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The measurement of wear in dental restorations using laser dual-source contouring
91
Wear, 76 (1982) 91 - 104
THE MEASUREMENT OF WEAR IN DENTAL LASER DUAL-SOURCE CONTOURING
RESTORATIONS
USING
J. T. ATKINSON, D. GROVES and M. J. LALOR Department of Mechanical, Marine and Production Engineering, Liverpool (Gt. Britain)
Liverpool Polytechnic,
J. CUNNINGHAM Department of rental Surgery, School of Operative Dental Surgery, Liverpool, Liverpool (Gf. Britain)
University of
D. F. WILLIAMS Department of Dental Sciences, School of Dental Surgery, University of Liverpool, Liverpool (Gt. Britain) (Received September 28,198l)
Summary
The development of a technique for the accurate me~~ement of wear during the use of dental restorations is described. Measurements were made by comparing suitable impressions of the restorative and surrounding area before and after test. Detailed information about the topology of the prewear and post-wear restoratives obtained from contour maps of the impressions was processed to find the volume lost by the restoration during test. The technique, an extension of earlier experiments, relies on the precise reproduction of dental surfaces by the impression material used. The accuracy and precision of vinyl polysiloxane was investigated and found to be adequate. Three methods of interpreting the contour maps are presented, incfuding a computer technique, for the estimation of volume loss. The computer technique also produces “difference” contour maps of the wear scars. Calibration tests on extracted teeth showed that volume loss due to wear can be measured to an accuracy of between 2% and 10% depending on the data-processing technique used.
1. Introduction
Composite materials are widely used for the restoration of anterior teeth and are generally successful, complying with the requ~ements of an 0043-1648/82/0000-0000/$02.75
0 Elsevier Sequoia/Printed in The Netherlands
92
ideal tooth-coloured filling material [l] . One of the main problems that arises with these materials when used in the conventional class III, IV and V cavities is the staining that arises, especially at the margins. A good technique can obviate this to a certain extent [Z] but the staining that results from plaque accumulation subsequent to the roughening of the surface by abrasive wear is very much dependent on the properties of the materials. Wear, which is related to fundament~ properties of fracture toughness and hardness, is the most serious physical limitation of most dental composites and is a major factor that has restricted their use in class I and class II cavities where they are subjected to greater occlusal loads and abrasive action during mastication. In several clinical studies the wear of composites has been compared with that of amalgams over a period of time. It has been a universal finding that with the conventional BIS-GMA composites wear becomes noticeable on the occlusal surface of the restoration within 1 year, with a progressive loss of anatomical form thereafter [3, 41. The results of clinical studies, however, are usually expressed in qualitative or subjective terms, and it has been difficult to measure quantitatively the amount of wear occurring in clinical practice and to identify the underlying mechanisms. The literature does, however, contain an abundance of reports on the laboratory testing of the abrasion of restorative materials [ 5, 61. The methods of abrading the sample of material and of quantifying the wear are numerous and varied. This has resulted in an appreciable scatter in the experimental results, with discrepancies arising in the ranking order of amalgams, unfilled resins, composites and silicates. The main problem arises from the fact that different materials may wear by different mechanisms and each wear test may only give meaningful results when used to compare materials that abrade by the same me~h~ism. It is difficult, therefore, to devise satisfactory in uitro wear tests that will give results that can be extrapolated to the clinical situation. The sense of urgency and the need to devise alternatives to amalgam for posterior restorations because of a tightening of toxicological standards relating to mercury has led to a reappraisal of the methods of evaluating the clinical performance of composites in class I and II cavities. The introduction of submicron filler composites in recent years has led to materials with improved mechanical properties and to the probability that such materials will function satisfactorily in posterior restorations. The need therefore arises for methods to quantify and to characterize the wear that takes place in class I and II composite restorations. In the present paper we describe one method by which these objectives can be achieved. The method involves optical contouring and computer evaluation of contour maps. The method has been developed and refined by studying artificially induced wear in amalgam restorations and may be used for any similarly shaped object. The technique has previously been used for studying wear of amalgam specimens in laboratory wear-testing machines [7] and has also been used successfully to study the wear patterns on orthopaedic joint replacement prostheses.
93
2. Outline of the measurement
procedure
The aim of the procedure is to quantify the volume lost by a dental restoration over a period of normal use by a patient. The procedure involves three basic steps. (i) Impressions of the tooth are made before and after the test period. (ii) The impressions are contoured using the optical arrangement described in Section 3. (iii) The prewear and post-wear contour maps are compared quantitatively to find the shape, depth and/or volume of any wear scars. The salient experimental restrictions for each of these steps are as follows* (i) The precision of the impression-making material and process must be an order of magnitude greater than the depth of the wear scars under investigation. This restriction is discussed in Section 4. (ii) The contour intervals on the prewear and post-wear maps of the impressions must be identical. Also the reference plane must have the same orientation with respect to the two impressions. The first restriction is easily observed in practice; the second restriction is discussed in Section 5. (iii) The contour fringes should be resolvable over the areas of interest on both impressions. In Section 3 methods for estimating the volume loss are applied to some calibration tests on extracted teeth. Section 7 contains a general discussion about the use of the technique and its further refinement.
