H OLOGRAPUY is a method used mainly in technical

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1 J Neurosurg 58: , 1983 A study of human head vibrations using time-averaged holography HEINz-E. HOYER, D.S.c., AND Ji3nCEN D/)RHEIDE, ENC. Division of Functional and Applied Anatomy, Medical School of Hannover, Hannover, West Germany ~/ Intact human cadaver heads were subjected to vibrations. The resonant frequencies over a range of 500 to 3000 Hz were determined. Vibration patterns at three frequencies were presented by means of timeaveraged holography. The displacements were quantified and the highest amplitudes were found in the temporal region. Antinode centers were found superimposed on the squamatic suture. This method of holographic interferometry allows sensitive deformation measurements to be taken on intact human heads or skulls. KEY WORDS 9 time-averaged holography resonant frequencies 9 skull vibration patterns ~ skull deformation 9 interferometry H OLOGRAPUY is a method used mainly in technical fields; however, in recent years it has also been used in such medical specialties as orthopedics 7 and otology. 1. Another field of holographic application is the study of deformation of the human skull caused by external forces? One kind of external force is the conduction of vibrations into the skull, generating rapid displacements there. Considering the skull is a continuous vibratory system, it has a great number of resonant frequencies, although only a few of these frequencies are relevant. At each resonant frequency a special vibration pattern is generated. The aim of the most recent experiments was to determine the resonant frequencies, the vibratory amplitudes, and the vibration patterns pertaining to them. The dry skull has been the subject of several investigations of vibration patterns or deformation, either by conventional methods 2,4 or by means of holography?,8 However, such investigations may lead to a misinterpretation of the results, because cartilage and fibrous tissues are not present in dry skulls. Thus, in some cases vibrations may be different from those in vivo or in a non-macerated skull. Fresh or preserved human heads have not yet been investigated. In order to measure deformation in an intact human head by means of holographic interferometry, there should be no movement of the head. If it is possible to eliminate movement or rotation of the object, holographic interferometry is a technique superior to conventional methods, because it requires no contact with the object. It is known that the deformation of objects like human skulls or heads is often complicated, and contactive measurements do not always give accurate information. Holographic interferometry enables us to measure deformation with a high sensitivity, which depends on the wavelength of the laser. However, the fact that only one component of the deformation vector is presented may be disadvantageous. Holographic studies have already been performed on macerated human skulls; 3 however, in this study, two preserved human heads were investigated to determine the vibration patterns at the four lowest resonant frequencies. It was our aim in the present study to show the applicability of holographic interferometry to analysis of deformations in the intact human head. Materials and Methods To evaluate vibration patterns of the human head, time-averaged holograms were recorded as follows. Two preserved cadaver heads, with the skin partially removed (on the left side) and the mandible totally removed, were fixed on a metal block at the condylus occipitalis and supported by adhesive. Vibration patterns, caused by a conduction vibrator fixed at the occipital bone, were investigated over a frequency range of 500 to 3000 Hz. Resonant frequencies could be identified by maximum amplitudes. In order to make a quantitative estimate of vibration deformations, amplitudes of resonant frequencies were chosen so that the number of interference lines could be J. Neurosurg. / Volume 58 / May,

