There is general consensus that root canal procedures should be limited within the confines of the root canal, with the logical endpoint for preparation and filling being the narrowest part of the canal, the so-called apical constriction. It is not possible to predictably detect the position of the apical constriction clinically; indeed, the constriction is not uniformly present or may be irregular. Equally, it is not logical to base the endpoint of root canal procedures on an arbitrary distance from the radiographic apex as the position of the apical foramen is not related to the apex of the root. Electronic root canal length measuring devices (ERCLMDs) offer a means of locating the most appropriate endpoint for root canal procedures, albeit indirectly. The principle behind most ERCLMDs is that human tissues have certain characteristics that can be modelled by means of a combination of electrical components. Then, by measuring the electrical properties of the model (e.g. resistance, impedance), it should be possible to detect the canal terminus. Thus, most modern ERCLMDs are capable of recording the point where the tissues of the periodontal ligament begin outside the root canal, and hence from this, a formula can be applied to ensure that preparation is confined within the canal. Most reports suggest that 0.5 mm should be subtracted from the length of the file at the point when the device suggests that the file tip is in contact with the PDL (zero reading). This does not mean that the constriction is located; rather it means that the instrument is within the canal and close to the PDL. It is not appropriate to rely on any device reading 0.5 mm short of the foramen as this will often be inaccurate. The use of “generation X” to describe and classify these devices is unhelpful, unscientific, and perhaps best suited to marketing campaigns. This chapter describes the fundamental operating principles of ERCLMDs and classifies them on this basis. Initially, a review of basic electronics is presented in order to provide an understanding of electronic devices and circuits. The electronic function and clinical application of ERCLMDs is then discussed.
The presence of bacteria and their by-products within the root canal system results in apical periodontitis . In essence, treatment of a microbial inflammatory disease is directed at the elimination of the antigenic source through the elimination of infection [2–4]. Root canal treatment involves removing microorganisms from the pulp space and filling the root canal system to prevent reinfection , followed by coronal restoration to prevent recontamination and reinfection [6, 7]. In other words, the goal of root canal treatment is to control infection through the debridement, disinfection, and filling of the root canal system . It is generally accepted that root canal treatment procedures should be limited to within the root canal system [9–11]. To attain this objective, the endpoint of the root canal system, the canal terminus should be detected as precisely as possible during preparation of the canal . Therefore, one of the main concerns in root canal treatment is to determine how far instruments should be advanced within the root canal and at what point the preparation and filling should terminate [9, 12, 13].
10.2 Morphology of the Root Canal Terminus
Kuttler  concluded that a root canal had two main sections, a longer conical section in the root encased in dentine, and a much shorter funnel-shaped section consisting of cementum located in the apical portion. The shape of this apical portion is considered to be an inverted cone (Figure 10.1), its base being located at the major apical foramen. The apex of the inverted cone is the minor foramen that is often thought to coincide with the apical constriction regarded as being at or near the cemento-dentinal junction (CDJ) . In other words, the most apical portion of the root canal system narrows from the opening of the major foramen on the external surface of the root, which is theoretically lined by cementum, to a constriction (minor foramen) before widening out in the main canal to produce an asymmetric hour-glass shape (Figure 10.1).
It is well known that the major apical foramen is not a uniform shape and is most often asymmetrical [16, 17]. Furthermore, its position on the root tip varies (Figure 10.2). For example, Stein and Corcoran  reported that with increasing age the deviation of the major foramen from the root tip increased, whilst others have reported that the frequency of the deviation depended on the type of teeth [16, 19]. Moreover, deviation of the foramen can occur as a result of pathological changes, the most common being external apical root resorption [20, 21]. In addition, apical deltas and lateral canals occur frequently in the apical third of all teeth, especially multi-rooted molars and premolars .