3. Dual-source
contouring
A schematic diagram of the dual-source contouring arrangement shown in Fig. 1, A laser beam is expanded and spatially filtered before ing through a prismatic beam splitter. The position of the beam splitter adjusted so that the two divergent beams cross over in the region of
Laser
pinhole
imx33fession
\/, J
beamsplitter
/
ca
\
/
pr era
/’
Fig. 1. The dual-source contouring arrangement.
is passis the
93
object to be contoured, usually between 50 and 100 cm from the point source. Interference fringes will be formed in the region of the cross-over and will be projected along the bisector of the angle between the beams illuminating the object, perpendicular to the plane of the paper. If the object is small compared with the distance 2 between the illuminating source and the object then the perpendicular spacing Ah between the adjacent fringes is constant and is given by
where a is the separation of the two apparent point sources and h is the laser wavelength. Ah can be varied by adjusting the beam splitter to vary a. The object is viewed at an angle 8 with respect to the plane of the fringes. The image is then recorded on a photographic film. In general it is necessary to prepare the sample in such a way that it scatters light into the camera; this is achieved by vacuum flash coating with aluminium and, in the case of very smooth surfaces, the application of an even coat of matting spray. Photographic prints of the contour patterns obtained from specimens differing in shape (due to wear) may be compared by one of the methods outlined in Section 5 to give the amount of wear that has taken place. In practice, values of Ah in the region 100 - 200 pm are used. Ah is measured in the region of the object using a travelling microscope. When the angle 8 is 90” the fringe pattern observed is a true contour map of the object. For all other values of 8 this is not strictly true. The fringe interpretation methods discussed later are not affected by this fact. The only reason for viewing the object at values of 6’ other than 90” is to allow the object to be pho~~aph~ with larger apertures at the high ma~ifi~ation required and hence to obtain good resolution.
4. Impression
fidelity
To measure accurately the in uiuo wear of restorations (placed in teeth or dentures) it is necessary to make impressions or replicas of the restorative and surrounding tooth before and after wear (e.g. over a period of from about 6 months to 2 years) and to compare contour maps of these impressions. In order to do this it is vital to ensure that the fidelity and precision of the impression process are much better than the depth of wear to be measured. Having established that this demand has been met there is no reason why in uiuo wear cannot be measured. The precision of the impression material used here was checked experimentally by making four impressions of an extracted tooth containing a restoration. The four impressions and the tooth were then contoured. Their maps were compared with one another in order to assess the degree of similarity between them.
(b) Fig. 2. (a) Contour maps of two impressions of the same tooth (Ah = 152 Pm; 0 = 46”; magnification, 4.8~); (b) superimposed line tracings of the maps shown in (a) (only the region of restoration is shown).
Figure 2 shows two of these maps (Ah = 152 pm; 0 = 46”) together with line tracings of the maps superimposed (Fig. 2(b)). The degree of similarity is very good. The contour lines do not coincide exactly for two reasons. The (arbitrary) zero fringes on each map are not coincident, so that the fringes on one map are shifted relative to those on the other map by a constant amount. Also the two impressions were mounted at slightly different values of 0, so that the mi~i~ment of the fringes increases linearly with distance measured from the zero fringe. These small differences in the position of corresponding fringes do not appear to alter their shape. Small displacements and rotations of one impression relative to another when the two contour maps are made can be taken into account when the volume loss is calculated. This is done by shifting one of the superposed maps by a small amount until the prewear and post-wear fringes of interest coincide exactly
96
on unworn parts. Where wear has occurred coincidence will not be possible and the prewear and post-wear contour lines are drawn and processed as described later. There is, of course, a limit on how big these seemingly arbitrary adjustments to the maps can be made. Empirical evidence has shown that overall displacements of the maps of less than half a fringe spacing do not affect the accuracy of the volume loss found by more than 10%. In many cases, this accuracy is acceptable. The above adjustments are not necessary when the computer is used to process the maps as small differences in ali~ment are taken into account by the software. Also, the computer stores the height information contained by the prewear and post-wear maps as a matrix, not a fringe pattern. Hence, computer processing is the most accurate method of analysing the maps. 5. Specimen
relocation
Throughout this paper it is assumed that prewear and post-wear specimens are contoured relative to the same reference plane, with the same eontour depth, and that the maps have the same magnification. During the calibration trials described in Section 6 these conditions were met by comparing the negative of the prewear contour map with the image of the postwear map as seen on the ground glass screen of the monorail camera. Adjustments were made to the position and orientation of the post-wear impression until the unworn areas on both maps displayed the same fringe pattern. This technique works well but is time consuming (30 min per map pair). For elinical trials the conditions are met more easily by using a relocation jig described below. The rig is described in terms of its use in proposed clinical trials. We consider that 50 patients are to be investigated over a period of 3 years and that the wear of the restoration under test is to be measured every 6 months. Seven different maps of each restoration need to be made. After the restoration is completed an impression of the restored tooth together with an adjacent tooth is made. A model of the adjacent tooth is made from this impression. The model is secured to a metal flag positioned as shown in Fig. 3. The flag defines the position and orientation of the contour map reference plane. The impression is then fitted onto the cast and the gimbal holding the impression in position is tightened; the flag with cast can now be removed. The flag post and stop are left in position to realign the flag for future use. The camera is now adjusted to give the best picture and is left in position for future use. Post-wear impressions are made to include the adjacent tooth. All postwear impressions are aligned in the contouring ~angement by replacing the flag and fitting the impression of the adjacent tooth onto its model. The above procedure ensures that the restorations are contoured relative to the position of the adjacent tooth. Small variations in the position of the reference teeth over the test period may occur, but it is unlikely that changes large enough to affect the measurements will take place; if they do it is still possible to realign the tooth manually.
