone of panoramic tomography as one of the examination criteria before and after occlusal treatment in an occlusal maltreatment patient Things about.

  Although it has been said that the vertebrae including the cervical vertebrae bend due to malocclusion and the posture deteriorates, there is no confirmation of the mechanism of action. In addition, it was difficult to quantify the effects on the whole body such as malocclusion and curvature of the spine.

  Among Xray photographs, panoramic tomography has a large amount of information on dental diseases, and is an X-ray examination method indispensable for diagnosis. However, standardization using straightness of radiation has not been performed so far.

  The hyoid bone midline and mandibular midline on the front of the cervical vertebra should match in healthy subjects, and the influence on the whole body due to malocclusion by digitizing the lateral relationship between the hyoid bone and the mandible from panoramic tomograms This is one of the criteria.

When panoramic tomography is taken, the head is fixed by biting the incisor mounting bar with the upper and lower jaw incisors in the front part and sandwiching both heads with the gripping bars in the rear part. The part is installed at a predetermined position. In this method, it is difficult to obtain the uniformity of the head installation position, and it is not possible to obtain reference only by determining the amount of lateral displacement of the hyoid bone relative to the center line of the panoramic tomogram. Therefore, the displacement state of the mandible with respect to the center line of the panoramic tomography is measured from the anterior portion of the lower jaw and the posterior portion of the lower jaw, and the lateral displacement amount of the hyoid midline with respect to the lower midline of the mandible is calculated.

Hereinafter, means for solving the problems of the present invention will be described with reference to the drawings. In order to achieve the above object, first, a method of calculating the lateral deviation amount a of the anterior part of the lower jaw will be described.

As in FIG. 1, the model or at the oral cavity to measure the actual mandibular central incisor teeth tooth crown width size I _1.

Subsequently, as shown in FIG. 2, the width I ₂ of the mandibular central incisor tooth on the panoramic tomographic image and the distance I ₃ between the middle line between the central incisors of the lower jaw and the panoramic tomographic center line are measured. . When the middle line is deviated to the left with respect to the center line of the panoramic tomography, the sign is +, and when the middle line is deviated to the right, the sign is-(in the figure, the sign- Become). The actual lateral deviation amount a of the anterior portion of the lower jaw can be calculated by the following mathematical formula.

Formula 1 a (mm) = I ₃ × I ₁ ÷ I ₂

Next, a symmetrical metal frame simulating the positional relationship between the mandible and the hyoid bone as shown in FIG. 3 so that the lateral deviation amount α of the posterior portion of the lower jaw and the lateral deviation amount β of the hyoid bone can be measured simultaneously. It was created. The model structure consists of four wires corresponding to the bilateral mandibular branch width diameter, one wire corresponding to the midline of the mandibular central incisors, and two wires as the hyoid bone in the midline of the model. Measurement points were provided.

FIG. 4 is a panoramic tomographic photograph obtained by photographing the model on the center line of a panoramic tomographic photographing apparatus ASAHI-AUTO3 (manufactured by Asahi Roentgen Kogyo Co., Ltd.). In this way, a substantially bilaterally symmetric image can be obtained due to the high left-right symmetry accuracy of the rotational and revolving motions of the panoramic tomography apparatus trajectory.

On the other hand, FIG. 5 is an Xray image obtained by translating the model to the left by about 5 mm from the center line of the panoramic tomography apparatus. Both the wire installed at the rear side of the model and the wire installed at the center of the model are projected with the reduced side reduced, and the enlarged side is projected with the non-shifted side.