The root canal terminus is considered by many to be the CDJ [9, 14, 15, 17, 23]. In some instances, the CDJ coincides with the junction of the pulp and periodontal tissues, where the pulp tissue changes into the apical periodontal tissue . Theoretically, the CDJ is the appropriate apical limit for root canal treatment as at this point the area of contact between the periradicular tissues and root canal filling material is likely to be minimal and the pulp wound smallest [9, 13, 23–25]. The term theoretically is applied here because the CDJ is a histological site and it can only be detected in extracted teeth following sectioning or micro-CT analysis; in the clinical situation it is impossible to identify its position. In addition, the CDJ is not a constant or consistent feature; for example, the extension of the cementum into the root canal can vary . Therefore, it is not possible to use this landmark clinically as the endpoint for root canal preparation and filling. Defining the apical constriction as the canal terminus and not the CDJ is also problematic, as the topography of the apical constriction is not located in the same area in various types of roots . Indeed, the apical constriction can have a variety of morphological variations that makes its identification unpredictable (Figure 10.3).
In clinical practice, the minor apical foramen is a more consistent anatomical feature [13, 17, 27] that can be regarded as the narrowest portion of the canal system, and thus, the preferred landmark for the apical endpoint for root canal preparation. However, with infected necrotic pulps and periapical disease, the cemental canal beyond the minor foramen may also be infected and act as a reservoir of pathogens (particularly anaerobic bacteria), therefore, in an attempt to clean the cemental canal, a limited amount of instrumentation beyond the minor foramen, a feature of apical patency, has been advocated [27–31].
10.3 Determining the Root Canal Terminus
Various techniques have been used for determining the position of the canal terminus and thus measure the working length of root canals. The most popular method has been the use of periapical radiographic images. However, although it is generally accepted that the minor apical foramen and apical constriction is on average located 0.5–1.0 mm short of the radiographic apex [13, 31–33], there are wide variations in the relationship of these landmark that would result in under- or over-preparation of canals with an obvious impact on canal debridement and the position of the root filling [18, 34, 35]. Thus, many studies have reported that canal lengths determined radiographically vary from actual root canal lengths by a considerable amount [14, 15, 26, 36–41]. The accuracy of radiographic methods of length determination depends on the radiographic technique that has been used [13, 38, 42, 43]. For example, Sheaffer et al.  revealed that higher density radiographs were more desirable for measuring working length. Forsberg  reported that tooth length determined that using the bisecting angle technique, either correctly or incorrectly angulated, was less accurate than the paralleling technique. Although radiographic imaging is a critical and an integral part of endodontic therapy , there is an ongoing need to reduce exposure to ionizing radiation whenever possible [46, 47]. The use of other adjunct methods that optimise the benefits and reduce risks whenever possible is advantageous [48, 49].
It is well known that the major apical foramen is not always located at the radiographic apex of the root; rather, it often lies on the lingual/buccal or mesial/distal aspect. If the major foramen deviates in the lingual/buccal plane (Figure 10.4), it is difficult to locate its position using radiographs alone, even with multiplane angles [50, 51].
One of the innovations in root canal treatment has been the development and production of electronic devices [52, 53] for detecting the canal terminus. Their functionality is based on the fact that the electrical conductivity of the tissues surrounding the apex of the root is greater than the conductivity inside the root canal system, provided the canal is either dry or filled with a nonconductive fluid [54, 55].
Suzuki  indicated that the electrical resistance between a root canal instrument inserted into a canal and an electrode applied to the oral mucous membrane registered consistent values. Based on these findings, Sunada  reported that when the tip of an endodontic instrument touched the periodontal membrane through the apical foramen, the electrical resistance between the instrument and the oral mucous membrane was a constant value. Based on this fundamental principle, these resistance-based devices should be able to detect the periodontal tissue at the apical foramen.
It is obvious that such devices do not assess the position of the root apex and the name “electronic apex locator” is not appropriate; “electronic apical foramen locator” or “electronic root canal length measurement device” (ERCLMD) as a generic name would be more appropriate. The manufacturers of more recent electronic devices claim their products locate the apical constriction (www.vdw-dental.com/home_e/index.html, www.jmoritausa.com/Marketing/pdf/RootZX_IFU.pdf, www.averon.ru/english/dental/equipment/apex.htm, www.micromega.com/anglais/produits/apexpointer/index.php, www.parkell.com/master. html, www.parkell.com/foramatron.html).