97
Fig. 3. The repositioning
6. Interpretation
jig.
of the contour
maps
Three methods for finding the volume loss from the contour maps are now presented. They are (a) the fringe displacement method, (b) the moire method and (c) a computing method. Each of the methods is described as a worked example from some calibration tests performed on extracted human molars. In these tests, an experienced clinician (J-C.) made two realistic wear scars (with a dental burr) on the amalgam restoration placed in the teeth. The mass loss was determined gravimetrically. Prewear and post-wear impressions were taken. All the measurements were made from photographic enlargements (30 cm X 35 cm) of the maps shown. 6.1. Fringe displacement method Figure 4 shows the prewear and post-wear contour maps of a tooth which has lost 0.0261 g during the simulated wear process (found by weigh-
(4
fb)
Fig. 4. Contour maps of (aj a prewear impression and (b) a post-wear impression human molar: Ah = 179 pm; 6 = 59”. (Magnifications, 5.4x.)
of a
(a)
tb)
Fig. 5. Line tracings of Fig. 4: (a) the prewear impression;(b) The wear scars are marked A and B.
the post-wear impression.
ing). Figure 5 shows line tracings of these maps. The wear scars A and B are marked. Figure 6 shows the prewear and post-wear contour maps superimposed in the region of the wear scars only. The wear scar is visible as an area where the prewear and post-wear fringes do not coincide (the post-wear fringes are shown as broken lines). Figure 7 shows a close-up of the impressions mounted in the contouring arrangement (schematic). The prewear and post-wear impressions are shown together represented by the full lines and broken lines respectively.
Fig. 6. Superposed line tracings of wear scars. The wear sears are drawn as an array of n squares of equal area a. Fig. 7. A schematic view of the impressions mounted in the contouring arrangement: prewear; -, post-wear.
----,
99
To find the depth of wear at some point it is necessary to measure the fringe displacement Af (the distance between prewear and post-wear fringes measured along a line parallel to the direction of propagation of the contour fringes, i.e. A-B) and the fringe spacing fin the same region. Both Ah and 8 must also be known. The depth d of wear parallel to the direction of view can be found by using similar triangles. Clearly d
Af
(2)
dh’=f Therefore
dzAf--
Af
f
(3)
sin 8
To find the volume of the wear scar, of n small squares of equal area a, as value of d (di) by measuring Afi and plying the area of one square by the
the area of the scar is drawn as an array shown in Fig. 6. Each area is assigned a fi . The volume loss is found by multisum of the d values. Hence (4)
In this case Ah = 179 pm, 13= 59” and * Afi ax i=O
= 9.6 mm3
fi
Therefore V = 2.0 mm3 and the mass loss is 0.024 g, assuming a density of 12 g cmP3. This method is best applied when A f < fi. When Afi > fi the following method is better. 6.2. Loire method Figure 8 shows the prewear and post-wear contour maps of another tooth used in the calibration tests. This tooth has lost 0.0267 g (found by weighing) during the simulated wear process. The wear scars are marked C and D on the post-wear contour map (Fig. 9). When the two maps are superposed a moire pattern will be observed. This moire pattern corresponds to a contour map of the difference between the two surface topologies, i.e. a contour map of the wear scar. The visibility of the moirit fringes is strongly dependent on the intensity profile of the primary (contouring) fringes and the spacing of the primary fringes. Better results are obtained with a square fringe profile; also the spacing of the primary fringes should be less than about 0.1 of the spacing of the moirk fringes for good results. These two conditions are not met in the experiments
Fig. 8. Contour maps of (a) a prewear impression and (b) a post-wear impression of another molar: Ah = 179 pm;@ = 52”. (.~agnificat~ons, 5.4x.)
Fig. 9. Line tracings of the prewear and post-wear maps (superimposed) moiri: maps of the wear scars. (Magnification, 14~ .)
and corresponding
described here; however, it is still possible to draw a difference map from the maps shown in Fig. 8. Figure 10 shows line tracings of the prewear and post-wear maps (superimposed) in the region of the wear scars. The difference contour maps of the wear scars are shown adjacent to the superimposed line tracings, for clarity. The moire maps show loci of constant height difference. The height difference between contours is Allh/sin 8. The superscript difference contour is found by joining those points where the post-wear fringes have crossed m prewear fringes (m = 0, 1, 2, . . . ).
101
Fig. 10. Computer-drawn fication, 28X .)
difference
maps of the wear scars A and B: Ah = 70 pm. (Magni-
The volume of wear between two adjacent difference contours (m = 0 and m = 1, say) can be found (to a good approximation) by measuring the areas A0 and Al enclosed by the contours and multiplying the average of these areas by Ah/sin 19.The total volume of the wear scar is found by summing the volumes between each pair of contours. If the scar is not an integral number of difference contours then it is possible to estimate the volume under the last contour using method (a). However, a rough approximation will often suffice. In the example shown in Figs. 9 and 10, Ah = 169 pm and 8 = 39”. The total volume loss was found to be 2.25 mm3. If we assume the density of amalgam to be 12 g cme3 the mass loss is 0.027 g. This value for the mass loss compares very well with the value found by weighing. However, the accuracy of the moire method depends to a large extent on the geometry of the wear scar. This is because assumptions made about the shape of the wear scar between moire contours may not be valid. 6.3. Computer-aided analysis A computer technique has been developed which will process the prewear and post-wear maps to give the volume lost by the tooth (to an accuracy of 4%) and will plot out the distribution of wear in the form of a “difference” contour map [ 81 . The contours of the difference map are loci of constant change of depth of the surface of the tooth from an arbitrary reference plane which is orthogonal to the direction of view in the prewear map of the tooth. The difference map is equivalent to a moire pattern generated by superposition of prewear and post-wear contour maps but with significant advantages. (i) Moire patterns require the prewear and post-wear primary contour intervals to be equal. The computer technique can accommodate any combination of contour intervals.