FIG. 6 is a schematic diagram showing measurement points of the displacement amount α, the displacement amount a, and the displacement amount β that the model appears in the panoramic tomography. As an index of the amount of deviation behind the model, the width of the left and right mandibular branches was imitated. As the measurement points, four positions on the right side (X _{1 to} X ₄ ) and left side (Y _{1 to} Y ₄ ) were provided, and the lines connecting the midpoints of the respective wire images were measured as L _{1 to} L ₄ , respectively. Hyoid part having a measuring point on the model center, right width diameter _(x 1 _~x 5), the left width diameter _(y 1 _~y 5) 5 points provided, the mid-point distance between the lateral width size _m 1 ~ They were measured respectively as m _5. In the model front midline, a single wire was installed vertically, imitating the midline of the mandibular central incisors, and used as an index for determining the lateral displacement amount a of the model front.

FIG. 7 shows how to obtain the lateral displacement amount α behind the model with respect to the center line of the panoramic tomogram. First, the midpoint CR point and the CL point of the right side X line and the left side Y line of the same part of two symmetrical subjects are obtained. The CR point and the CL point are connected to form an L line. Then, with the CR point and the CL point as the center, the X line and the Y line are drawn with the same length as the X line and the Y line. Subsequently, the lines are drawn so that the upper and lower ends of the X ｀ line and the Y ｀ line are crossed. Let this intersection point be D point.
Finally, the midpoint (LC point) of the L line is obtained.
The distance between the point D and the LC point can be converted from the actual lateral displacement amount α ′ with respect to the center line of the X-ray apparatus as the displacement amount α on the Panrama tomogram. As shown in FIG. 7a, when X = Y, α = 0, and as shown in FIG. 7b, the left-right difference in magnification can be measured as the distance between point D and LC, and the length of X and Y can be measured. Reversal is represented by positive and negative reversals.

Α can be expressed by the following equation.

Formula 2 α = L × X / (X + Y) −1 / 2L

Similarly to the displacement amount α, the displacement amount β obtained from the subject imitating the hyoid bone in the midline part of the model is also the right side width diameter (x _{1 to} x ₅ ), left side width diameter (y _{1 to} y ₅ ), and left and right width. The distance between the midpoints of the diameters (m _{1 to} m ₅ ) was substituted into the following formula to determine the deviation amounts β _{1 to} β ₅ .

Formula 3 β = m × x / (x + y) −1/2 m

FIG. 8 is a copy diagram showing the imaging conditions of Experiment 1 using the model, which is translated laterally by a certain amount with respect to the center line of the panoramic tomography apparatus, and further from the front to the rear. Slide continuously at regular intervals. Further, the lateral translation (a) was arbitrarily determined, and several samples were prepared.

According to Experiment 1, the ratio of the actual lateral displacement amount α ′ to the center line of the panoramic tomographic apparatus and the lateral displacement amount α on the panoramic tomographic image and the correlation of L corresponding to the ratio, the panoramic tomographic image The actual lateral deviation amount β ′ with respect to the center line of the apparatus, the ratio of the lateral deviation amount β on the panoramic tomogram, and the correlation between m corresponding to the ratio can be obtained.

FIG. 9 is a scatter diagram in which a polynomial approximate curve expression of f (L) = α / α ′ is obtained from all samples of Experiment 1 by the method of least squares. It is possible to analyze the difference in the magnification of the projected image due to the difference in the imaging region (L).

FIG. 10 is a scatter diagram in which a polynomial approximate curve expression of g (m) = β / β′m is obtained from all samples of Experiment 1 by the method of least squares. This is the actual deviation amount obtained by calculating the ratio of β ′ to the deviation amount β on the panoramic tomography and the correlation of m corresponding to the ratio, and further dividing the ratio by m. As a result, the discrete scatter diagram was approximated and a characteristic cubic curve was obtained. It is possible to analyze the difference in magnification of the projected image due to the difference in the imaging part (m).

Then, as shown in FIG. 11, it is assumed that the ratio of the longitudinal distance (L ₀ , m ₀ ) of the actual α ′ and β ′ measurement points is equal to the ratio of the longitudinal distance (L, m) on the panoramic tomogram. Then the following proportional expression holds.