Their claims are based on the fact that these devices operate using different electronic principles compared with the original resistance-based devices [54, 58, 59]. However, the evidence suggests their claims are not correct; for example, Hoer and Attin  reported that accurate determination of the apical constriction was only successful in 51–64% of canals depending on the device used. The probability of determining the position between the minor and major foramen was between 81 and 82% of cases. Welk et al.  also reported that the ability of various types of ERCLMDs to determine the minor diameter was between 90.7 and 34.4%. Because of the hazards of radiation [13, 49], as well as the technical problems associated with radiographic techniques [38, 62] and to avoid over-instrumentation beyond the canal terminus [63–65], electronic working length determination has gained popularity amongst both general dentists and endodontists [52, 66].
The electronic method is also more convenient to the patient and has potential to enable root canal treatment to be performed during pregnancy . Unfortunately, most manufacturers do not define the exact nature of their devices nor how they operate electronically. Classifying and describing the devices by generation is not helpful to clinicians and is better suited to marketing campaigns. In essence, it is not possible to classify all the various products on the market; rather, only those whose fundamental operating principles have been released by the manufacturer can be categorized (Table 10.1). Clearly, with the limited information provided by manufacturers, the classification of electronic devices used to measure canal length is a matter of controversy and ignorance .
|Resistance-based ERCLMDs||Endodontic Meter ®||Parkell Inc., New York, NY, USA|
|Low -requency oscillation||Sono-Explorer®||Hayashi Dental Supply, Tokyo, Japan|
|High-frequency devices (Capacitance-based devices)||Endocater®||Hygenic Corp., Akron, OH, USA|
|Capacitance and resistance look-up table||Elements® Diagnostic unit||SybronEndo, Orange, CA, USA|
|Voltage gradience (difference in impedance with three nodes)||No commercial model available|
|Two frequencies, impedance difference||Apit®||Osada, Tokyo, Japan|
|Two frequencies, impedance ratio (quotient)||Root ZX®||J. Morita Co., Kyoto, Japan|
|Multifrequency||Ai-Pex®||Guilin Woodpecker Medical Instrument, Guilin, Guangxi, China|
10.4 An Overview of Basic Electronics
10.4.1 Atom Structure
To understand the basics of electronics, the structure of the atom, which is the smallest particle of materials that retain their characteristics, should be defined. Atoms are made of electrons, protons, and neutrons. According to the classic Bohr model , atoms have a planetary type of structure that comprises a central nucleus surrounded by orbiting electrons. The nucleus consists of positively charged particles called protons and uncharged particles called neutrons. The basic particles of negative charge are called electrons. Electrons orbit the nucleus of an atom at certain distances from the nucleus. Electrons that are in orbits further from the nucleus are less tightly bound than those closer to the nucleus. This is because the force of attraction between the positively charged nucleus and the negatively charged electron decreases with increasing distance from the nucleus. Therefore, electrons existing in the outermost shell of an atom are relatively loosely bound to the atom. For example, in the copper atom, the most outer shell has one electron and when that electron gains sufficient thermal energy it can break away from the parent atom and become a free electron. In copper at room temperature, a large number of these free electrons are present that are not bound to any atom and are free to move. Free electrons make copper an excellent conductor and make electrical current possible. Other conductive materials may have similar characteristics but with different conductivity determined by their atom structure.
10.4.2 Ions and Electrolytes
When the number of electrons changes in an atom, the electrical charge will change. If an atom gains electrons, it picks up an imbalance of negatively charged particles and will become negative. If an atom loses electrons, the balance between positive and negative charges is shifted in the opposite direction and the atom will become positive. In either case, the magnitude (+1, + 2, -1, -2, etc.) of the electrical charge will correspond to the number of electrons gained or lost. Atoms that carry electrical charges are called ions (regardless of whether they are positive or negative). A cation is an ion that has lost electrons and acquired a positive charge; an anion is an ion that has gained electrons and acquired a negative charge. Not only do electrons flow along a wire in an electric circuit, but electrons can also be carried through water if it contains ions in solution. Ionic solutions that conduct electricity in a manner similar to wire are called electrolytes. The conductance of electrolytes is the result of the movement of ions through the solution towards the electrodes. When two electrodes in a solution are part of a complete electrical circuit, the cations (+) are attracted to the negative pole (cathode) and the anions (-) are attracted to the positive pole (anode). The conductivity of any particular ion will be affected by the ease with which the ion can move throughout the water. The ease with which any ion moves through a solution depends on factors such as the total charge and the size of the ion; large ions offer greater resistance to motion through the electrolyte than small ions. The greater the number of ions present, the greater the electrical conductivity of the solution.