102
(ii) MO% patterns require prewear and post-wear maps to be taken from the same viewing angle, The computer technique can correct for small changes in the viewing angle. (iii) Moire patterns cannot generate a difference contour of less than one primary contour interval and then can only generate contours at integer multiples of the primary contour interval. The computer technique can generate difference contours to one-tenth of the larger primary contour interval and can plot any contour value above this value. (iv) The computer technique is unique in yielding an accurate measure of the change in volume for any surface. The technique invofves first recording the contour lines and three reference points on the surface of the tooth from the prewear and post-wear maps. This recording is performed by placing greatly enlarged photographs of the maps on a digitizing table and following the contour lines with the handset. The recorded contour maps are scaled and related to make them coincident using the equations X=Ax+By+Cz+D Y=Ex+Fy+Gz+H
Z=Gx+Hy+Iz+J where A, B, C, D, E, F, G, H, I and J are constants. The equations transform any Cartesian coordinate system (x, y, z) to any other Cartesian coordinate system (X, Y, 2). The positions of the reference points in the prewear and post-wear maps are used to determine the transform constants A, B, C, D, E, F, G, H, I and J. The transformed coincident prewear and post-wear contour maps are recorded on respective two-dimensional matrices by giving to the nearest matrix elements along each contour the value of the height of that contour, the matrix being of such dimensions to cover the surface of the tooth. The surface between the contours is determined by algorithms which scan the matrix vertically, horizontally and along the two diagonals. The accuracy and generality of the algorithms give the technique its accuracy. The complete prewear and post-wear surfaces of the tooth are now recorded as matrices of point heights, the heights being orthogonal and measured from the same reference plane fixed in orientation and position from the tooth. The subtraction of one matrix from the other yields a difference matrix. This is a matrix of changes in height between the prewear and post-wear surfaces, the changes in height being parallel to the direction of view in the prewear map. The change in volume is simply V=A
n=N x
n=l
h,
(6)
103
where A is the area associated with a single element of the difference matrix projected in a direction orthogonal to the reference plane and h, is the nth element of the difference matrix which has N elements. N is typically 10s. The difference contour map is generated by scanning the difference matrix for the elements between which the difference contours pass and by linear interpolation we deduce the path of such contours. The contour maps shown in Section 6.1 were processed using this technique. The volume difference determined was 2.161 mm3 and the difference maps of contour interval 70 pm are shown in Fig, 10. The computer result was within 2% of the gravimetric result.
7. Discussion The most accurate method of determin~g volume loss is the computer method. The only drawback in using this method is the length of time needed to digitize the contour maps. At present two methods of overcoming this difficulty are under conside~tion. These are as follows. 7.1. Automation of the digitizingprocess
It is planned to automate the digitizing process by replacing the photographic camera with a photodiode array and a television monitor. The photodiode array will replace the photographic enlargement and hand digitizing process. The television monitor will be used to check the array outputs visually. This check will enable minor adjustments to the set-up to be made easily. The photodiode array will have about 400’ elements. A lens will be used to image the maps onto the array. It is estimated that this set-up will be sufficient to resolve fringe centres to within Ah/lo. 7.2, Direct display of the difference maps using a moire’ technique
It is possible to produce a moire map of the wear scars directly by superimposing prewear and post-wear contour maps of a tooth. This can be done using photographic negatives of the maps. Alternatively the negative of the post-wear map can be placed over the image of the prewear map on the ground glass screen of the camera. These methods were tried during the calibration tests described in Section 5. In both cases moire fringes were discernible but not usable. There are two reasons for this. To obtain good moire fringes, the primary (contou~ng) fringe spacing f should be less than one-tenth of the moire fringe spacing. Also, the intensity profile primary fringes should be a square wave for the best results. Other workers have reported similar methods [9, lo] with good results. It is proposed to repeat the calibration tests using a smaller contour depth (about 50 ,um) and a square wave fringe profile to try to improve the technique. If good moire difference maps can be obtained then simpler software will be used to find the volume loss from the digitized moire maps.
There are two drawbacks to using this type of moire method. (a) It is not possible to find the sign of the surface height change. (b) Changes of less than Ah/sin 8 in the surface height are not easily measured.
Acknowledgment The authors are pleased to acknowledge Research Council for the work reported.
the support
of the Science
References 1 D. F. Williams and J. Cunningham, Materials and Clinical Dentistry, Oxford University Press, Oxford, 1979. 2 F. Lutz and M. Kull, Helv. Odontol. Acta, 24 (1980) 455. 3 R. W. Phillips, D. R. Avery and R. Mehra, J. Prosthet. Dent., 30 (1973) 891. 4 R. P. Kussy and K. F. Leinfelder, J. Dent. Res., 56 (1977) 544. 5 L. Ehruford, T. Derand, L. Larsson and A. Suensson, J. Dent. Res., 59 (1980) 216. 6 J. M. Powers and P. L. Fan, J. Dent. Res., 59 (1980) 815. 7 J. T. Atkinson, M. J. Lalor, J. F. Jaworzyn and J. B. Cantwell, Comparative wear studies of dental amalgams in using two novel techniques, laser facing contouring and surfometry, 1 I th Int. Biomaterials Symp., Clemson, SC, 1979. 8 D. Groves, M. J. Lalor, J. T. Atkinson and N. Cohen, J. Phys. E, 13 (1980) 741. 9 J. Shamir, Opt. Laser Technol., (April 1973) 78. 10 J. N. Butters, R. Jones, S. McKechnie and C. Wyker, in H. G. Gerrard (ed.), Proc. Laser Int. 80 U.K. Conf, IPC, Guildford, 1980, p. 139.