Equation 1 L: m = (α'-a): (β'-a)

Further, in Experiment 1, approximate curve equations of f (L) = α / α ′ and g (m) = β / mβ ′ are obtained, and the lateral deviation amount β calculated together with the proportional equation is expressed as a mathematical expression. Assuming B, the following formula is derived:

Equation 2 B = g (m) × m {L × a + m × α / f (L) −m × a} / L
When the amount of lateral displacement of the hyoid calculated from Equation B above matches the actual amount of lateral displacement β of the hyoid bone in the panoramic tomogram, the lateral displacement of the hyoid bone is determined from the lateral displacement state of the mandible. The mathematical formula that can estimate the amount of position is standardized in advance, and the mathematical formula B can have generality when calculating the lateral deviation amount of the hyoid bone.

In order to confirm the correlation between the mathematical formula B and the hyoid displacement amount β, in Experiment 2, as shown in FIG. The panoramic tomographic images were taken continuously by rotating at regular intervals. Further, the lateral translation (a) was arbitrarily determined, and several samples were prepared.

FIG. 13 is a scatter diagram showing the relative relationship between the calculated value obtained from Formula B and the corresponding lateral displacement amount β of the hyoid bone. A linear approximation formula was obtained from the scatter diagram by the least square method. Regardless of the lateral movement amount a, the linear approximation formulas of the samples all show substantially the same slope, and the slope of the ideal linear approximation formula is obtained by multiplying the calculated value B by the constant η. Since the intersection of the linear approximation formula and the y-axis was in a proportional relationship with the forward lateral displacement amount a, statistical adjustment was made as a proportionality constant γ.

Expression B is expressed as follows, which is statistically adjusted so that Expression B can be estimated most optimally.

Formula 3 Formula C = γ × a + η × B
a: lateral deviation amount γ, η: constant of anterior part of lower jaw

FIG. 14 is a scatter diagram showing the correlation between the measured value β and the calculated value C. From the linear approximation obtained from the scatter diagram, an ideal mathematical formula C in which β and C substantially coincide with each other was obtained. That is, when the mandibular median line and the hyoid bone median line coincide, the lateral displacement amount of the hyoid bone can be estimated by measuring the mandibular deviation state.

In the means for solving this problem, a wire frame imitating the mandibular hyoid bone was created and used, but the structure is not limited to this. In addition, the measurement values obtained in Experiments 1 and 2 are each obtained from an arbitrary amount of movement in a predetermined direction, and are not limited thereto. Furthermore, although this experiment used the panoramic tomography apparatus ASAHI-AUTO3 (manufactured by Asahi Roentgen Kogyo Co., Ltd.), the present invention is not limited to this. Further, when the midline of the mandible and the midline of the hyoid bone coincide, the formulas B and C for estimating the lateral shift amount of the hyoid from the lateral shift amount of the mandible are not limited to the above-described formulas.

  The present invention is a mathematical formula obtained by utilizing the left-right symmetry of the trajectory of the panoramic tomography apparatus, the accuracy of temporal symmetry of rotation and revolution, and the straightness of X-rays. The characteristic polynomial approximation curve formula g (m) = β / β′m is similar to the trajectory of the panoramic tomography apparatus.

So far, it has been difficult to quantify facial effects, moire photos, etc., as an assessment of systemic effects on mandibular deviation, but in particular, the left and right positional relationship between the mandible and the hyoid bone is numerical. And helps diagnosis before and after occlusal treatment. Further, by examining the positional relationship between the mandible and the hyoid bone by lateral X-ray standard photographs and 3DCT at the same time, the diagnosis of the hyoid bone after the preoperative operation by the occlusal treatment becomes more reliable.

The positional change of the hyoid bone follows the correction of the mandibular deviation and the change of posture, and it is desirable that the X imaging is performed at intervals of several months to one year.

The best mode for carrying out the present invention will be described below with reference to the drawings.
15, 16, 17, 18, and 19 describe how to obtain the lateral deviation amount α of the posterior portion of the lower jaw and the lateral displacement amount β of the anterior portion of the hyoid relative to the center line of the panoramic tomography. FIG.

