SU1727784A1 - Method for diagnosis of maxillodental anomalies - Google Patents

Description

Relative information obtained by various methods is transferred into the model of one of the types of stereo photographing, hereinafter referred to as the main model, according to at least three common points using the model exterior orientation formula

AX + BY +, (2)

where a, b, C are the coefficients of the level of the plane,

compose the error equation for each point using the formula

AXi + BYi + CZi + 1 Vi,

(3)

R A (Rl-R o),

0)

where a

311 312313 321 322 323 331 332 333

Where

I - point number;

V - random error. The system of error equations for all points in the matrix form is represented as BU + L V, (4)

Next, the imaging of the elements of the SCLE is projected onto the median, gnatical and condillary plane of the SCG, while it is possible to determine the position of the jaws in the skull, taking into account the resulting ini2zi2 2xi2zi x22z222x22z2

s

X nZ n2Xn2Zn

The least squares solution is found by the formula

(BTPB) 1BTPL

The square of the standard error of the unit of weight is

„2 UTRU f n -4

and the dispersion-covariance matrix is calculated by the formula

Diw-A B PB) -1.

(nineteen)

Using the decision vector L, the determinant values are

if det 5 0, det 0 0, then this is a parabola;

if qia q23 0, a qn q22 - R, then this curve is a circle;

if det d 0, a det Q O, then this curve is a hyperbole. The definition of the type of curve is necessary for the collection of statistics and the establishment of regularities of individual norms.

The generally accepted norm of the shape of the curve of the dental arch in the projection on the X2 plane is considered an ellipse with the ratio of semi-axes

If, as a result of determining the patient's dental arc shape, it turned out not to be an ellipse, but a different curve, providing the functions and aesthetics of the face, then it is taken as LNDF, otherwise LNDF is taken to be an ellipse with the conventional ratio of semi-axes. To do this, re-approximation of the dental arch is performed using the formula

qn (X2 +) + 2Q23Y-1 V, K

where Hisp X Xol Zi / icn Z - Zo,

X0 hchz

Q11

.-, q23: Z0-g-.

q22

(24)

(25) (26)

The system of equations of error compiled

& (BTPB) 1BTPL;

„2 VTPV n -2

D (tm22 (VRV) 1.

Using the qn and q23 values found and specifying the Z values, calculate the X curve of the ellipse using the formula

X ± V

1 - 2q23 Z

The coordinates found are plotted on the gnathic projection of the ellipse curve, which is the LNDD for the patient.

Then, on the constructed LNZD, the normal position of the teeth is marked so that the meso-distal sections of the crowns of the teeth and the points of the single occlusal curve lie on the ellipse curve; the intercut point was located on the Z axis; right, passing through the distal surfaces of the last paired teeth - on the axis X. The sum of the mezio-. steel sizes of teeth should be equal to the perimeter of the curve. If the perimeter of the arc does not match the sum of the mesiodistal dimensions of the teeth, for example, if there are three, the corrections are made in the semi-axis of the ellipse as follows:

a P-40%,:

where P is the perimeter of the semi-ellipse.

The outcome of this yes 5p-0.4.

Since the ellipse axis

and Vq, then 5qn (5p-0.4) 2, where 5p is the sum of the gaps between the teeth.

calculated by

Corrected qiincn formula

qiiKicn

and then its value is used to determine the LDLE, instead of in formula (25).

LPSD in the projection on the YZ plane is determined by approximating the actual position of the teeth with a circle using the error equation

qn (Z2 + Y2) + 2qi3Z + 2q23Y-1-V. (28) The system of equations of errors, compiled for all points of the right and left dental row, can be represented in the matrix form as B $ + L Y.

where / Zi2 + Yi2 2Zi 2Yi

Z22 + Y22 2Z22Y2 V

V

 Z2n + Y2n 2Zn 2Yn /

V

Vn

BUT

D - {VTRVGVTP1;

25

. .2 УТ Р V Р

ogdg / "2 (tue) -1.

Next, calculate the coordinates of the center

circles 2.0 and YO according to the formulas Z0

: .Ч13. qii

35

q23 qn

If the center of the circle falls into the orbital region, then this circle is a personal norm, but if it does not fall into the orbital region, then you need to re-fit the dental row with a circle centered in the orbit. For this, the following conditions are imposed: the coordinates Zo and Y0 are measured on the median projections of the center of the orbit, after which the error equation is used

q 1 i (Z2 + Y2 + 2Z0Z + 2Y0Y) - 1 V, (29)

which is obtained by the substitution qi3 q23 Yoqn b (28).

The system of equations of error, compiled for all points of the dental row, in matrix form can be represented as

BA + L Y,

Where

AT

/ Z21 + Yi2 + 2Z0Zi + 2Y0Yi V Z22 + Y22 + 2Z0Z2 + 2Y0Y2

 Z2n + Y2n + 2Z0Zn + 2Y0Yn;

/ -eleven

 -one

/

Vi V2

V

Vbj q qn;

A) 1BTPL;

.D.- VT PV n -1

Dur tB PB) 1.

Using the value found, given the value Z, calculate the Y points of the circle using the formula

Y -Y0 ± YY2 Z2 2

Z0Z +

(thirty)

Using the found coordinates Y for each Z, a dental arch is plotted and the teeth are in a normal position.