Wear, 76 (1982) 91 - 104
THE MEASUREMENT OF WEAR IN DENTAL LASER DUAL-SOURCE CONTOURING
RESTORATIONS
USING
J. T. ATKINSON, D. GROVES and M. J. LALOR Department of Mechanical, Marine and Production Engineering, Liverpool (Gt. Britain)
Liverpool Polytechnic,
J. CUNNINGHAM Department of rental Surgery, School of Operative Dental Surgery, Liverpool, Liverpool (Gf. Britain)
University of
D. F. WILLIAMS Department of Dental Sciences, School of Dental Surgery, University of Liverpool, Liverpool (Gt. Britain) (Received September 28,198l)
Summary
The development of a technique for the accurate me~~ement of wear during the use of dental restorations is described. Measurements were made by comparing suitable impressions of the restorative and surrounding area before and after test. Detailed information about the topology of the prewear and post-wear restoratives obtained from contour maps of the impressions was processed to find the volume lost by the restoration during test. The technique, an extension of earlier experiments, relies on the precise reproduction of dental surfaces by the impression material used. The accuracy and precision of vinyl polysiloxane was investigated and found to be adequate. Three methods of interpreting the contour maps are presented, incfuding a computer technique, for the estimation of volume loss. The computer technique also produces “difference” contour maps of the wear scars. Calibration tests on extracted teeth showed that volume loss due to wear can be measured to an accuracy of between 2% and 10% depending on the data-processing technique used.
1. Introduction
Composite materials are widely used for the restoration of anterior teeth and are generally successful, complying with the requ~ements of an 0043-1648/82/0000-0000/$02.75
0 Elsevier Sequoia/Printed in The Netherlands
92
ideal tooth-coloured filling material [l] . One of the main problems that arises with these materials when used in the conventional class III, IV and V cavities is the staining that arises, especially at the margins. A good technique can obviate this to a certain extent [Z] but the staining that results from plaque accumulation subsequent to the roughening of the surface by abrasive wear is very much dependent on the properties of the materials. Wear, which is related to fundament~ properties of fracture toughness and hardness, is the most serious physical limitation of most dental composites and is a major factor that has restricted their use in class I and class II cavities where they are subjected to greater occlusal loads and abrasive action during mastication. In several clinical studies the wear of composites has been compared with that of amalgams over a period of time. It has been a universal finding that with the conventional BIS-GMA composites wear becomes noticeable on the occlusal surface of the restoration within 1 year, with a progressive loss of anatomical form thereafter [3, 41. The results of clinical studies, however, are usually expressed in qualitative or subjective terms, and it has been difficult to measure quantitatively the amount of wear occurring in clinical practice and to identify the underlying mechanisms. The literature does, however, contain an abundance of reports on the laboratory testing of the abrasion of restorative materials [ 5, 61. The methods of abrading the sample of material and of quantifying the wear are numerous and varied. This has resulted in an appreciable scatter in the experimental results, with discrepancies arising in the ranking order of amalgams, unfilled resins, composites and silicates. The main problem arises from the fact that different materials may wear by different mechanisms and each wear test may only give meaningful results when used to compare materials that abrade by the same me~h~ism. It is difficult, therefore, to devise satisfactory in uitro wear tests that will give results that can be extrapolated to the clinical situation. The sense of urgency and the need to devise alternatives to amalgam for posterior restorations because of a tightening of toxicological standards relating to mercury has led to a reappraisal of the methods of evaluating the clinical performance of composites in class I and II cavities. The introduction of submicron filler composites in recent years has led to materials with improved mechanical properties and to the probability that such materials will function satisfactorily in posterior restorations. The need therefore arises for methods to quantify and to characterize the wear that takes place in class I and II composite restorations. In the present paper we describe one method by which these objectives can be achieved. The method involves optical contouring and computer evaluation of contour maps. The method has been developed and refined by studying artificially induced wear in amalgam restorations and may be used for any similarly shaped object. The technique has previously been used for studying wear of amalgam specimens in laboratory wear-testing machines [7] and has also been used successfully to study the wear patterns on orthopaedic joint replacement prostheses.
93
2. Outline of the measurement
procedure
The aim of the procedure is to quantify the volume lost by a dental restoration over a period of normal use by a patient. The procedure involves three basic steps. (i) Impressions of the tooth are made before and after the test period. (ii) The impressions are contoured using the optical arrangement described in Section 3. (iii) The prewear and post-wear contour maps are compared quantitatively to find the shape, depth and/or volume of any wear scars. The salient experimental restrictions for each of these steps are as follows* (i) The precision of the impression-making material and process must be an order of magnitude greater than the depth of the wear scars under investigation. This restriction is discussed in Section 4. (ii) The contour intervals on the prewear and post-wear maps of the impressions must be identical. Also the reference plane must have the same orientation with respect to the two impressions. The first restriction is easily observed in practice; the second restriction is discussed in Section 5. (iii) The contour fringes should be resolvable over the areas of interest on both impressions. In Section 3 methods for estimating the volume loss are applied to some calibration tests on extracted teeth. Section 7 contains a general discussion about the use of the technique and its further refinement.