First, as shown in FIG. 15, a gonial point (Gor, which is formed by the deepest point (Nr1, Nl1 point) of the fold at the center of the bilateral mandibular notch, the posterior edge of the bilateral mandibular branch, and the bilateral mandibular inferior planes. Gol points) are connected on the left and right sides (Nr1-Gor line, Nl1-Gol line). Subsequently, the Nr2 point that is the midpoint of the Nr1-Gor line is extracted on the right side. Similarly, N12 points are extracted on the left side.

As shown in FIG. 16, the right Nr2 point and the left Nl2 point are connected to form an L line. Intersections between the L line and the lower edge of the lower jaw branch are Nr3 and Nl3 points. Then, intersection points formed by extending the L line to the trailing edge of the lower jaw branch are defined as Nr4 and Nl4 points.
Moreover, the accuracy of the L line can be confirmed by adding a notch line and a gonial line as shown in the figure and observing the parallelism with the L line.

In the hyoid bone, the measurement point in front of the right hyoid body is Hr1, the upper notch portion of the posterior joint of the hyoid bone is Hr2, and the lower notch portion is Hr3 point. Similarly, for the measurement point in front of the left hyoid body, the Hl1, Hl2, and Hl3 points are obtained.

As shown in FIG. 17, the length of the right Nr3-Nr4 line is X (mm), and the length of the left Nl3-Nl4 line is Y (mm). The length between the midpoints of the left and right N3-N4 lines is L (mm).

In the hyoid bone, the right Hr2 point and the Hr3 point are connected by a line, and the middle point is defined as the Hr4 point. Then, the Hr1 point and the Hr4 point are connected by a line, and the midpoint is extracted. Similarly, H4 points are extracted for the measurement points in front of the left hyoid body.

Finally, as shown in FIG. 18, X and Y are orthogonally crossed with respect to the L line, and the upper end and the lower end of each are crossed, and the difference between the intersection and the midpoint of L is measured. The lateral displacement amount α behind the jawbone is calculated.

Also in the hyoid bone, the length of the right Hr1-Hr4 line is x (mm) and the left Hl1-Hl4 line is y (mm). The length of the midpoint between x and y is m (mm). The amount of lateral displacement β of the hyoid bone is calculated.

Next, the tongue calculated from Formula C when it is assumed that the mandibular midline and the hyoid bone midline determined from the lateral deviation amount a of the anterior portion of the lower jaw and the lateral displacement amount α of the posterior portion of the lower jaw coincide with each other. Estimate the lateral displacement of the hyoid midline relative to the mandibular midline by subtracting the hyoid lateral displacement β calculated from the same panoramic tomogram as the lateral displacement of the bone it can.

  Further, in the panoramic tomographic image, the magnification rate of the subject varies depending on the photographing part (m). FIG. 19 is a scatter diagram showing the relationship between the ratio of the actual lateral deviation β ′ of the hyoid bone and the lateral deviation β on the X-ray and m corresponding to the ratio obtained from Experiment 1. It is. From the scatter diagram, a polynomial approximate curve formula h (m) is obtained by the method of least squares.

The polynomial approximate curve formula h (m) also applies to the actual lateral displacement of the hyoid bone and the lateral displacement of the hyoid on the X-ray (β-C), and the actual lateral displacement of the hyoid bone. The unit quantity is expressed by the following formula Z.

Equation 4 Z = (β-C) / h (m)

Normalizing the difference in the magnification of the subject depending on the panoramic tomographic region by deriving the actual hyoid lateral displacement amount instead of the hyoid lateral displacement amount on the panoramic tomographic image by the mathematical formula Z. Thus, the mathematical formula Z for calculating the lateral displacement amount of the hyoid bone can have generality.

