DE102013225739B4 - Method for determining a position of the apex of a root canal of a tooth - Google Patents

Abstract

Method for determining a position of the apex (A) of a root canal (4) of a tooth, with values of an impedance as impedance measurement values (I1, I2, I3) between a first electrode (1) inserted into the root canal (4) and one with the oral mucosa (5) contacted second electrode (2) are measured for an applied AC voltage with a controllable frequency (f) and wherein an impedance end value determined on the basis of the impedance measurement values (I1, I2, I3) is compared with a desired value, the first electrode (1) has reached the position of the apex (A) when the final impedance value corresponds at least approximately to the target value, characterized in that- a locus curve (10) of the impedance is calculated on the basis of the impedance measurement values (I1, I2, I3), that- an impedance value of the Locus for f = ∞ is determined and that this impedance value is the impedance end value.

Description

technical field

The invention relates to a method for determining a position of the apex of a root canal of a tooth, wherein values of an impedance between a first electrode inserted into the root canal and a second electrode in contact with the oral mucosa are measured for an applied AC voltage with a controllable frequency and a determined Impedance value is compared with a target value, wherein the first electrode has reached the position of the apex when the impedance value determined corresponds at least approximately to the target value.

State of the art

When treating the root canal of a tooth, it is often helpful or even necessary to know the length of the root canal or the position of the apex, i.e. the tip of the tooth root, as precisely as possible.

The position of the apex is often determined by a resistance or impedance measurement, for which a first electrode is inserted into the root canal and the resistance or impedance of the tissue lying between this first electrode and a second electrode placed on the oral mucosa is measured. If the first electrode reaches the apex, the resistance is reduced to a characteristic value. This characteristic value of the tissue resistance at the apex is approx. 6 to 6.5 kΩ regardless of the tooth shape and tooth type or the age and condition of the patient.

Direct current measuring devices are known which, in order to localize the apex, detect the change in resistance or the tissue resistance that occurs when the apex is reached. However, such direct current measurements or direct current measuring devices are sensitive to the environment, e.g. dryness or moisture in the root canal and to possible polarization effects.

For this reason, alternating current measuring devices are now mostly used, with various methods being known for inferring the position of the apex from the impedance that can be determined.

the JP 2009/011470 A describes a method and a device for apex localization by means of impedance measurement, using a quotient method. The method described is based on an equivalent circuit diagram for the measurement setup and an equation system corresponding to the equivalent circuit diagram with three unknowns, which can be solved using three measured impedances for three different frequencies.

the US 2011/0039227 A1 performs an apex localization based on current amplitude measurements. For different frequencies from a very wide frequency range, the current drop is measured at a reference resistor as a function of the penetration depth into the root canal and the position of the apex is determined from an intersection of a measured curve for a low frequency and a measured curve for a high frequency.

the DE 10 2008 012 677 A1 also describes a measuring device with two electrodes, with differences and ratios of measured impedance values being determined for apex localization. Alternatively, the apex position is also detected by measuring the current density or the like, other than a change in impedance.

From the WO 2007/057878 A2 an AC current measuring device and a method for apex localization by means of an AC current are also known, with impedance values being measured by means of two electrodes as a function of several different positions of the electrode in the root canal.

In the U.S. 5,080,586 A describes a method for apex localization. The position of the apex corresponds to a predetermined difference between two output voltages as a comparison value. The impedances at frequencies of 1 kHz and 5 kHz are compared with each other.

From the DE 697 28 065 T2 a method for diagnosing caries is known in which a locus curve is reconstructed from measured impedance values.

The object of the present invention is to provide a method that enables apex localization by means of impedance measurement in the simplest possible way.

Disclosure of Invention

The method according to the invention for determining a position of the apex of a root canal is based on measuring impedance values between a first electrode inserted into the root canal and a second electrode in contact with the oral mucosa for an applied AC voltage with a controllable frequency and an impedance final value determined from these impedance measurement values compared to a target value. Does the final impedance value at least approximately match the target value? clean, the first electrode has reached the position of the apex.

The final impedance value is determined by the following method steps: A locus of the impedance is calculated on the basis of the impedance measurement values and an impedance value of the locus for f=∞ is determined, this impedance value being the final impedance value.

At the apex, i.e. between the apex and the oral mucosa, a patient-independent tissue resistance occurs, which typically differs significantly from a tissue resistance between an electrode located at the beginning of or at least still within the root canal and the electrode located on the oral mucosa or lip. Apex localization can therefore be performed by finding this characteristic tissue resistance at the apex.

The method according to the invention now makes it possible to determine the real resistance between the two electrodes, i.e. the resistance of the tissue located between the electrodes or the tissue resistance, and thus the characteristic tissue resistance at the apex and thus the position, from an impedance measurement, i.e. the measurement of an AC resistance to locate the apex.

