The kinesiographic measurement of jaw displacement

The kinesiographic

measurement of jaw displacement

A. G. Hannam, B.D.S., Ph.D., F.D.S., R.C.S.,* R. E. DeCou,** W. W. Wood, B.D.Sc., D.D.S., M.A.**** University

of British Columbia,

J. D. Scott, B.Sc.,***

and

Vancouver. British Columbia

F

unctional movements of the jaw have been recorded by a variety of methods including direct electromagnetically cinematography, observation, inductive and photoconductive transducers, and, most recently, radionuclide tracking.‘. :’ During normal movements, the translations and rotations which accompany jaw motion are so complex that only those systems capable of expressing information with 6 degrees of freedom are properly able to measure displacement patterns at a given point?’ Although such devices exist,“. ’ most studies have been carried out with techniques involving two or three degrees of freedom and they have been confined to the description of incisor point movement only.” 2 Reasons for the acceptance of limited expressions of motion probably include the relative noninvasiveness of incisor point movement, the physical ease of the technique, its applicability to large numbers of subjects, the restriction of data to manageable proportions, and not least, the general lack of alternative instrumentation with desirable properties. Several investigators have used the Kinesiographt to monitor three-dimensional linear movement of an incisor point on the mandible?” Apart from the major theoretical limitations as outlined, the instrument offers properties which should be taken into account whenever quantitative measurement is contemplated. This article describes how they can be controlled in an experimental environment.

Fig. 1. Modified stereotaxic apparatus for calibration of the Kinesiograph. Brass micromanipulators, A, move an aluminum bar, B, carrying the magnet, C. ‘The magnet can be moved in O.l-mm increments over a three-dimensional lattice, relative to the fixed planes of reference of the Kinesiograph’s framework, D.

METHODS The Kinesiograph basically consists of a set of magnetometers which sense the displacement, in three planes, of a small magnet cemented to the

*Professor, Department of Oral Biology. **Research Technician, Department of Oral Biology. ***Programmer, Department of Oral Biology. ****Assistant Professor, Department of Restorative Dentistry TMyotronics

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lower anterior teeth. These sensors are carried on a light framework supported by a spectacle-like device which is worn by the patient in a conventional fashion and stabilized with an elastic strip behind the head. The framework is arranged about the magnet in a prescribed way and usually zeroed to the intercuspal position of the patient before any recordings are carried out. The fundamental signals derived from the device are three voltages representing

0022-3913/80/070088

+ 06$00.60/0 0 1980 TIM: C. V. Mosby Co.

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LATERAL

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vertical, lateral, and anteroposterior jaw movement, respectively. The voltages are referenced to the planes of orientation of the magnetometers. This system is described in more detail elsewhere.’ During bench tests, we have found the instrument to be a stable indicator of the position of the magnet provided the latter is not rotated. It responds acceptably to frequencies of displacement up to 150 Hz. Aside from these limitations, two other aspects of the instrument’s pkrformance are notable. These are its inherent nonlinearity over certain prescribed ranges of linear displacement and the question of its orientation relative to craniofacial landmarks. Our observations concerning the management of both aspects are based upon experience with the earlier. K2 version of the Kinesiograph. The principles involved, however, can be applied equally to later versions of the instrument.

Nonlinearity The position of the magnet relative to the sensors on the framework of the kinesiograph determines the nature of the nonlinearity. If the magnet-to-frame relationship during set-up is as the manufacturers suggest, distortions are least near the intercuspal position (the zero point) and greatest at the more

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Fig. 2. Output voltage grid obtained by moving the magnet within a rectangular matrix in a frontal plane through the center of the magnet in its zeroed position. Vertical output voltage (ordinate) has been displayed against lateral output voltage (abscissa). The figures on each axis indicate the actual displacement of the magnet in millimeters.

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Fig. 3. Output voltage grid obtained magnet within a rectangular matrix in through the center of the magnet in its Vertical output voltage (ordinate) has against anteroposterior output voltage figures on each axis indicate the actual the magnet in millimeters.

by moving the a sagittal plane zeroed position. been displayed (abscissa). The displacement of

extreme positions, for example, n(Par maximum opening or maximum lateral excursions. Because any correcting operation has its greatest source of error where the distortion is most marked, it is prudent to first determine the range of movement anticipated under operational conditions and then to choose a set-up zeroed position of magnetto-frame which is best able to distribute the nonlinearity as evenly as possible over the user’s intended range. If, as in many cases, the entire range of the masticatory cycle is to be included, we have found it better to set the magnet 1 cm higher than suggested by the manufacturers. This not only serves to improve the distribution of the distortion but has the practical benefit of permitting added clearance between the chin and the lower sensor. Some kind of micromanipulator is necessary to bench-calibrate the system. Its resolution should be sufficient to permit small incremental steps in three dimensions, and it should be nonferrous. Fig. 1 demonstrates one method which can be used for calibration. Three brass micromanipulators from a sterectaxic apparatus* have been arranged so that a 12-inch aluminum beam can be moved in linear *Narishig-e Scientific Instrument

Lab.. Tokvo. ,Japan.