  In the best mode for carrying out the present invention, the amount of lateral deviation of the lower jaw is obtained from the central incisor of the lower jaw from the central incisor of the lower jaw, and from the width diameter of the central portion of the lower jaw branch at the rear of the lower jaw. Not limited to this. Although the measurement site | part at the time of calculating | requiring the amount of lateral displacement of the hyoid bone is calculated | required from the up-and-down notch part of the joint part of a hyoid bone body, a measurement site | part is not restricted to this. Furthermore, the mathematical formula Z for obtaining the amount of lateral displacement of the hyoid bone is not limited to the mathematical formula described above. Further, as the least square method, not only a general Gauss-Neuton method and a conjugate direction method, but also an arithmetic expression having performance equivalent to those may be used. Furthermore, the mathematical formula Z for obtaining the amount of lateral displacement of the hyoid bone is not limited to the mathematical formula described above.

FIGS. 20a), b), c), and d) are four panoramic tomographic photographs taken of the same patient within about two months. FIG. 21 shows measured values of respective panoramic tomograms according to the present invention, anterior mandibular lateral displacement amount a, posterior mandibular lateral displacement amount α, hyoid lateral displacement amount β, mandibular midline. Is the result of the lateral displacement Z of the hyoid relative to The hyoid bone displacement direction in all cases of left mandibular deviation was confirmed as the rightward deviation. In addition, the amount of left lateral deviation with respect to the upper jaw was about 2 mm, while the amount of deviation of the hyoid bone was as large as 7 to 10 mm.

In addition, about 91% of our 130 cases of lateral mandibular deviation, hyoid displacement to the opposite side of the mandibular deviation side was observed. In addition, although not described in detail, the asymmetric posture in the elderly is a posture that attempts to shift the hyoid bone to the opposite side by twisting and tilting the trunk with respect to the lateral shift of the lower jaw. Suggested.

It is the schematic diagram showing the measurement point on the model at the time of calculating deviation | shift amount a. It is a schematic diagram showing the measurement point on the panoramic tomography when calculating the deviation | shift amount a. It is a perspective view of the wire model which imitated the mandible and hyoid used for calculating | requiring the numerical formula of this invention. FIG. 4 is an X-ray image obtained by photographing the model of FIG. 3 on the center line of the panoramic tomography apparatus. 2 is an X-ray image obtained by translating the model of FIG. 1 to the left by about 5 mm from the center line of the panoramic tomography apparatus. It is the schematic diagram showing the measurement point on the panoramic tomography photograph of the model of FIG. It is a schematic diagram showing a calculation method of the lateral displacement amount α and the lateral displacement amount β. It is the schematic diagram showing the imaging conditions of Experiment 1 which moved the model back and forth further once parallelly moved to the side. FIG. 5 is a scatter diagram showing the ratio of the deviation amount α on the X-ray and the actual deviation amount α ′ obtained from Experiment 1 and the correlation of L corresponding to the ratio. It is a scatter diagram showing the correlation of m corresponding to the ratio obtained by Experiment 1 by dividing the ratio of the deviation amount β on the X-rays and the actual deviation amount β ′ by m. In the panoramic tomography apparatus, the displacement amount a, the actual displacement amounts α ′ and β ′, the actual distances L ₀ and m _{0 of} the actual α and β, the longitudinal distances L and m of α and β on the X-ray It is a schematic diagram showing the relationship It is the schematic diagram showing the imaging condition of the experiment 2 which carried out the rotational movement centering on the front front tooth | gear part further after parallel translation once to the side. 6 is a scatter diagram showing the correlation between a calculated value B obtained from Experiment 2 and an actual measurement value β. FIG. It is a scatter diagram showing the correlation between the calculated value C obtained by correcting the calculated value B with constants γ and η and the actual measured value β. It is the schematic diagram showing the calculation method of deviation amount (alpha) and deviation amount (beta) from a panoramic tomography photograph. It is the schematic diagram showing the calculation method of deviation amount (alpha) and deviation amount (beta) from a panoramic tomography photograph. It is the schematic diagram showing the calculation method of deviation amount (alpha) and deviation amount (beta) from a panoramic tomography photograph. It is the schematic diagram showing the calculation method of deviation amount (alpha) and deviation amount (beta) from a panoramic tomography photograph. FIG. 10 is a scatter diagram showing the correlation between the ratio of the displacement amount β on the panoramic tomographic photograph, the actual displacement amount β ′, and m obtained from Experiment 1. (A), (b), (c), (d) are panoramic tomograms of the same patient obtained within about two months. 20 is a table of the displacement amount a, the displacement amount α, the displacement amount β, and the lateral displacement amount of the hyoid bone.