10.4.3 Electrical Charge, Voltage, and Current
Electrical charge, symbolized by Q, is either positive or negative. The electron is the smallest particle that exhibits negative electrical charge. When an excess of electrons exists in a material, there is a net negative electrical charge, and conversely, a deficiency of electrons forms a net positive electrical charge. Materials with charges of opposite polarity are attracted to each other and materials with charges of similar polarity are repelled. A certain amount of energy must be used in the form of work to overcome the forces and move the charges a given distance apart. All opposite charges possess a certain potential energy because of the separation between them. The difference in potential energy of the charges is voltage. Voltage, symbolized by “V,” is the driving force in electric circuits and is what establishes current. The unit of voltage is the volt. Voltage provides energy to electrons or ions that allows them to move through a circuit. This movement is electrical current characterized by “I,” which results in work being done in an electric circuit. The measurement unit of current is ampere.
When there is a current of free electrons in a material, then electrons occasionally collide with atoms. These collisions cause the electrons to lose some of their energy and thus restrict their movement. The more collisions, the more the flow of electrons is restricted . This restriction varies with the type of material, the property of which is called resistance and is designated as “R”; it is expressed in the unit of ohms (Ω) . However, when electrical current is formed by ions, the current is restricted by other means. When a voltage (potential difference) is applied between two points in an electrolyte, ions between them will be attracted by the opposite charge and so will move between the points and produce a current. The resistance of such electrolytic solutions depends on the concentration of the ions and also on the nature of the ions present, in particular, their charges and mobilities. Thus, resistance is a variable that depends on concentration [70, 72]. This physical effect is called resistivity, which is represented by ρ. For each material, ρ can be a constant value at a given temperature. Thus, the resistance of an object can simply depend on three factors: (1) resistivity, (2) length, and (3) cross-sectional area. The formula for the resistance of an object of length l and cross-sectional area A is:
The formula shows that resistance increases with resistivity and length, and decreases with cross-sectional area. In fact, resistivity “ρ” is the parameter that classifies conductive materials from insulators. Insulators cannot conduct electric currents because all their electrons are tightly bound to their atoms. A perfect insulator would allow no charge to be forced through it; however, no such substance is known at room temperature. The best insulators offer high but not infinite resistance at room temperature. For instance, the resistivity of a human thorax bone at normal temperatures is approximately 16000 Ω m-1  whilst for blood it is 100 times less at approximately 162 Ω m-1 . Thus, bone is a relatively poor conductor whilst blood is a relatively good conductor of electric current.
10.4.5 Electric Circuits and the Human Body
Current through the body, not voltage, is the cause of an electrical shock. When a point on the body comes in contact with a voltage and another point comes in contact with different voltage, there will be a current through the body from one point to the other. The severity of the resulting electrical shock depends on the amount of voltage and the path that the current takes through the body . To measure the effects of current on the human body, the amount of current should be calculated. This is dependent on the potential difference, the impedance driving the potential difference and the resistance within the body between the points of contact . The human body has resistance that depends on many factors, including body mass, skin moisture, and points of contact of the body with a voltage potential. The human body does not sense currents less than a few milliamperes . However, about hundred milliamperes of current will cause fatal damage; especially if it is connected for more than several seconds .
10.4.6 Ohm’s Law
Ohm’s law describes the mathematical relationship between voltage, current, and resistance in a circuit. Ohm determines that if the voltage across a resistor is increased, the current through the resistor will increase; conversely, if the voltage is decreased the current will decrease. Ohm’s law also shows that if the voltage (V) is kept constant, less resistance (R) results in more current (I), and more resistance results in less current. Ohm’s law can be stated as follows:
Electrolyte solutions also obey Ohm’s law just as metallic conductors do. From a macroscopic point of view, ionic conduction of solutions is similar to electron conduction through solid objects. In the latter, electrons are moving without ion cores, whilst in the former, charges are moving as ions. Although water itself is a poor conductor of electricity, the presence of ions in solution decreases the resistance considerably. The resistance of such electrolytic solutions depends on the concentration of the ions and also on the nature and size of the ions present.