For this purpose, the first measuring electrode is inserted into the root canal step by step, typically by hand, and for each step, ie each position, the tissue resistance is determined by means of at least two measured impedance values. The first measuring electrode is inserted further into the root canal until the determined tissue resistance matches the target value, for example the characteristic tissue resistance at the apex, and the tip of the first measuring electrode has thus reached the apex.

According to the invention, the determination of the tissue resistance is based on the reconstruction of the locus of the impedance. The locus refers to the impedance of the measurement setup as a function of the frequency of the applied alternating current in the complex plane, i.e. the progression of the impedance in the complex plane. The locus thus includes all impedance values of the measurement setup or depicts them. Consequently, it also includes the tissue resistance sought, which can be determined accordingly from the locus curve.

In order to reconstruct the locus curve, geometric considerations are used, for example. In this way, progressions or curves or functions can be clearly reconstructed using individual points. For example, a straight line can be unambiguously reconstructed using two points lying on the straight line, or a circle can be unambiguously reconstructed using three points lying on the circle. Accordingly, it is possible to reconstruct the locus of the impedance using a finite number of arbitrary impedance values.

Based on the tissue resistance determined from the locus curve reconstructed in this way, it can be determined whether the tip of the first measuring electrode has already reached the position of the apex or even exceeded it, since in this case the determined tissue resistance corresponds to the characteristic value of the tissue resistance between the tip of the tooth root and the lip, which is independent of the individual patient assumes that is about 6 to 6.5 kΩ.

The invention makes it possible to determine the tissue resistance sought on the basis of several impedance measurements for any frequencies of the applied AC voltage, without having to measure the tissue resistance sought directly, i.e. in particular independently of the frequency for which the tissue resistance sought would occur in the measurement setup. This is necessary because a direct measurement of the tissue resistance would only be possible as an approximation, since an AC frequency of infinity cannot be realized.

A measured impedance value is advantageously measured for at least two different frequencies of the applied AC voltage.

An equivalent circuit diagram, i.e. a model of the measurement setup, can be used to reconstruct the locus curve. The electrode impedances of the first and second electrodes, which are often also referred to as contact resistance, are mapped together, for example, by connecting an ohmic resistor and a capacitor in parallel. The electrode impedances each reflect the electrode contact resistance. The electrode impedances combined in the RC element are connected in series with the tissue resistance between the two electrodes, for example. Depending on the position of the first electrode, the tissue resistance includes the resistance of the root canal and/or only the resistance of the other tissue between the end of the root canal, i.e. apex, and the oral mucosa or lip, i.e. the position of the second electrode.

For this equivalent circuit diagram, for example, the locus curve in the complex plane has a circular shape with a center point on the real axis. This locus has for the Fre quenching f = 0 and f = ∞ points of intersection with the real axis. For f = 0, the resistance of the RC element is reduced to the ohmic resistance, so that the locus depicts the sum of the series-connected ohmic resistances of the equivalent circuit diagram, i.e. the sum of the tissue resistance between the electrodes and the real resistance of the electrode. For f = ∞, the locus shows the tissue resistance alone, since the impedance of the RC element, i.e. the electrode impedance, is reduced to zero.

Based on the equivalent circuit diagram described above, the electrode impedances can thus be neutralized and the desired tissue resistance between the two electrodes can be determined by allowing the frequency of the AC voltage to approach infinity. However, a direct measurement for f = ∞ can only be carried out approximately.

Therefore, the impedance measurements are carried out for realizable frequency values and the locus curve is then reconstructed using the impedance measurement values, so that the final impedance value sought can be read from the reconstructed locus curve.

Due to geometrical considerations, the exact spatial course of a circle can be clearly determined using two points lying on the circle and a circle center lying on a known straight line.

Since the locus curve for the equivalent circuit diagram described runs in a circle around a center point lying on the real axis, it is possible to calculate the locus curve of the impedance for this model of the measurement setup using two measured impedance values for two different frequencies of the alternating current applied.

Since the impedance value of this calculated locus for the case f=∞ precisely reflects the ohmic tissue resistance of the root canal and other tissue, the tissue resistance of the measurement setup can be determined or read from the reconstructed locus.

Advantageously, a measured impedance value is measured for at least three different frequencies of the applied AC voltage and a locus curve of the impedance is calculated on the basis of the three measured impedance values.

The course of a circle can be clearly reconstructed using three points lying on the circle. Therefore, at least three impedance measurement values measured for different frequencies make it possible to unambiguously reconstruct the course of a circular locus curve in the complex plane, regardless of whether other boundary conditions, for example the position of the center of the circle, are known.