Explanation of symbols

1 Plastic lower jaw incisor setting stick
2 panoramic tomographic center line
3 Lower jaw middle line
4 lower middle anterior teeth
5 Mandibular branch width
6 Hyoid bone
7 Lateral deviation of the anterior part of the lower jaw a
8 Actual lateral deviation α 'of the lower jaw
9 Actual amount of lateral displacement of the hyoid bone β '
10 Distance L of α measurement site on panoramic tomography
11 Distance m of β measurement site on panoramic tomography
12 Actual front-rear distance L ₀ of α ′ measurement site
13 Actual front-rear distance m ₀ of β ′ measurement site
14 Start axis trajectory
15 Rotating shaft
16 Notch line
17 L line
18 Gonial Line
19 Lateral deviation α of the posterior part of the lower jaw
20 Hyoid bone lateral displacement β

Claims (16)

  Hyoid bones assuming that the subject's mandibular midline and hyoid midline coincide with the lateral deviation amount a of the mandibular anterior portion and the lateral deviation amount α of the posterior portion of the mandible with respect to the center line of the panoramic tomography The lateral displacement amount of the hyoid bone is estimated by the formula C. On the other hand, the hyoid lateral displacement amount β with respect to the center line of the same panoramic tomogram is calculated, and the estimated formula C and the hyoid lateral displacement amount β are calculated. A method of creating an enclosing mathematical formula Z and calculating a lateral displacement amount of the hyoid midline with respect to the mandibular midline from a panoramic tomographic photograph. The hyoid bone relative to the midline of the mandible according to claim 1, wherein an arithmetic expression for obtaining the lateral deviation amount a of the anterior part of the lower jaw with respect to the center line of the panoramic tomographic image is expressed as follows: A method of calculating the lateral deviation of the median line from the panoramic tomography.
a (mm) = I ₃ × I ₁ ÷ I ₂
I _1: Actual mandibular central incisor crown width I ₂ : Mandibular central incisor crown width on panoramic tomographic image I ₃ : Middle line between mandibular central incisors on panoramic tomographic image Distance from the centerline of panoramic tomography The hyoid bone relative to the midline of the mandible according to claim 1, wherein an arithmetic expression for obtaining a lateral deviation amount α of the posterior portion of the lower jaw with respect to the center line of the panoramic tomogram is expressed as follows: A method of calculating the lateral deviation of the median line from the panoramic tomography.
α (mm) = L × X / (X + Y) −1 / 2L
L: Distance between center points of left and right mandibular branches in panoramic tomography X: Width diameter of right mandibular branch in panoramic tomography Y: Width diameter of left mandibular branch in panoramic tomography 2. The median hyoid bone relative to the midline of the mandible according to claim 1, wherein an arithmetic expression for calculating a lateral displacement amount β of the hyoid relative to the center line of the panoramic tomographic image is expressed as follows: A method for calculating the amount of lateral deviation of a line from a panoramic tomogram.
β (mm) = m × x / (x + y) −1/2 m
m: distance between the center points of the left and right hyoid bone images in the panoramic tomography x: the width of the right hyoid body in the panoramic tomography y: the width of the left hyoid body in the panoramic tomography   The estimation formula C is a model in which left and right symmetrical bilateral mandibular branch width diameters are imitated, and the model is moved in a predetermined direction at arbitrary intervals at the same time, and at the same time, continuously taken in panoramic tomography, The ratio of the lateral deviation amount α of the posterior portion of the lower jaw projected on the panoramic tomography image and the actual lateral displacement amount α ′ of the posterior portion of the lower jaw portion with respect to the center line of the panoramic tomography apparatus, and the right and left corresponding to the ratio This is a mathematical expression including the approximate expression f (L) obtained by displaying the correlation of the distance L between the mandibular branch center points on a two-dimensional coordinate axis in a scatter diagram form and using the least square method from the scatter diagram. 2. The method of calculating a lateral deviation amount of the hyoid midline with respect to the mandibular midline according to claim 1 from a panoramic tomographic image. 2. The lateral displacement of the hyoid midline with respect to the mandibular midline according to claim 1, wherein the estimation formula C is a formula including the approximate formula f (L) expressed as follows. Method f (L) = α / α ′ for calculating quantity from panoramic tomography