10.4.7 Direct Current and Alternating Current
Direct current (DC) is a fixed amount of current per unit of time, whereas the amount of an alternating current (AC) alternates with time. The sine wave (or sinusoidal wave) is the fundamental type of alternating current and alternating voltage. Figure 10.5 is a graph showing the general shape of a sine wave, which can be either an alternating current or an alternating voltage.
In fact, when a sinusoidal voltage source is applied to a resistive circuit, it will result in an alternating sinusoidal current. The current (or voltage) varies with time, starting at zero, increases to a positive maximum, returns to zero, and then increases to a negative maximum before again returning to zero, thus completing a full cycle. The time (in seconds) required for a given sine wave to complete one full cycle is called the period (T).
Frequency is the number of cycles that a sine wave completes in 1 s. The more cycles completed in 1 s, the higher the frequency. Frequency is symbolized by f and is measured in units of hertz (Hz).
A structure of two conductive materials with an insulator between them forms an electrical device called a capacitor. In its simplest form shown in Figure 10.6, a capacitor is constructed of two parallel metal plates separated by an insulating material called a dielectric. When a capacitor is connected to a DC voltage source, electrons (negative charge) move from one plate to another, making one plate acquire a negative charge and the other a positive charge. When the voltage source is disconnected, the capacitor would still retain the stored charge and a voltage will remain across it. The amount of charge that a capacitor can store will determine its capacitance.
The following parameters are important in establishing the capacitance of a capacitor: plate area (A), plate separation (d) and dielectric constant (ε). A large plate area produces a large capacitance and a smaller plate area produces a smaller capacitance. Conversely, the plate separation (d) is inversely proportional to the capacitance, i.e. a greater separation of the plates reduces the capacitance. Finally, the insulating material between the plates (the dielectric) will directly influence the capacity by its dielectric constant (ε) as shown in the equation:
As a result of the insulator, a capacitor will block constant DC. However, it allows the AC to pass with an amount of opposition that depends on its capacitance and the frequency of the AC. This opposition is called capacitive reactance (XC) calculated from the following formula:
where π is almost equal to 3.14, f is the frequency and C is the capacitance. When f is zero (DC), XC becomes infinite and so blocks the DC. At nonzero frequencies (alternating current) it takes other values and becomes analogous to the resistance of a resistor; hence, Ohm’s law applies to capacitive circuits as follows:
10.4.9 Impedance and its Measurement
In a circuit that has both capacitors and resistors, the total amount of opposition to an alternating current is called impedance, which is represented by Z. Again, Ohm’s law applies to these circuits:
The value of impedance in a circuit that has both resistors and capacitors depends on the resistance values (R) of its resistors and the reactance (XC) values of its capacitors. There are several methods to measure the impedance value of a material. The basic method is to apply an electrical current to the material and measure the resulting voltage. According to Ohm’s law (equation 6), the division product of the voltage value over the current value gives the value of impedance. If the material comprises resistive elements only, a DC can be enough for this measurement (using equation 2). However, in the presence of capacitive elements, an AC highlights the capacitive characteristics of the impedance as well as the resistive part. The frequency of the AC will influence the measured impedance value as the capacitive component of the impedance is variable with frequency (see equation 4). The use of DC is impractical for measurement of the resistance of an electrolyte because the electrodes become polarized. The behaviour of electrolytic solutions is of huge technological importance as well as of great scientific interest. However, during electroconductivity measurement, polarization can be prevented by using a high-frequency alternating current so that the quantity of electricity carried during one half-cycle is insufficient to produce any measurable polarization, although various electrolytes in different conditions may exhibit different conductivities. It should be added that an impedance, in electrical terms, has two properties: amplitude (or simply value) and phase. For simplicity in the context of this book, impedance is normally identified with its value. In addition, as mentioned previously, there are a number of methods to measure impedance value or phase electrically, e.g. Wheatstone bridge , phase-sensitive detection , and sine-wave correlation .