Advantageously, at least one further impedance measurement value is measured for the at least two or at least three impedance measurement values (I1, I2, I3) and is used to calculate the locus curve.

This makes it possible to increase the accuracy of the reconstruction of the locus or to compensate for errors in the measured values or at least to reduce their influence on the result. For example, a first locus curve can be calculated using at least two or three measured impedance values and used as the starting value for a compensating calculation based on all available measured impedance values.

The target value is advantageously between 6.0 kΩ and 6.5 kΩ. This corresponds to the known literature value for the ohmic resistance between a root canal tip and the oral mucosa or the lip.

character list

• 1 einen Messaufbau zur Bestimmung der Apexlokalisierung,
• 2 ein Ersatzschaltbild für den Messaufbau aus 1,
• 3 eine Ortskurve der Impedanz für das Ersatzschaltbild aus 2.

The inventive method is explained with reference to the drawing. Show it:

• 1 a measurement setup to determine the apex localization,
• 2 an equivalent circuit diagram for the measurement setup 1 ,
• 3 a locus curve of the impedance for the equivalent circuit diagram 2 .

embodiment of the invention

1 outlines a measuring setup for the method according to the invention, which comprises two measuring electrodes 1 , 2 and an alternating current source 3 with variable frequency f and a measuring device 6 . The first measuring electrode 1 is inserted into the root canal 4 of a tooth. For this purpose, the first measuring electrode 1 is designed, for example, as a thin rod or file. The second measuring electrode 2 is arranged on the gums 5 . For this purpose, the second measuring electrode 2 is designed, for example, as a hook that can be hung over the lip of a patient.

To determine the position of the apex A, an alternating current or an alternating voltage is applied to the measuring electrodes 1, 2 by means of the alternating current source 3 and the first measuring electrode 1 is gradually introduced into the root canal of the tooth. For each step, so each position of the first Measuring electrode 1, an impedance measurement value I1, I2, I3 is measured by means of the measuring device 6 for different frequencies f of the alternating current.

For each step, a locus curve 10 is created from the measured impedance values I1, I2, I3, as shown, for example, in 3 is shown, calculated and from the locus 10 a desired impedance end value determined or read. This final impedance value is compared with a target value, with the first electrode 1 or a tip of the first electrode 1 having reached or exceeded the apex A if there is a match.

In 2 is an equivalent circuit for the in 1 outlined measurement setup. The ohmic resistance 7 corresponds to a series connection of the resistance value in the root canal 4 and the resistance of the other tissue, such as the gums 5. A parallel connection of a resistor 8 and a capacitor 9 forms the electrode impedances of the first and second electrodes 1, 2, i.e. the contact resistances of the electrodes 1, 2 and is connected in series with the resistor 7.

For this equivalent circuit diagram, the result is in 3 shown locus curve 10 as the course of the impedance as a function of the changeable frequency f in a complex plane. The locus curve 10 has a circular profile with a center point M(x _M ,y _M ) lying on the real axis and a radius r. The point of intersection S1 of the locus curve 10 with the real axis for f=0 corresponds to the sum of the ohmic resistances 7, 8 and the point of intersection S2 for f=∞ reflects the value of the resistance 7 alone.

Due to the circularity of the locus curve around a center point on the real axis, it is possible to clearly calculate the course of the locus curve using two measured impedance values I1 and I2, which are measured for two different frequencies f of the alternating current present. In this case, at least two measured impedance values I1, I2 for at least two different frequencies f are necessary in order to determine the final impedance value sought.

$${\text{x}}_{\text{M}}{}^2-{\text{r}}^2-2*{\text{x2*x}}_{\text{M}}=-\left({\text{x2}}^2+{\text{y2}}^2\right)$$

This is based on geometric considerations that lead to the following system of equations. The position x _M of the center point on the real axis and the radius r of a circle that is to pass through the points P1(x1,y1) and P2(x2,y2) can be found by solving the following system of equations from two equations with two Calculate unknowns: $${\text{<figure-callout id="2" label="x M" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">x</figure-callout>}}_{\text{M}}{}^2-{\text{right}}^2-2*{\text{x1*x}}_{\text{M}}=-\left({\text{<figure-callout id="2" label="x1" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">x1</figure-callout>}}^2+{\text{y1}}^2\right)$$

$${\text{<figure-callout id="2" label="x M" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">x</figure-callout>}}_{\text{M}}{}^2-{\text{right}}^2-2*{\text{x2*x}}_{\text{M}}=-\left({\text{<figure-callout id="2" label="x2" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">x2</figure-callout>}}^2+{\text{y2}}^2\right)$$

If only a circular course of the locus can be assumed without knowing anything about the position of the center point, the course of the locus can be clearly calculated using at least three measured impedance values I1, I2, I3 measured for different frequencies.