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Fig. 4. Output voltage grid obtained by moving the magnet within a square matrix in a horizontal plane through the center of the magnet in its zeroed position. Anteroposterior output voltage (ordinate) has been displayed against lateral output voltage (abscissa). The figures on each axis indicate the actual displacement of the magnet in millimeters. Note the asymmetry between right and left sides.

J i= !z LATERAL Fig. 5. Diagram demonstrating the linearizing process for data in the frontal plane. The squared grid represents an idealized plot of vertical output voltage against lateral output voltage in which the voltages are directly and equally proportional to displacement of the magnet. The, curved lines represent part of the actual output grid obtained (see Fig. 2). For a given position of the magnet, voltage coordinates indicated by the open circle should actually be those of the solid circle if a linear system exists. The first correction of lateral output voltage therefore alters the coordinates to reflect a position indicated by the solid square. The correction of the vertical voltage then changes them to mark a position labeled with the triangle, and a final recorrection of the lateral voltage results in the coordinates indicated by the solid circle.

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steps of 0.1 mm through three planes parallel to the framework carrying the magnetometers. The magnet is carried in a slot at the end of the aluminum bar. The whole assembly is portable so .:hat calibrations can be carried out in locations where the subject’s head is normally placed during recording sessions, thereby ensuring that any ferrous or magnetic influences in the recording environment are taken into account. Nonlinearities in the system become apparent when the magnet is moved in rectangular lattices under these conditions. Figs. 2 to 4 illustrate typical calibration curves for the three planes of movement when the magnet is moved within a 2 cm wide by 2 cm deep by 4 cm high three-dimensional lattice whose top face is centered upon the zeroed position of the magnet. In our system. the three displacement signals from the Kinesiograph are filtered to excl.lde frequencies above 55 Hz, corrected for gain. sampled continuously at 1 msec intervals for preselected periods by a disk-based minicomputer,* and then linearized. During the linearizing process, which is based upon a method of approximations and carried out by the minicomputer, it is arbitrarily assumed that within the expected range of use the anteroposterior position of the magnet does not sigrificantly affect the lateral or vertical signals, that both lateral and vertical positional changes may affect the anteroposterior signal? and that lateral posi::ional changes markedly affect the vertical signal. These assumptions make sense intuitively when on’: considers the arrangement of the sensors in the K2 instrument. They are important to the linearizimg procedure as they form the logical basis for the sequence of corrective steps that are taken. Two representative calibration curves derived from the family of midfrontal curves (Fig. 2) are used to obtain single sets of multiplication factors. When applied to the sampled lateral and vertical output voltages of the Kinesiograph, these factors change the curvilinear relationships illustrated to linear ones. For any given pair of lateral and vertical voltages, the lateral voltage is corrected first, and most of its distortion is eliminated in this step. Lateral displacement affects the vertical voltage, so the corrected lateral voltage is now used to alter the vertical output voltage by a similar process. Substitution of *Hewlett-Packard Packard Ltd.

21 MX Canada.

Series

E and peripherals,

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newly corrected values in this sequence, and repetition of the calculations, finally produces a redefined and more accurate pair of “linearized” lateral and vertical values. The entire sequence is summarized diagrammatically in Fig. 5. Nonlinearities in the anteroposterior output voltage are corrected in a similar way. Correction factors derived from the curves in Figs. 3 and 4 are used with the computed, “linearized” lateral and vertical voltages to provide more accurate anteroposterior values by a two-step process. When the computer has been programmed to carry out the above linearizing process, it is possible to perform a through-calibration of the system by setting it up in the micromanipulator. moving the magnet to precise coordinates, and then printing or displaying the “linearized” versions of these coordinates. In this way, the error of measurement between actual and computed values can be assessed. Fig. 6 shows the spatial distribution of 36 such points (representing 108 coordinate variables) likely to be within the limits of incisor point movement during natural mastication. The points occupy a zone 25 mm inferior, 7.5 mm lateral, 2 mm anterior, and 7.5 mm posterior to the planes of reference of the system which pass through the magnet when it is in its zeroed position. If the error of measurement is defined as the positive or negative difference in millimeters between a single pair of actual and computed variables, then a typical, single run through this kind of calibration yields a combined mean error for all 108 pairs of coordinate variables of 0.18 mm, SD +- 0.20. The mean error for the 69 pairs within 10 mm vertical from the zeroed position (a zone of particular relevance to the chewing cycle) is 0.14 mm, SD + 0.14 under similar conditions of measurement.