α: Lateral deviation of the posterior part of the mandible in panoramic tomography α ′: Lateral deviation of the posterior part of the lower jaw with respect to the center line of the panoramic tomography apparatus   The speculative formula C is projected on the panoramic tomographic image by an experiment in which a model imitating the hyoid bone is created, and the model is moved at several intervals in a predetermined direction and at the same time the panoramic tomographic image is taken continuously. The ratio of the lateral displacement amount β ′ of the hyoid bone and the lateral displacement amount β ′ of the hyoid bone to the actual center line of the panoramic tomography apparatus is further set to the distance m between the left and right hyoid bone center points corresponding to the ratio. The correlation between the ratio obtained by dividing the discretized distribution frequency and m and the correlation of m is displayed in a scatter diagram on a two-dimensional coordinate axis, and the approximate expression g ( The method of calculating a lateral deviation amount of the hyoid midline with respect to the mandibular midline from the panoramic tomographic image according to claim 1, wherein m) is included. The lateral deviation of the hyoid midline with respect to the mandibular midline according to claim 1, wherein the estimation formula C is a formula including the approximate formula g (m) expressed as follows. A method of calculating the amount from panoramic tomography.
g (m) = β / β′m
β: lateral displacement of the hyoid bone in the panoramic tomogram β ′: lateral displacement of the hyoid bone relative to the center line of the panoramic tomographic apparatus m: the center point of the left and right hyoid image in the panoramic tomographic image Distance between The inference formula C statistically adjusts the formula B so that the formula B including the proportional formula expressed as follows and the lateral displacement amount β of the hyoid corresponding to the formula B coincide with each other. The method of calculating a lateral deviation amount of the hyoid bone midline with respect to the lower midline of the mandible from the panoramic tomography according to claim 1, wherein
L: m = (α′−a): (β′−a)
L: Distance between center points of left and right mandibular branches in panoramic tomography m: Distance between center points of hyoid image divided into left and right in panoramic tomography β ′: Hyoid bone side relative to center line of panoramic tomography apparatus Amount of lateral displacement α ′: A lateral displacement amount of the posterior portion of the lower jaw with respect to the center line of the panoramic tomography apparatus a: A lateral displacement amount of the anterior portion of the lower jaw with respect to the center line of the panoramic tomography apparatus The inference formula C is obtained by statistically adjusting the formula B so that the formula B expressed as follows and the lateral displacement amount β of the hyoid corresponding to the formula B coincide with each other. The method for calculating a lateral deviation amount of the hyoid midline with respect to the mandibular midline from the panoramic tomographic image according to claim 1, which is a mathematical formula.
Formula B = g (m) × m {L × a + m × α / f (L) −m × a} / L