2 H. E. Hoyer and J. D6rheide defined. The time of exposure, which depends on laser power, was 0.5 seconds. The output of the argon-ion laser was 1 watt, with a wavelength of nm. A diagram of the mechanical and holographic set-up is shown in Fig. 1. During the reconstruction and on the photograph of the holographic interferogram, light and dark lines are visible. The light regions of the interference patterns are nodes; these are regions where deformations are absent. The increasing number and density of the dark lines represent the areas of increasing displacement, whereas the dark lines depict the constant am- plitudes. The displacement at any point on the object is always perpendicular to the focal plane. The quantitative evaluation of the photographed holograms is derived from the distribution of intensity, in which the dark lines are related to the zeros of Bessel's function I~. Hence the displacement a(x) at a particular point is defined as a(x) = ~ N~ in which N~ are the arguments of the zero i of the quadratic Bessel function of the order zero, and ~ is the wavelength of the laser. Resonant Frequencies Results The resonant frequencies of the two heads investigated are listed in Table I. There is a difference between the first and second resonant frequencies in the two heads, whereas the third resonant frequencies are almost identical. Some measurements of the resonant frequencies were made with skin and muscles intact. Here only bands of the highest amplitudes could be recognized. The vibratory amplitudes of the quasi-resonant frequencies vary. Apparently, the mea- TABLE 1 Resonantfrequencies~twohumanhea~* FIG. 1. Diagram of holographic equipment. 1: laser; 2: beam splitter; 3: reference beam; 4: object beam; 5: hologram plate; 6: vibration transducer; 7: conduction vibrator; 8: amplifier; 9: function generator; 10: oscilloscope; 11: frequency counter. Head No. fi(hz) ~(Hz) ~(Hz) I II * The heads were preserved, the scalp removed at one side, and the mandible totally removed, f = frequency measured. FIG. 2. Holographic vibration patterns of a skull with an intact scalp. Left: Vibration pattern at a frequency of 1402 Hz. The deformation lines are very irregular and a great number of maximum vibrations spread out over the scalp. Center: Vibration pattern at a frequency of 1940 Hz. At this frequeficy, maximum vibrations are localized in the temporal region. A distinct deformation is represented by a dark line, which is superimposed on the region where the temporal muscle originates. Right: Vibration pattern at a frequency of 2788 Hz. The deformations are reduced to a region sited above and behind the external ear. 730 J. Neurosurg. / Volume 58/May, 1983

3 Holography in study of human head vibrations surements of resonant frequencies on the heads with scalps intact were dependent on the place where the oscillation gauge touched the skin. Vibration Patterns The vibration patterns of the heads with a scalp are shown in Fig. 2. The patterns, visible at the skin surface, are complicated. A great number of circumscribed nodes or antinodes seem to be typical of skin vibrations at a low frequency (1402 Hz, Fig. 2 left). At the second resonant frequency range (1940 Hz, Fig. 2 center), nodes are concentrated in the temporal region, while a dark interference line is superimposed on the two temporal lines of the osseous skull. At the third resonant frequency range (2788 Hz, Fig. 2 right), vibratory amplitudes were observed above or behind the external ear. The vibration patterns of the heads with the scalp removed are less complicated. The results are shown in Figs. 3 to 7. The distribution of the displacements seen on the left side of the skull showed the highest vibratory amplitudes in the temporal region, whereas only few interference lines were observed at the vault. The lines of all three frequencies run in a constant manner; both anterior and posterior portions of the skull are displaced. The lines are not complete, as no vibrations are recorded in the subtemporal regions. FIG. 4. Quantitative evaluation of the vibration pattern of a skull at the second resonant frequency (2435 Hz). The antinode center is now superimposed on the suture line. a(x) = amplitude of deformation; x --- site of deformation. FIG. 3. Quantitative evaluation of the vibration pattern of a skull, with the scalp removed, at the first resonant frequency (2078 Hz). The antinode center can be seen on the temporal bone below the squamatic suture, a(x) -- amplitude of deformation; x -- site of deformation. FIG. 5. Quantitative evaluation of the vibration pattern of a skull at the third resonant frequency (2862 Hz). The antinode center is found on the anterior squamatic suture. The amplitudes of deformation are the lowest of all three resonant frequencies, a(x) = amplitude of deformation; x = site of deformation. J. Neurosurg. / Volume 58 / May,