Frame placement Uncontrolled frame placement provides as much or as great a source of error as nonlinearity. It is possible for the operator to satisfy the requirements for correct magnet-to-frame relationships under practical conditions yet introduce sufficient rotations of the framework about the magnet to produce large errors in recorded incisor point movement, particularly in excursions away from the intercuspal position. We use a conventional dental face-bow* with minor modifications to help position the framework. *Whipmix,

Louisville,

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Fig. 6. Distribution of the 36 magnet jiocations used in the calibration run described in the text. The planes of reference are those of the Kinesiograph framework. The locations occupy a zone likely to include most chewing cycles and are evenly distributed in three dimensions around the zeroed position of the magnet, O. Figures represent millimeters of displacement from this position for all three axes. The additions include a removable midline pointer parallel to the arms of the face-bow and two 4-inch vertical rods each projecting downward at right angles to a face-bow arm. Before the framework is aligned, a midsagittal line and two lateral lines representing the Frankfort horizontal plane are drawn on the face with the aid of the face-bow. At this time, the midline pointer on the face-bow is also used to locate an incisor point that is midsagittal to the cranium irrespective of its position in the dental arch. The magnet is then cemented to the lower anterior teeth over this point. The sensors on the Kinesiograph framework are next positioned around the magnet by means of perspex spacer bars cut to the correct dimensions. The face-bow (minus its pointer) is used again, this time to assist in the visual alignment of the framework to the midsagittal line, in a plane parallel to the Frankfort plane and in a plane at right angles to the Frankfort plane. Here the two vertical rods are also useful in ensuring that the entire framework is not

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Before each recording session, a bite-fork registration of the arch can be made with conventional face-bow apparatus. At the end of the session, but before the Kinesiograph framework is removed, the bite-fork record is reinserted and held rigidly by the subject. The hinge-axis and orbital indicators are then reversed and aligned so as to signify coplanar points on the two lateral and single vertical sensors of the Kinesiograph. On its removal. this modified facebow record indirectly provides a measure of the angular relationship between the actual reference planes of the Kinesiograph during the recording session and the conventional reference planes of semiadjustable or fully adjustable articulators. The maxillary dental arch provides the common reference for relating one data set to the other; therefore, any simple measuring device can be used to estimate angular relationships between the two sets of planes. DISCUSSION

Fig. 7. Modified face-bow framework used for aligning the Kinesiograph frame. The face-bow side arms carry two vertical rods, A. When the side arms are aligned parallel to the Frankfort horizontal plane, 8, these projections allow visual orientation of the Kinesiograph frame and its sensors to a frontal plane at right angles to the Frankfort horizontal plane. The midline support of the frame, C. is aligned to a midsagittal line (not shown) previously drawn on the face on which the magnet cemented to the teeth also lies. (The pointer used for establishing this line has been omitted for clarity.) rotated about a vertical axis, as their ends lie close to the lateral sensors of the Kinesiograph. The face-bow is then removed, and a final check is made with the spacer bars to verify that magnet-to-sensor dimensions are still correct. The entire system is illustrated diagrammatically in Fig. 7. Positioning the framework is approximate at best. The method nevertheless ensures that consequent errors are at least minimized. In a previous experiment,“’ we have used it repeatedly (15 times over 3 days) to remeasure a standardized jaw position in the same subject. The mean coordinates of this fixed point were estimated to be 19.3 mm SD -t 0.4 vertical, 3.2 mm SD 2 0.8 mm lateral, and 3.5 mm SD +- 1.3 mm anteroposterior (n = 15), the variances expressing errors due to frame placement alone. We believe that it may be possible to reduce errors in day-to:day measurement still further by referencing the framework to the maxillary dental arch.