L: Distance between the central points of the left and right mandibular branches in the panoramic tomogram m: Distance between the central points of the left and right hyoid bone images in the panoramic tomography α: Side displacement of the posterior part of the lower jaw in the panoramic tomogram a: g (m) with respect to the center line of the panoramic tomographic apparatus, f (L): variable   The estimation formula C is based on an experiment in which a model in which the midline of the mandible and the hyoid bone midline coincide with each other, and the model is moved in a predetermined direction at an arbitrary interval at the same time and simultaneously taken in panoramic tomography. Assuming the lateral displacement of the hyoid in conjunction with the formula B, the correlation between the lateral displacement β of the hyoid corresponding to the mathematical formula B is displayed in a scatter diagram on a two-dimensional coordinate axis. The formula B is a mathematical formula obtained by statistically adjusting the mathematical formula B so that the lateral displacement amount β of the hyoid bone is coincident with the lower midline of the lower jaw. A method of calculating lateral deviation of the hyoid midline from panoramic tomographic images. The inference formula C is obtained by statistically adjusting the formula B so that the formula including the formula B expressed as follows and the lateral displacement amount β of the hyoid corresponding to the formula match. The method of calculating a lateral deviation amount of the hyoid midline with respect to the mandibular midline from the panoramic tomography according to claim 1, wherein the formula is an obtained mathematical formula.
C = γ × a + η × B
a: Lateral deviation of the anterior part of the mandible in panoramic tomography B: Lateral deviation of the hyoid calculated from the deviation of the mandible assuming that the center line of the mandible and the hyoid bone are coincident Quantity γ, η: Constant   The mathematical formula Z assumes that the subject's mandibular midline and hyoid bone midline coincide with each other, and the panoramic tomographic image shows the lateral deviation amount a of the mandibular anterior portion and the lateral deviation amount α of the posterior portion of the mandible. The amount of lateral displacement of the hyoid is calculated by subtracting the amount of lateral displacement β of the hyoid relative to the center line of the panoramic tomographic image, which is the same as the estimation formula C in which the amount of displacement of the hyoid can be estimated The method for calculating a lateral deviation amount of the hyoid midline relative to the mandibular midline according to claim 1 from a panoramic tomographic image. The mathematical formula Z converts the lateral displacement amount of the hyoid midline with respect to the mandibular midline on the panoramic tomogram into the actual lateral displacement amount of the hyoid bone, which is expressed as follows. 14. The method of calculating a lateral deviation amount of the hyoid midline with respect to the mandibular midline according to claim 1 or 13, from a panoramic tomogram.
Z = (β−C) / h (m)
β: Hyoid bone lateral displacement amount in panoramic tomography C: Hyoid bone displacement amount projected on panoramic tomography photo can be estimated when it is assumed that the mandibular midline matches the hyoid bone median line Formula h (m): Variable   The approximate expression h (m) is based on the panoramic tomographic image obtained by creating a model imitating the hyoid bone, moving the model several times in a predetermined direction at an arbitrary interval, and continuously shooting the panoramic tomographic image. Of the hyoid bone side projection β projected onto the center and the ratio of the actual hyoid bone side displacement β ′ to the center line of the panoramic tomography apparatus and the distance between the left and right hyoid bone center points corresponding to the ratio The relation of m is an approximate expression obtained by displaying the relationship of m on a two-dimensional coordinate axis as a scatter diagram and obtaining the scatter diagram from the scatter diagram using the least square method. Of calculating lateral displacement of the hyoid midline relative to the mandibular midline from the panoramic tomogram. The hyoid bone midline with respect to the lower midline of the mandible according to claim 1, 13 or 14, wherein the mathematical formula Z includes the approximate expression h (m) expressed as follows. A method of calculating the amount of lateral deviation from panoramic tomographic images.
h (m) = β / β ′
β: lateral displacement of the hyoid bone in the panoramic tomogram β ′: lateral displacement of the hyoid bone relative to the center line of the panoramic tomographic apparatus m: the center point of the left and right hyoid image in the panoramic tomographic image Distance between

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