10.5 Electrical Features of Tooth Structure
Root canals are surrounded by dentine and cementum that are insulators to electric current. At the minor apical foramen, however, there is a small hole (foramen) in which conductive materials within the canal are electrically connected to the periodontal ligament that is a conductor of electric current. The resistive material of the canal (dentine, tissue, fluid) with a particular resistivity forms a resistor, the value of which depends on the length, cross-sectional area, and resistivity of the materials (Figure 10.5). If an endodontic file penetrates inside the canal and approaches the canal terminus, then the resistance between the end of the instrument and the apical portion of the canal decreases because the effective length of the resistive material inside the canal (l in Figure 10.5) decreases.
As well as resistive properties, the structure of the tooth has capacitive characteristics. Assume the file, with a specific surface area, to be one side of a capacitor and the conductive material (e.g. periodontal ligament) outside the dentine being the other plate of that capacitor. Tissue and fluid inside the canal, in addition to the cementum and dentine of the canal wall, can be considered as separators of the two conductive plates and determine a dielectric constant e. This structure forms a capacitor, much more complex than symbolized in Figure 10.6. The electrical structure of the canal is more complicated than the resistive and capacitive elements described previously and the exact modelling of it is not a straightforward task [54, 81]. Meredith and Gulabivala  proposed an equivalent circuit that modelled the root canal system including periapical tissues. They found that the root canal acted as a complex electrical network with resistive and capacitive elements. It exhibited complex impedance characteristics having series and parallel resistive and capacitive components with a simplified model shown in Figure 10.7. Huang et al.  proposed a sophisticated equivalent circuit model of the apical third of the of the human tooth root canal system that mimics clinical situation to describe the electrochemical features of the tooth structure as a bioelectric complex, particularly at the apical area (Figure 10.7).
10.6 Electronic Root Canal Length Measurement Devices (ERCLMDs)
10.6.1 Fundamental Assumption
The fundamental assumption of ERCLMDs is that human tissues have certain characteristics that can be modelled by means of a combination of electrical components. Therefore, by measuring the electrical properties (e.g. resistance, impedance) of that equivalent electric circuit, some clinical properties (such as the position of a file) can be deduced .
Custer  introduced a new electrical approach for locating the canal terminus that was dependent on the fact that the electrical conductivity of the tissues surrounding the apex of the root is greater than the conductivity inside the root canal system, coronal to the canal terminus. Custer  noted that this difference in conductivity values could be detected more easily if the canal was dry or filled with a nonconductive liquid such as alcohol. In other words, he discovered that the electrical resistance, the inverse value of conductivity, near the foramen was much less than in the coronal region of the root canal. Therefore, Custer  located the position of the foramen by applying a voltage between the alveolus opposite the root apex and the broach inside the pulp and measuring the value of the electrical current (with a milliammeter). In his pioneer experiment, using the technology of that time, Custer’s electrical circuit had three dry cells: a milliammeter, and a negative and a positive electrode. When the circuit was connected, a small positive voltage was applied to the fine insulated broach which was introduced into the pulp and slowly penetrated inside it. When the broach approached the foramen, as a result of a significant increase in the electrical conductivity, the electrical current became more and as a consequence a “certain movement in the index finger” of the ammeter was observed. Custer  concluded that this movement, which was proportional to the electrical current and so the electrical conductivity, would be a reliable guide to the position of the broach relative to the apical foramen.
Subsequently, Suzuki  in his experimental study on iontophoresis in dog’s teeth indicated that the electrical resistance between a root canal instrument inserted into a canal and an electrode applied to the oral mucous membrane registered consistent values.