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More efficient: and perhaps more accurate, methods for linearizing and referencing the system may be possible than those described here. ‘Whether these are worth pursuing depends upon the user’s needs. In terms of bench performance with a linear calibrator, the instrument can resolve small changes in displacement, and it is theoretically possible. following suitable filtering procedures, to devise very accurate linearizing procedures under these cocditions. These efforts, however, must be balanced against the fixed limitations inherent in the overall system, which produce errors that are difficult or impossible to control under functional conditions. Rotations at or around the incisal point cannot be measured, while the process of physical orientation and fixation of the apparatus 1s at best an imprecise exercise. However, once the decision is made to accept the instrument’s restriction to expressing linear but not rotational motion of a single incisor point, the remaining limitations of the Kinesiograph can clearly be minimized to an extent that permits acceptable errors of measurement for many tasks. Such procedures may be entirely unnecessary if the system is only used to display jaw movements in a qualitative way. On the other hand, if comparative measurements are to be performed on a day-,to-day basis, especially outside the intercuspal area, then additional techniques of this kind are obviously essential. Although the suggested principle of zeroing the system to the intercuspal position seems to be satis-

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factory for most purposes, the alterations to this area which occur as a consequence of occlusal or orthognathic reconstruction frequently require the zeroed position to be related to more fixed, conventional, mandibulo-masillary references such as centfic relation. This is especially true Lvhen there is an ambiguity in the intercuspal position, for example. in patients lvith excessive occlusal lvear. or with “freedom in centric relation.” In this regard. it should be noted that esternal manipulation of the mandible when the framelvork is in place can be difficult. Several points have been mentioned which are not peculiar to the Kinesiograph alone. Any system used for measuring jaw movement should be recalibrated at regular intervals and under conditions resembling the actual recording environment as closely as possible. Identifiable planes of reference must be used and some kind of estimation made of the errors associated lvith placing the transducers on the subject. Finally, any system. whether it records the displacement of one or several points on the mandible in more than one dimension. creates a formidable problem in data management and its expression. Under these circumstances, digital conversion becomes an almost essential part of the process whenever quantitative measurement is contemplated. CONCLUSIONS Whenever the Kinesiograph is used to measure functional jaw movement. three factors should be taken into account. The instrument is theoreticall) limited by its expression of data with only 3 degrees of freedom of measurement, it has nonlinear response characteristics over the entire range of functional jaw movement. and it requires referencing to fixed craniofacial landmarks. Although the first limitation is inherent in its design and cannot be altered. the remaining two can be controlled sufficiently to permit the day-to-day expression with an acceptable error of measurement of linear incisor point movement.

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REFERENCES Bates. J F . StatTord. G. D . and Harrrson .A hlasucdtorv functions-.A review of the hterature (Ii .rhe form of the maattcatorv c\cIc. J Oral Rehabll 2:281. 197.5 Hannam, A G Masticanon m man Itr Br.,ant. P Gale. E . and Ruqh, J . editors: Oral hlotor Behavmurs. Impact an Oral Conclltvm\ and Dental Treatment National Inwtutes of Health. \Vashinqton. 1979 Glllnqs,. B. R D . C;raham, C: H . and Du:kmanton. N A Jaw movement, m \ounq adult men durlnq chewinq J PROSIIIFI Dt\r 29:616. 1975 Goodson. J bl and Johansen. E. Analvw of human mandibular mo\ernent. IN Rivers. H hi.. editor: hlonographs m Oral Science, 101 5 New York, 1975. S. Karger. Lemmer. J , Leum. meawrement of ,a\\ 36:21 I. lc)i(i

.-I. and van RenTburg-. L B. The movement. Part I J PROSIH~~ DL\~

Gbb,. C: H hleyserman. J Funrtmnal mo\ernrnt< 26:604. 19; I

T . Reswck. J II. and Derda. H of the mandible. J PKOS~HF 1 DFXT

SoIt. S R , Gibbs, C: H 1 and Benz. S T : Study of ghdmg tooth contacts durq mawcation. ,J Periodontol 47:331, 1976 Jankelwn. B . Swain. C: \I’. Crane. P F . .md Radke. J C: IilneGometr~c instrumentatmn: .\ neu wchnolog\ J .\m Dent .\\soc 90:83f. 1975 Rlorlmoto. T., Takebe. H Sakan. I.. and Kawamwa. 1 Interdental thickness discrimmatlon and mandtbular positlon wn\e J Dent Res 56(Sperial i5wr 1~1 Dlf4. 1977 (Abstract, Hannam. A. G Scott. J D . and DeCou. R E .-\ computerba\ed s\~tcm for the \Imultaneous meawrement of muscle actlvIt\ and ja\\ mo\wnent durlnq mawcanon m man Arch Oral BIOI 22:17. 1977 Hannam. 4 C.. D&XI. R E . Scott. J U . and \Vood. \$ \\ .l‘he relatwnship between dental occlusion. muscle actixlt\ and associated jaw movement in man Arch Oral BlOl 22:Li. 197i

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