3. Dual-source
contouring
A schematic diagram of the dual-source contouring arrangement shown in Fig. 1, A laser beam is expanded and spatially filtered before ing through a prismatic beam splitter. The position of the beam splitter adjusted so that the two divergent beams cross over in the region of
Laser
pinhole
imx33fession
\/, J
beamsplitter
/
ca
\
/
pr era
/’
Fig. 1. The dual-source contouring arrangement.
is passis the
93
object to be contoured, usually between 50 and 100 cm from the point source. Interference fringes will be formed in the region of the cross-over and will be projected along the bisector of the angle between the beams illuminating the object, perpendicular to the plane of the paper. If the object is small compared with the distance 2 between the illuminating source and the object then the perpendicular spacing Ah between the adjacent fringes is constant and is given by
where a is the separation of the two apparent point sources and h is the laser wavelength. Ah can be varied by adjusting the beam splitter to vary a. The object is viewed at an angle 8 with respect to the plane of the fringes. The image is then recorded on a photographic film. In general it is necessary to prepare the sample in such a way that it scatters light into the camera; this is achieved by vacuum flash coating with aluminium and, in the case of very smooth surfaces, the application of an even coat of matting spray. Photographic prints of the contour patterns obtained from specimens differing in shape (due to wear) may be compared by one of the methods outlined in Section 5 to give the amount of wear that has taken place. In practice, values of Ah in the region 100 - 200 pm are used. Ah is measured in the region of the object using a travelling microscope. When the angle 8 is 90” the fringe pattern observed is a true contour map of the object. For all other values of 8 this is not strictly true. The fringe interpretation methods discussed later are not affected by this fact. The only reason for viewing the object at values of 6’ other than 90” is to allow the object to be pho~~aph~ with larger apertures at the high ma~ifi~ation required and hence to obtain good resolution.
4. Impression
fidelity
To measure accurately the in uiuo wear of restorations (placed in teeth or dentures) it is necessary to make impressions or replicas of the restorative and surrounding tooth before and after wear (e.g. over a period of from about 6 months to 2 years) and to compare contour maps of these impressions. In order to do this it is vital to ensure that the fidelity and precision of the impression process are much better than the depth of wear to be measured. Having established that this demand has been met there is no reason why in uiuo wear cannot be measured. The precision of the impression material used here was checked experimentally by making four impressions of an extracted tooth containing a restoration. The four impressions and the tooth were then contoured. Their maps were compared with one another in order to assess the degree of similarity between them.
(b) Fig. 2. (a) Contour maps of two impressions of the same tooth (Ah = 152 Pm; 0 = 46”; magnification, 4.8~); (b) superimposed line tracings of the maps shown in (a) (only the region of restoration is shown).
Figure 2 shows two of these maps (Ah = 152 pm; 0 = 46”) together with line tracings of the maps superimposed (Fig. 2(b)). The degree of similarity is very good. The contour lines do not coincide exactly for two reasons. The (arbitrary) zero fringes on each map are not coincident, so that the fringes on one map are shifted relative to those on the other map by a constant amount. Also the two impressions were mounted at slightly different values of 0, so that the mi~i~ment of the fringes increases linearly with distance measured from the zero fringe. These small differences in the position of corresponding fringes do not appear to alter their shape. Small displacements and rotations of one impression relative to another when the two contour maps are made can be taken into account when the volume loss is calculated. This is done by shifting one of the superposed maps by a small amount until the prewear and post-wear fringes of interest coincide exactly
96
on unworn parts. Where wear has occurred coincidence will not be possible and the prewear and post-wear contour lines are drawn and processed as described later. There is, of course, a limit on how big these seemingly arbitrary adjustments to the maps can be made. Empirical evidence has shown that overall displacements of the maps of less than half a fringe spacing do not affect the accuracy of the volume loss found by more than 10%. In many cases, this accuracy is acceptable. The above adjustments are not necessary when the computer is used to process the maps as small differences in ali~ment are taken into account by the software. Also, the computer stores the height information contained by the prewear and post-wear maps as a matrix, not a fringe pattern. Hence, computer processing is the most accurate method of analysing the maps. 5. Specimen
relocation
Throughout this paper it is assumed that prewear and post-wear specimens are contoured relative to the same reference plane, with the same eontour depth, and that the maps have the same magnification. During the calibration trials described in Section 6 these conditions were met by comparing the negative of the prewear contour map with the image of the postwear map as seen on the ground glass screen of the monorail camera. Adjustments were made to the position and orientation of the post-wear impression until the unworn areas on both maps displayed the same fringe pattern. This technique works well but is time consuming (30 min per map pair). For elinical trials the conditions are met more easily by using a relocation jig described below. The rig is described in terms of its use in proposed clinical trials. We consider that 50 patients are to be investigated over a period of 3 years and that the wear of the restoration under test is to be measured every 6 months. Seven different maps of each restoration need to be made. After the restoration is completed an impression of the restored tooth together with an adjacent tooth is made. A model of the adjacent tooth is made from this impression. The model is secured to a metal flag positioned as shown in Fig. 3. The flag defines the position and orientation of the contour map reference plane. The impression is then fitted onto the cast and the gimbal holding the impression in position is tightened; the flag with cast can now be removed. The flag post and stop are left in position to realign the flag for future use. The camera is now adjusted to give the best picture and is left in position for future use. Post-wear impressions are made to include the adjacent tooth. All postwear impressions are aligned in the contouring ~angement by replacing the flag and fitting the impression of the adjacent tooth onto its model. The above procedure ensures that the restorations are contoured relative to the position of the adjacent tooth. Small variations in the position of the reference teeth over the test period may occur, but it is unlikely that changes large enough to affect the measurements will take place; if they do it is still possible to realign the tooth manually.
97
Fig. 3. The repositioning
6. Interpretation
jig.
of the contour
maps
Three methods for finding the volume loss from the contour maps are now presented. They are (a) the fringe displacement method, (b) the moire method and (c) a computing method. Each of the methods is described as a worked example from some calibration tests performed on extracted human molars. In these tests, an experienced clinician (J-C.) made two realistic wear scars (with a dental burr) on the amalgam restoration placed in the teeth. The mass loss was determined gravimetrically. Prewear and post-wear impressions were taken. All the measurements were made from photographic enlargements (30 cm X 35 cm) of the maps shown. 6.1. Fringe displacement method Figure 4 shows the prewear and post-wear contour maps of a tooth which has lost 0.0261 g during the simulated wear process (found by weigh-
(4
fb)
Fig. 4. Contour maps of (aj a prewear impression and (b) a post-wear impression human molar: Ah = 179 pm; 6 = 59”. (Magnifications, 5.4x.)
of a
(a)
tb)
Fig. 5. Line tracings of Fig. 4: (a) the prewear impression;(b) The wear scars are marked A and B.
the post-wear impression.
ing). Figure 5 shows line tracings of these maps. The wear scars A and B are marked. Figure 6 shows the prewear and post-wear contour maps superimposed in the region of the wear scars only. The wear scar is visible as an area where the prewear and post-wear fringes do not coincide (the post-wear fringes are shown as broken lines). Figure 7 shows a close-up of the impressions mounted in the contouring arrangement (schematic). The prewear and post-wear impressions are shown together represented by the full lines and broken lines respectively.
Fig. 6. Superposed line tracings of wear scars. The wear sears are drawn as an array of n squares of equal area a. Fig. 7. A schematic view of the impressions mounted in the contouring arrangement: prewear; -, post-wear.
----,
99
To find the depth of wear at some point it is necessary to measure the fringe displacement Af (the distance between prewear and post-wear fringes measured along a line parallel to the direction of propagation of the contour fringes, i.e. A-B) and the fringe spacing fin the same region. Both Ah and 8 must also be known. The depth d of wear parallel to the direction of view can be found by using similar triangles. Clearly d
Af
(2)
dh’=f Therefore
dzAf--
Af
f
(3)
sin 8
To find the volume of the wear scar, of n small squares of equal area a, as value of d (di) by measuring Afi and plying the area of one square by the
the area of the scar is drawn as an array shown in Fig. 6. Each area is assigned a fi . The volume loss is found by multisum of the d values. Hence (4)
In this case Ah = 179 pm, 13= 59” and * Afi ax i=O
= 9.6 mm3
fi
Therefore V = 2.0 mm3 and the mass loss is 0.024 g, assuming a density of 12 g cmP3. This method is best applied when A f < fi. When Afi > fi the following method is better. 6.2. Loire method Figure 8 shows the prewear and post-wear contour maps of another tooth used in the calibration tests. This tooth has lost 0.0267 g (found by weighing) during the simulated wear process. The wear scars are marked C and D on the post-wear contour map (Fig. 9). When the two maps are superposed a moire pattern will be observed. This moire pattern corresponds to a contour map of the difference between the two surface topologies, i.e. a contour map of the wear scar. The visibility of the moirit fringes is strongly dependent on the intensity profile of the primary (contouring) fringes and the spacing of the primary fringes. Better results are obtained with a square fringe profile; also the spacing of the primary fringes should be less than about 0.1 of the spacing of the moirk fringes for good results. These two conditions are not met in the experiments
Fig. 8. Contour maps of (a) a prewear impression and (b) a post-wear impression of another molar: Ah = 179 pm;@ = 52”. (.~agnificat~ons, 5.4x.)
Fig. 9. Line tracings of the prewear and post-wear maps (superimposed) moiri: maps of the wear scars. (Magnification, 14~ .)
and corresponding
described here; however, it is still possible to draw a difference map from the maps shown in Fig. 8. Figure 10 shows line tracings of the prewear and post-wear maps (superimposed) in the region of the wear scars. The difference contour maps of the wear scars are shown adjacent to the superimposed line tracings, for clarity. The moire maps show loci of constant height difference. The height difference between contours is Allh/sin 8. The superscript difference contour is found by joining those points where the post-wear fringes have crossed m prewear fringes (m = 0, 1, 2, . . . ).
101
Fig. 10. Computer-drawn fication, 28X .)
difference
maps of the wear scars A and B: Ah = 70 pm. (Magni-
The volume of wear between two adjacent difference contours (m = 0 and m = 1, say) can be found (to a good approximation) by measuring the areas A0 and Al enclosed by the contours and multiplying the average of these areas by Ah/sin 19.The total volume of the wear scar is found by summing the volumes between each pair of contours. If the scar is not an integral number of difference contours then it is possible to estimate the volume under the last contour using method (a). However, a rough approximation will often suffice. In the example shown in Figs. 9 and 10, Ah = 169 pm and 8 = 39”. The total volume loss was found to be 2.25 mm3. If we assume the density of amalgam to be 12 g cme3 the mass loss is 0.027 g. This value for the mass loss compares very well with the value found by weighing. However, the accuracy of the moire method depends to a large extent on the geometry of the wear scar. This is because assumptions made about the shape of the wear scar between moire contours may not be valid. 6.3. Computer-aided analysis A computer technique has been developed which will process the prewear and post-wear maps to give the volume lost by the tooth (to an accuracy of 4%) and will plot out the distribution of wear in the form of a “difference” contour map [ 81 . The contours of the difference map are loci of constant change of depth of the surface of the tooth from an arbitrary reference plane which is orthogonal to the direction of view in the prewear map of the tooth. The difference map is equivalent to a moire pattern generated by superposition of prewear and post-wear contour maps but with significant advantages. (i) Moire patterns require the prewear and post-wear primary contour intervals to be equal. The computer technique can accommodate any combination of contour intervals.