Based on Suzuki’s finding, Sunada  reported that a specific value of the resistance would determine the position of the root canal terminus. He determined that when the tip of an endodontic instrument had reached the periodontal membrane through the apical foramen, the electrical resistance between the instrument and the oral mucous membrane was approximately equal to 6.5 KΩ. He also claimed that if the reamer perforated the canal wall or floor of the pulp chamber and reached the periodontal membrane, the electrical resistance between the mucous membrane and the perforated periodontal membrane was almost equal to the resistance shown at the apex. In his first in vivo experiment, Sunada  used a simple microammeter to measure the length of 71 canals. The microammeter had two electrodes, one attached to the oral mucous membrane and the other to an endodontic instrument positioned in the root canal; the resistance was measured when the tip of the endodontic instrument was situated at the apex (the length of the teeth were already known “by means of a measuring wire and X-ray”). The resistance of the periodontal membrane was calculated by dividing the voltage by the value of current that the device measured. In other words, dentine, enamel, and cementum are electrical insulators; soft tissue, including the periodontal ligament, is a conductor. The device established a circuit in the mouth that originated in the device, ran through an endodontic file via the attached probe, and extended down the canal out of the foramen and into the periodontal ligament. The circuit continued through the patient’s mucosa and eventually completed the loop by running into the lip clip that was connected to the device through a return wire. Sunada  also reported that the patient’s age, type, or shape of teeth and the diameter of the canal had no influence on the results. The mean value of the resistance of the circuit between the canal terminus and the lip clip was 6.5 KΩ.
10.6.3 Resistance-based ERCLMDs
Resistance-based ERCLMDs relied on the assumption that the circuit between the endodontic file and the lip clip could be modelled by a simple resistive circuit (Figure 10.8).
Therefore, a small DC was applied to that circuit and the voltage was measured. By dividing the value of the voltage by the value of the current, the resistance value of the circuit was calculated. Many electronic root canal length measuring devices have since been marketed (Table 10.1) using the same principles. The differences between them are basically in the design of the electrical circuits and in the mode of their display. However, they can all be classified as resistance-based ERCLMDs.
Although many of the resistance-based ERCLMDs have been shown to be accurate in dry conditions within the canal, it has been reported they were not always accurate when strong electrolytes, excessive haemorrhage, pus, or pulp tissue were present [83–86] As soon as the file tip touches the electroconductive solution (electrolyte), in these situations, the DC voltage polarizes the tissues and varies its resistivity , thus completing the electrical circuit; the device incorrectly indicates that the minor apical foramen has been reached . Another disadvantage of the DC is that an electric shock can be felt by the patient [58, 86]. To eliminate the disadvantages of DCs, Suchde and Talim  proposed using AC to measure the resistance. However, they still used a simple electronic ohmmeter, a “bridge circuit,” to overcome the disadvantages of the simple resistance method. The advantages of AC are that it causes less damage to the tissue and improves functionality in wet conditions as the resistivity of the electrolytes experience better stability [84, 88]. However, the disadvantage is that the capacitive component of the canal, which is variable with many parameters, will have an additional effect on the circuit. Therefore, in wet conditions when the capacitive component is more dominant, these devices lack accuracy [54, 79, 84, 89].
10.6.4 Low-frequency Oscillation ERCLMDs
As discussed previously, in practical endodontic experiments, the structure of the endodontic instrument, canal, and tissues have capacitive characteristics as well as resistive characteristics. Therefore, modelling the circuit with a simple resistive characteristic is not sufficient [54, 68, 79, 90]. Unfortunately, these capacitive characteristics are variable and can change with the shape of the canal and other physical parameters such as the dielectric constant of the liquids inside the canal . Based on this view, Inoue [90–92] developed a different ERCLMD that worked through the principle of electrical resistance but was modified by the addition of an audible “marker tone.” The principle of measuring root canal length by this device is based on the assumption that the low-frequency oscillation, as produced by the resistance and capacity between the oral mucous membrane and the gingival sulcus, is the same as the frequency between the periodontal ligament (at the canal terminus) and the oral mucous membrane . When the file reaches the canal terminus, the oscillating tones produced by the gingival sulcus and the canal terminus are coincident. As the impedance between the two electrodes is included in the feedback loop of the oscillator circuit, it influences the oscillated frequency value. Therefore, the frequency of the measured current changes as the load varies. In other words, the impedance of the root canal depends on many parameters and is not the same in different canals. However, it can be assumed that the impedance between the oral mucous membrane and the depth of the gingival sulcus closely resembles the impedance between the canal terminus and the oral mucous membrane. Based on this assumption, Inoue’s device, the Sono-Explorer (Figure 10.9) (Hayashi Dental Supply, Tokyo, Japan), measures these two impedances and identifies the canal terminus when the readings approach each other. The frequency of this impedance is directed to a speaker that develops an auditory tone generated by means of low-frequency oscillation. The most important disadvantage of this device was the need for individual calibration. The device had to be calibrated at the periodontal sulcus in each tooth. The technique involved inserting a file with a silicon plastic sheath (Figure 10.10) into the gingival crevice of the tooth to be measured and the sound produced was named the gingival crevice sound. Then, the conventional endodontic file was inserted into the root canal and when the sound produced by this file became identical with the gingival crevice sound, the rubber stop was aligned with the reference point and the measurement taken.