$${\text{x}}_{\text{M}}{}^2+{\text{y}}_{\text{M}}{}^2-{\text{r}}^2-2*{\text{x2*x}}_{\text{M}}-2*{\text{y2*y}}_{\text{M}}=-\left({\text{x2}}^2+{\text{y2}}^2\right)$$

$${\text{x}}_{\text{M}}{}^2+{\text{y}}_{\text{M}}{}^2-{\text{r}}^2-2*{\text{x3*x}}_{\text{M}}-2*{\text{y3*y}}_{\text{M}}=-\left({\text{x3}}^2+{\text{y3}}^2\right)$$

The following system of equations results from geometric considerations. The position (x _M ,y _M ) of the center and the radius r of a circle that is to pass through three points P1(x1,y1), P2(x2,y2), P3(x3,y3) can be found by solving the calculate the following system of equations from three equations with three unknowns: $${\text{<figure-callout id="2" label="x M" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">x</figure-callout>}}_{\text{M}}{}^2{\text{+<figure-callout id="2" label="y M" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">y</figure-callout>}}_{\text{M}}{}^2-{\text{right}}^2-2*{\text{x1*x}}_{\text{M}}-2*{\text{y1*y}}_{\text{M}}=-\left({\text{<figure-callout id="2" label="x1" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">x1</figure-callout>}}^2+{\text{y1}}^2\right)$$

$${\text{x}}_{\text{<figure-callout id="2" label="M" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">M</figure-callout>}}{}^2+{\text{<figure-callout id="2" label="y M" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">y</figure-callout>}}_{\text{M}}{}^2-{\text{right}}^2-2*{\text{x2*x}}_{\text{M}}-2*{\text{y2*y}}_{\text{M}}=-\left({\text{<figure-callout id="2" label="x2" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">x2</figure-callout>}}^2+{\text{y2}}^2\right)$$

$${\text{x}}_{\text{<figure-callout id="2" label="M" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">M</figure-callout>}}{}^2+{\text{<figure-callout id="2" label="y M" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">y</figure-callout>}}_{\text{M}}{}^2-{\text{right}}^2-2*{\text{x3*x}}_{\text{M}}-2*{\text{y3*y}}_{\text{M}}=-\left({\text{<figure-callout id="2" label="x3" filenames="DE102013225739B4\_0006.png,DE102013225739B4\_0007.png" state="{{state}}">x3</figure-callout>}}^2+{\text{y3}}^2\right)$$

Correspondingly, the center M and radius r of the locus 10 can be calculated from the two or three measured impedance values I1, I2, I3 or their respective real and imaginary parts.

The final impedance value sought, which corresponds to the ohmic tissue resistance between the first and second measuring electrodes 1, 2, can then be determined from the course of the locus curve. for the inside 2 shown equivalent circuit or the in 3 In the locus curve shown, this final impedance value is the value of the locus curve for f = ∞, i.e. the intersection point S2.

reference list

1

first measuring electrode

2

second measuring electrode

3

AC power source

4

root canal

5

gums

6

measuring device

7

ohmic resistance

8th

ohmic resistance

9

capacitor

10

locus curve

A

apex

f

frequency

I1

impedance reading

I2

impedance reading

I3

impedance reading

M

center of the locus curve

right

Radius of the locus

S1

Intersection of the locus curve with the real axis

S2

Intersection of the locus curve with the real axis

Claims (5)

Method for determining a position of the apex (A) of a root canal (4) of a tooth, with values of an impedance as impedance measurement values (I1, I2, I3) between a first electrode (1) inserted into the root canal (4) and one with the oral mucosa (5) contacted second electrode (2) are measured for an applied AC voltage with a controllable frequency (f) and wherein a final impedance value determined on the basis of the measured impedance values (I1, I2, I3) is compared with a target value, wherein the first electrode (1) has reached the position of the apex (A) when the final impedance value corresponds at least approximately to the target value, characterized in that - a locus curve (10) of the impedance is calculated on the basis of the measured impedance values (I1, I2, I3), that - an impedance value of the locus curve for f = ∞ is determined and that - this impedance value is the impedance end value. procedure after claim 1 , characterized in that a measured impedance value (I1, I2) is measured for at least two different frequencies (f) of the applied AC voltage and is used to calculate the locus curve. procedure after claim 1 or 2 , characterized in that a measured impedance value (I1, I2, I3) is measured for at least three different frequencies (f) of the applied AC voltage and is used to calculate the locus curve. procedure after claim 2 or 3 , characterized in that at least one further impedance measurement value is measured for the at least two or at least three impedance measurement values (I1, I2, I3) and is used to calculate the locus curve. Procedure according to one of Claims 1 until 4 , characterized in that the target value is between 6.0 kΩ and 6.5 kΩ.

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