102
(ii) MO% patterns require prewear and post-wear maps to be taken from the same viewing angle, The computer technique can correct for small changes in the viewing angle. (iii) Moire patterns cannot generate a difference contour of less than one primary contour interval and then can only generate contours at integer multiples of the primary contour interval. The computer technique can generate difference contours to one-tenth of the larger primary contour interval and can plot any contour value above this value. (iv) The computer technique is unique in yielding an accurate measure of the change in volume for any surface. The technique invofves first recording the contour lines and three reference points on the surface of the tooth from the prewear and post-wear maps. This recording is performed by placing greatly enlarged photographs of the maps on a digitizing table and following the contour lines with the handset. The recorded contour maps are scaled and related to make them coincident using the equations X=Ax+By+Cz+D Y=Ex+Fy+Gz+H
Z=Gx+Hy+Iz+J where A, B, C, D, E, F, G, H, I and J are constants. The equations transform any Cartesian coordinate system (x, y, z) to any other Cartesian coordinate system (X, Y, 2). The positions of the reference points in the prewear and post-wear maps are used to determine the transform constants A, B, C, D, E, F, G, H, I and J. The transformed coincident prewear and post-wear contour maps are recorded on respective two-dimensional matrices by giving to the nearest matrix elements along each contour the value of the height of that contour, the matrix being of such dimensions to cover the surface of the tooth. The surface between the contours is determined by algorithms which scan the matrix vertically, horizontally and along the two diagonals. The accuracy and generality of the algorithms give the technique its accuracy. The complete prewear and post-wear surfaces of the tooth are now recorded as matrices of point heights, the heights being orthogonal and measured from the same reference plane fixed in orientation and position from the tooth. The subtraction of one matrix from the other yields a difference matrix. This is a matrix of changes in height between the prewear and post-wear surfaces, the changes in height being parallel to the direction of view in the prewear map. The change in volume is simply V=A
n=N x
n=l
h,
(6)
103
where A is the area associated with a single element of the difference matrix projected in a direction orthogonal to the reference plane and h, is the nth element of the difference matrix which has N elements. N is typically 10s. The difference contour map is generated by scanning the difference matrix for the elements between which the difference contours pass and by linear interpolation we deduce the path of such contours. The contour maps shown in Section 6.1 were processed using this technique. The volume difference determined was 2.161 mm3 and the difference maps of contour interval 70 pm are shown in Fig, 10. The computer result was within 2% of the gravimetric result.
7. Discussion The most accurate method of determin~g volume loss is the computer method. The only drawback in using this method is the length of time needed to digitize the contour maps. At present two methods of overcoming this difficulty are under conside~tion. These are as follows. 7.1. Automation of the digitizingprocess
It is planned to automate the digitizing process by replacing the photographic camera with a photodiode array and a television monitor. The photodiode array will replace the photographic enlargement and hand digitizing process. The television monitor will be used to check the array outputs visually. This check will enable minor adjustments to the set-up to be made easily. The photodiode array will have about 400’ elements. A lens will be used to image the maps onto the array. It is estimated that this set-up will be sufficient to resolve fringe centres to within Ah/lo. 7.2, Direct display of the difference maps using a moire’ technique
It is possible to produce a moire map of the wear scars directly by superimposing prewear and post-wear contour maps of a tooth. This can be done using photographic negatives of the maps. Alternatively the negative of the post-wear map can be placed over the image of the prewear map on the ground glass screen of the camera. These methods were tried during the calibration tests described in Section 5. In both cases moire fringes were discernible but not usable. There are two reasons for this. To obtain good moire fringes, the primary (contou~ng) fringe spacing f should be less than one-tenth of the moire fringe spacing. Also, the intensity profile primary fringes should be a square wave for the best results. Other workers have reported similar methods [9, lo] with good results. It is proposed to repeat the calibration tests using a smaller contour depth (about 50 ,um) and a square wave fringe profile to try to improve the technique. If good moire difference maps can be obtained then simpler software will be used to find the volume loss from the digitized moire maps.
There are two drawbacks to using this type of moire method. (a) It is not possible to find the sign of the surface height change. (b) Changes of less than Ah/sin 8 in the surface height are not easily measured.
Acknowledgment The authors are pleased to acknowledge Research Council for the work reported.
the support
of the Science
References 1 D. F. Williams and J. Cunningham, Materials and Clinical Dentistry, Oxford University Press, Oxford, 1979. 2 F. Lutz and M. Kull, Helv. Odontol. Acta, 24 (1980) 455. 3 R. W. Phillips, D. R. Avery and R. Mehra, J. Prosthet. Dent., 30 (1973) 891. 4 R. P. Kussy and K. F. Leinfelder, J. Dent. Res., 56 (1977) 544. 5 L. Ehruford, T. Derand, L. Larsson and A. Suensson, J. Dent. Res., 59 (1980) 216. 6 J. M. Powers and P. L. Fan, J. Dent. Res., 59 (1980) 815. 7 J. T. Atkinson, M. J. Lalor, J. F. Jaworzyn and J. B. Cantwell, Comparative wear studies of dental amalgams in using two novel techniques, laser facing contouring and surfometry, 1 I th Int. Biomaterials Symp., Clemson, SC, 1979. 8 D. Groves, M. J. Lalor, J. T. Atkinson and N. Cohen, J. Phys. E, 13 (1980) 741. 9 J. Shamir, Opt. Laser Technol., (April 1973) 78. 10 J. N. Butters, R. Jones, S. McKechnie and C. Wyker, in H. G. Gerrard (ed.), Proc. Laser Int. 80 U.K. Conf, IPC, Guildford, 1980, p. 139.