In the proposed method, a second variant of the definition of a LNZD in projection on the YZ plane is provided. It is defined by a circular arc with a center in the eye socket, passing through points 1 and 6 and the articular heads. The chord of this arc from the first to the sixth tooth is proposed to be located in the golden section parallel to the gnatic plane. Anthropologists have established that the ratios between individual parts of a person bounded by anthropometric points correspond with a sufficiently high accuracy to the golden section, including the chord of the dental arch also located in the golden section.

The principle of building the personal norm of this arc is as follows. First, determine the value of Y3c chord of the golden section by the formula

-Yi9 (

Y13 + Y14 + Y19 Yi3

2,618), (31)

where the number 2,618 is determined by the golden sections in which the points trichoion 13 take part, glabella 14, gation 19, subnote 17.

Then, to build the chord of the dental arch, the Z values of its ends are taken equal to Zi and Ze of the actual bite, calculate the deflection arrow using the formula

r20

U, (Zi-Z6p. (32) g4

Using Yi.e Yac and the deflection arrow h, the personal dental arch without pathology is graphically constructed and the normal position of the teeth is marked on it.

On the constructed curves of the dental arches in the projections on the corresponding planes, the pathology of the teeth and jaws is determined.

By pathology vector is meant

the difference between the actual position of each element of the FCL and his personal norm, and the vector with the opposite sign is the absolute vector of correction. In addition to the absolute correction vector,

practice, it is advisable to use the planned vector of correction for the purpose of minimal impact while ensuring life-saving functions and aesthetics consistent with the patient.

The proposed method allows to calculate the correction vector of each tooth, group of teeth, jaw displacement, as well as rotation angles and the position of their axes of rotation.

The components of the vector are determined for each tooth, on the X and Z axes from the XZ projection, and from the projection on the YZ and XY planes, a component of the correction vector on the Y axes is obtained.

The sum of correction vectors 2 F of all teeth is equal to

Ј + F2 + ... + Fn.

The total displacement of all teeth in the jaw is characterized by the average correction vector Fcp. calculated by the formula

Pep

iLL

(33)

The differences AFi between the correction vectors Fi and the average vector Fcp-L FI Fi - Fcp. allow you to determine the angles of rotation, and together with Fcp. also the position of their axes of rotation.

An AF analysis projected on the plane of the LЈ plane allows determining the tact of treating sagittal and transversal occlusion anomalies.

The center C of the half-ellipse (Fig. 2) lies on

Z axis and has

Z51 + Z5K

from 2

The position of the occlusal point of each tooth relative to C is determined by the vector Rci Re - Ri.

The angle of jaw rotation is determined by the formula

Sin On

{(Mc; n V lRc; uF; MRc; |

If a does not exceed 0.2 °, then it is inappropriate to find the position of the axis of rotation, since pathologists are caused by a parallel displacement of the jaw. If a exceeds 0.2 °, then calculate the magnitude of the radius of the vector jRxzoi of the position of the axis of rotation relative to point C using the formula

 I Fxzcp I

n, "

2 sin 2

(35)

and then find the components of the vector XR0 and ZR0 from the joint solution of the equations

Fxzcp x Rxzo sin (90- a / 2) fRxz0f | Fxzcp |

Fxzcp x Rxzo cos (90 - a / 2) i Rxzd I Fxzcpl

according to the formulas:

IRxzollFyZcpKcosteO-WgbXFcp-sinfao-eVziZF RO ° XeFcp + zScp

(36)

ZRO

sin () UxzoH F Zepl + XR0ZFcp

XPcp

(37)

5 Fcp. suck

ü LЈ you guitprit

15

about w-20 oor

is 25

(34)

thirty

reportedly who is 35 itel 35

40

XR0 and s

Fxzcp | 45

Fxzcpl

50

-eVziZF

cp

) 55

where, by the found components XRO, ZRO of the vector Rxzo relative to point C, the position of the axis of rotation of the jaw parallel to the Y axis of the SCG is found.

According to the values found: jaw rotation angle a, position of the axis of rotation Rxzo / XRO} ZRO)

and Fcp. the tactics of treating the patient and the choice of the designs of the medical apparatus are determined. The PD analysis in YZ pecting allows choosing the tactics of treatment of vertical occlusion anomalies by normalizing the arch of the dental arch due to the tooth-alveolar movement of the tooth groups in the opposite direction by the magnitude of the correction vector.

The remaining angles of rotation, the position of their axes of rotation are determined by the formulas similar to (34-37).

Based on the mathematical analysis of correction vectors, the application points, the direction and magnitude of the force (module) on the treatment device are calculated.

According to the degree of pathology and the possibilities of therapeutic intervention, orthopedic, surgical or combined treatment is selected, taking into account the minimal trauma of the patient.

At the stages of treatment, morphological and aesthetic changes are monitored.

Claims (1)

Claims Method for diagnosing dental-maxillary anomalies, including stereo photographing of a face in an arbitrary coordinate system, determining the coordinate system of the head and anthropometric points of a face, characterized in that, the points are combined, then a coordinate system is selected for all the existing anthropometric points of the face and jaws, after which the vectors of the teeth, jaws are corrected; The rotation and position of the axes of rotation and their changes diagnose anomalies. , 2 W I. Figz .26 ./6 / 7 .fco