4 H. E. Hoyer and J. D6rheide Differences between the three resonant frequencies measured are evident, indicating different displacement patterns. In all measurements, the antinode center of the first resonant frequency appears below the squamatic suture in the posterior region of the temporal bone. The amplitude centers of the second and the third resonant frequencies are located on the squamatic suture, showing that the centers have shifted in an anterior direction along the squamatic suture. Figures 3 to 5 show the interference patterns at the three resonant frequencies and their quantitative evaluation. The displacement reaches a maximum value of 1.13/~m, which is mainly found in the temporal region. The vibration patterns of some resonant fre- FIG. 6. Magnified detail of Fig. 5. Notice that some of the deformation lines shift as they cross the squamatic suture. FIG. 7. Vibration pattern of a skull at a resonant frequency of 2815 Hz. Notice the two antinodes in the frontal and in the parietal/occipital region. quencies are characterized by two antinodes (see Fig. 7), in which one antinode appears in the region of the frontal, sphenoid, and parietal bones while the other is found in the area of the temporal, parietal, and occipital bones. Figures 6 and 7 show the vibration patterns of the second and third resonant frequencies, in which a discontinuity is seen at the squamatic suture. The other sutures show no such discontinuities. Discussion A comparison of the results of an earlier study 3 with those of the present study reveals that the vibration in a macerated skull is not the same as in a preserved head. Even a skull in which the sutures were filled with paraffin, as in some pilot tests to this study, differs in its vibratory behavior. There are less resonant frequencies in the non-macerated skull; only three resonant frequencies over a range of 500 to 3000 Hz were measured. Kragt, et al.) are of the opinion that forces and displacements in a macerated skull are roughly the same as in a "living skull." However, the results of a recent investigation with an intact preserved head indicate that this type of head shows a different vibration pattern. At some sutures discontinuities are visible, which are thought to be absent in a living skull. Therefore, we agree with Ogura, et al., G who recommended that for holographic investigation a "specimen as fresh as possible" should be used. Obviously, the condition of the sutures in the skull, especially the condition of the squamatic suture, is important for measuring the vibration or displacements of the skull. Kragt, et al.) reported different reactions in various bones, which indicated separate movements of several parts of the dry human skull, as a result of the resonant frequency used. It might be possible that in a preserved head a minimal shearing of bones relative to each other occurs at vibratory stresses at certain frequencies. However, there is no doubt that an intact skull should be regarded as a continuity. Furthermore, the vibratory amplitudes of an intact head are lower than the amplitudes of a dry human skull. Obviously, the remaining tissue on one side and the skin on the other side both have a damping effect. It is not only the amplitudes upon which the skin has an attenuating effect. The vibration patterns of the scalp are not always similar to patterns on the skull bone itself. However, at some frequencies only the vibration patterns on the scalp may indicate displacements on the skull. A previous study concerning strain measurement of the skull by holographic interferometry 8 describes displacements on a macerated skull which resemble the vibration patterns at the resonant frequencies found here. Our study demonstrates that in intact human heads the highest vibratory amplitudes occur in the temporal region, with a shift of vibratory centers in an anterior direction. The maximum amplitude appears to be related to the temporal bone, which may act as a vibratory membrane. Con- 732 J. Neurosurg. / Volume 58/May, 1983

5 Holography in study of human head vibrations sidering that the temporal region is not as thick as the other bones in the skull and that the temporal regions are surrounded by "reinforcement columns" or by a frame-like structure, it is suggested that maximum vibration is possible only at this site. According to Ogura, et al, 6 the vibration patterns in this region could be related to the inertia bone conduction which might be important in the hearing mechanism. Holographic interferometry may provide a good tool for basic investigation into skull deformation. Further studies on the base of the skull by means of vibratory analyses or impact studies using intact heads may elucidate skull fracture mechanisms. Acknowledgment The authors are indebted to Sheila Fryk for her correction and typing of the English text. References 1. Bally G von: Holography in otology, in Bally G von (ed): Holography in Medicine and Biology. Berlin/Heidelberg/New York: Springer-Verlag, 1979, pp Christmann C, Holzweissig F: Eigenfrequenzund Knotenlinien an Sch~ideln. Anat Anz 142: , D6rheide J, Hoyer HE: Holografische Schwingungsuntersuchungen am menschlichen Schhdels. Unfallheilkunde 84: , Hoyer HE, Zech M: Eigenfrequenzen und Schwingungsformen des menschlichen Sch~idels. Unfaliheiikunde 83: , Kragt G, Ten Bosch JJ, Borsboom PCF: Measurement of bone displacement in a macerated human skull induced by orthodontic forces; a holographic study. J Biomech 12: , Ogura J, Masuda Y, Miki M, et al: Vibration analysis of the human skull and auditory ossicles by holographic interferometry, in BaUy G von (ed): Holography in Medicine and Biology. Berlin/Heidelberg/New York: Springer-Verlag, 1979, pp Piwernetz K, Bally G von: Holography in orthopedics, in Bally G von (ed): Holography in Medicine and Biology. Berlin/Heidelberg/New York: Springer-Verlag, 1979, pp Spetzler RF, Spetzler H: Holographic interferometry applied to the study of the human skull. J Neurosurg 52: , 1980 Manuscript received September 9, This study was supported by Deutsche Forschungsgemeinschaft Grant Ho 859/1-1. Address reprint requests to: Heinz-E. Hoyer, D.Sc., Zentrum Anatomic, Abteilung 4120, Medizinische Hochschule Hannover, Postfach , D-3000 Hannover 61, Federal Republic of Germany. J. Neurosurg. / Volume 58 / May,