10.6.5 High-frequency Devices (Capacitance-based Devices; ERCLMDs)
To further decrease the influence of the variable capacitive characteristics on measurements, insulated files were also used . As explained previously (equation 3), the value of a capacitor is directly proportional to the area of its plates. Here, the insulator covers most of the surface of the file to decrease its capacitance value. Unfortunately, the coated file cannot be used in narrow canals because the coating is easily abraded, thus disturbing the measurement . In addition, Himel and Schott  reported that the quality of the seal provided against electrical conductivity was decreased after autoclaving.
10.6.6 Capacitance and Resistance ERCLMDs (Look-up Tables)
In 2003, the Elements™ Diagnostic Unit (SybronEndo, Anaheim, CA, USA) was introduced. It measured the capacitance and resistance of the circuit separately [97–99]. As explained previously, these values are variable with many parameters. However, experimental look-up tables were developed that included the statistics of the values at different positions . The device exploits a composite signal with two frequencies to measure the resistance and capacitance of the system and then compares the measured values with its lookup table to diagnose the position of the file. As a result of modern electronic digital circuits, the manufacturer claims that this device has more consistent readings than its predecessors [99, 100]. Nevertheless, the fundamental principle of all the ERCLMDs is the same, i.e. an electrical model is assumed and the characteristics of that model are measured to diagnose the clinical properties. Based on clinical observations, Vera and Gutierrez  reported that when using the ElementsTM Diagnostic Unit the file should be withdrawn to the 0.5 mm mark instead of the 0.0 mm mark to achieve the accurate identification of the apical constriction that they assumed should be 0.5 mm short of the external (major) foramen. Therefore, taking the file to the 0.0 mark on the display and then withdrawing it 0.5 mm appears to be the most accurate way to use this device. In an attempt to achieve better results, Vera and Gutierrez  also recommended the access cavity should be dried before introducing the file into the canal.
10.6.7 Voltage Gradient ERCLMDs (Difference in Impedance with Three Nodes)
Several studies have been conducted to determine a constant electrical resistance or impedance in order to diagnose the position of the canal terminus, e.g. Sunada  who determined R = 6.5 kΩ. However, Meredith and Gulabivala  reported there is neither constant reference impedance nor constant resistance for all root canals. The reason that, for example, resistance-based devices work in a reasonable number of cases is that there is a substantial difference between the resistance (or the impedance) value at the pulp and periodontal junction compared with intracanal positions . Indeed, this is the property Custer  described many years ago. Based on this fact, Ushiyama  proposed a method to measure the variation in impedance when a file was inserted into the root canal. Using bipolar electrodes and applying a 400-Hz alternating current, this device monitored variations in the impedance value. Ushiyama  concluded that a sharp variation in the value determined the position of the file at the apical constriction, the narrowest portion of the root canal system. Ushiyama  also reported that in the presence of strong electrolytes the voltage gradient method could accurately detect the apical constriction. However, use of a special bipolar electrode is one of the main disadvantages of this device, as the electrode will not fit into narrow canals. No commercial product of the experimental device developed by Ushiyama  appears to be available.
10.6.8 Two Frequencies: Impedance and Difference ERCLMDs
Yamaoka (1984 – quoted in Saito and Yamashita ) developed a measurement device in which two frequencies were employed in the measurement . This device measures the impedance value at two different frequencies (f H and f L) and calculates the difference between the two values: