Computer aided measurement of biomechanical characteristics of cadaverous lumbar spines

Transcription

1 CEJP 2(3) Computer aided measurement of biomechanical characteristics of cadaverous lumbar spines Luděk Bartoněk 1,JiříKeprt 2,Jiří Charamza 3, Lumír Hrabálek 4 1 Department of Experimental Physics, Faculty of Natural Sciences, Palacký University, 17 Listopadu 50, Olomouc, Czech Republic 2 Joint Laboratory of Optics of Palacký University, Institute of Physics of the Academy of Sciences of the Czech Republic, 17 Listopadu 50, Olomouc, Czech Republic 3 Department of Anatomy Medical Faculty, Palacký University, 3 Hněvotínská, Olomouc, Czech Republic 4 Department of Neurosurgery, University Hospital, 6 I.P. Pavlova, Olomouc, Czech Republic Received 24 March 2004; accepted 11 May 2004 Abstract: Special computer-aided equipment was designed for measurement of biomechanical characteristics of lower part of the spine (L1-L5). When the stress is applied, it is necessary to observe the shift of the sample elements, together with measurement of the spine rigidity. This shift is determined with the help of circular targets fitted to the appropriate vertebra. The targets, illuminated by lamp or laser light, are monitored and their digitalized images are scanned by CCD camera is stored as computer media. The two dimensional Fourier transform of the digital optical signal is obtained by the fast Fourier transform algorithm. The period and direction of the interference fringes determine the size and the direction of the sample shift. c Central European Science Journals. All rights reserved. Keywords: lumbar spine, force gauges, speckle interferometry, fast Fourier transform PACS (2000): y barton@risc.upol.cz keprt@prfoptnw.upol.cz charamza@tunw.upol.cz hrabalek@tunw.upol.cz

2 L. Bartoněk et al. / Central European Journal of Physics 2(3) Introduction The goal of this work consists of a design for non-contact measurements for evaluation of the degree of stability of various surgical fixation methods. A biomechanical analysis of the human lumbar spine, as published in [1] [5], is employed. Measurements were carried out on cadaverous samples of the lumbar spine using precisely defined mechanical loads. In the experiments the fixation methods of screws (translaminal fixation TL), cages (interbody fusion ALIF), and screws and cages (TL and ALIF) were used. 2 Experimental methods of measurement Measurements were accomplished with several cadaveric specimens loaded in turn with axial compression, axial tension, sagittal flexion, extension, left and right bending, and their combinations. 1. A rigidity of axial compression is defined as the ratio of axial force (load) F and axial change of the length l of the specimen S c = F l ;[S c]= N mm. (1) 2. A rigidity of axial torsion can be expressed as the ratio of axial torque moment and the angle of rotation ϕ S t = Fr ϕ ;[S t]= Nm rad or in simplified form S t = Fr d ;[S t]= Nm (2) mm where ϕ is replaced with the shift d of the constant arm r. The shift d of the end if the arm r during axial torsion is proportional to the angle of rotation ϕ (d = k 1 ϕ). 3. A rigidity of the sagittal flexion and extension and lateral bending tests are both evaluated as the ratio of bending moment and the angle of flexion (extension, bending) S f = Fl α ;[S f]= Nm rad or in simplified form S f = Fl d ;[S f]= Nm (3) mm where also the angle α is replaced with the shift d of the arm l. Similarly as in the last case d = k 2 α and because of comparison of the measurement with the impact sample we can consider the simplified formula (3). All of our measurements will be comparative. That means our measurements after stabilization of the sample will be compared (in ratio) with the intact sample and the results will be given in normalized form (dimensionless)[2].

3 506 L. Bartoněk et al. / Central European Journal of Physics 2(3) Then it is possible to express the total stiffness accumulating all loads in a standard form. The measurement of the quantity F is carried out by force gauges Sensocar BS.1 of types 1000 N, 400 N, and 200 N with sensitivities 2mV/V. The output DC signal is digitized by an ADC1216D A/D converter, then calibrated and saved in a computer s memory or hard disk as a file. The contraction of the sample l was realized manually with the help of setscrews. Various observed vertebrae were provided with fixed circular targets (Fig. 3). The examination of movement of individual parts of the spine (via circular targets) has been maintained in two ways. Speckle interferometry (see [6]) was used for small deformations, whereas larger shifts of the vertebrae were determined by changes in the position of the targets centers. The changes in position of a point in a picture can be expressed either in Cartesian coordinates or, by the help of a Fourier transform, their meaning in a frequency domain of the picture. In the frequency domain a change in position of the point is represented by a system of parallel lines with a period p or equivalently by a spatial frequency f = 1 where the frequency f represents the p number of lines per unit of length (mm). While the small position changes of the points are difficult to measure, the period p of the line structure can be determined easily. We may write p = c r, (4) where the constant c can be determined experimentally (from known quantities p and r). The period of a line structure (fringes) gives the size of the shift and the direction of the fringes identifies the direction of the shift. This direction is normal to the lines. When a target is illuminated by laser light, the speckle effect occurs, see [6]. With respect to the interference of beams scattered by the surface roughness, the target seems to be covered by speckles. Taking into account two systems of points away at the same distance by target shifting, we can determine, using the frequency period, the distance of the corresponding speckle couples. A two dimensional Fourier transform therefore allows to calculate the target shift. The fast Fourier transform (FFT) algorithm was adopted as a routine. The discrete Fourier transform can be written in the form F (u, v) = 1 NM N 1 x=0 M 1 y=0 ux f (x, y) e j2π( N + vy M ), (5) where N M can be recognized as the resolution of the original image f(x, y). The FFT algorithm was implemented at the computer with the Visual C++ programming environment. From Fig. 1. we can see the dependence of the distance p of two neighbour fringes in the Fourier spectrum on the distance r of the number of pixels in the image file, see [8]. The values p and r are expressed in numbers of pixels. In the relation (4) the value c is a real constant which can be determined experimentally. In this case it was equal to 512. Hence, an empiric relation for the dependence of the distance between points, r and the distance of adjacent fringes, p in the Fourier spectrum is p = 512 r. (6)

4 L. Bartoněk et al. / Central European Journal of Physics 2(3) Fig. 1 The example of the interferograms and size periods (p x and p y shift in x and y axis, r equivalent period). We employed a CCD camera mounted as a chip of size 7.95 mm x 5.96 mm with 795 and 596 pixels and equipped with a lens of focal length 50 mm. The shift of one pixel is 0.2 mm. This method was used for measurements of deformation of various vertebrae under axial compression and torsion. For larger shifts in position of the vertebrae (l or d 1 mm), it is necessary to use a lens with a 12 mm focal length, in which case the constant c in the expression (4) is modified to a value of 128. The shift of one pixel is then 0.8 mm. We can conclude that evaluation of the shifts of the vertebrae from the movement of the positions of the circle targets is highly advantageous (Fig. 2). Fig. 2 Evaluation of target in coordinate X. The sample, illuminated together with the circle targets by lamp light, is scanned by the CCD camera. An image in the form of an optical signal is then send via an analogdigital unit into a computer memory. With the help of a computer program, comparing the common spots of the targets before and after shifting, we can find the new coordinates of the target centers. If we know the shift of the center we can calculate again the Fourier transform but now with another constant c. In such a way the distance between interference fringes gives visual information about the displacement of the targets, similarly to

5 508 L. Bartoněk et al. / Central European Journal of Physics 2(3) the case of speckle interferometry. 3 Measurement technique of biomechanical characteristics of spines The measurement of biomechanical characteristics of the lumbar part of the spine was carried out on special equipment designed exclusively for this purpose (Fig. 3). Fig. 3 A sample of cadaveric lumbar spine prepared for experiment and the mechanical device for measurement of biomechanical characteristics. The measurement of the parameters of the sample, while being strained under pressure in the spine axis, is carried out with a massive screw (of the pitch 2 mm) through force gauges (0 <F 1000) N. When the screw is turned a defined amount (in our case an addition to the axial length of the screw l =0.4 mm) a change in the axial strength F occurs on the spinal sample. This is expressed as a change in the tension U as measured by the force gauges in mv. The force gauges were tested and calibrated before each experiment so that changes in the tension U can be categorized as additional force F. A measurement of the rotation moment, when an axial torsion is applied, is made by the free movement of the axis of rotation around the axis of the spinal specimen. It was realized by a massive screw which affects on the shoulder at a constant distance of 80 mm through the force gauge of extent 0 <F 200 N. The study of mechanical characteristics of a spinal sample, which correspond to sagittal flexion, extension, and movement to the left or right is made by bending the upper part of the sample (of the fixed upper aluminium cylinder) at a distance d = 100 mm from the sagittal axis of rotation through the force gauge of extent 0 <F 400 N. The change of the force F and the bending moment M corresponds again in the force gauge to the change of the tension U in mv. During straining and measurement of the rigidity of the sample as a whole, it is also necessary to keep an eye on the movement of the individual parts of the sample, i.e. the parts L2, L3 and L4. Their behaviour is of interest especially from the point of view of the application of various types of destabilizing and fixation methods. This movement is monitored with the help of the circle targets fixed to the appropriate vertebra to be observed, as was described above. When various destabilizing and fixation methods are introduced, this method provides information about how the

6 L. Bartoněk et al. / Central European Journal of Physics 2(3) size of the deformations of the individual elements of the sample depends on the size of the fixation, (see Fig. 4). Fig. 4 A comparison of the shift of intact vertebrae before and after the best application of fixation methods (screws and cages) with the same load on the sample. 4 Results The results obtained from three samples are clearly seen in graphs (Fig. 5) for each of the tested characteristics. Results depicted graphically are related to an intact spinal sample (1.00 means 100 percent) and are therefore normative. Due to of the statistically low number of samples, we did not carry out a statistical analysis. Fig. 5 Graphical evaluation of the rigidity for three samples of cadaveric lumbar spines.

7 510 L. Bartoněk et al. / Central European Journal of Physics 2(3) Discussion All of the devices mentioned in the papers [1] [5] have measured the deformations and shifts by means of contact methods. Our aim was based on the idea of the application of contactless modern optical methods for measurement of the displacements of vertebrae during loading of the studied speciments. Employing the combination of the optical method and the discrete two-dimensional Fourier transform seems to be suitable for evaluation of biomechanical characteristics of lumbar spine samples. This makes possible the use of an inexpensive scanning camera. We hope the measured results can help the specialists in neuro-surgery to determine the method of a lumbar fixation that maximizes the rigidity of the fixation and promotes development of body fusion. Acknowledgment This research was supported by the Ministry of Education of the Czech Republic under the project LN00A015. References [1] D.S. Brodke, J.C. Dick, D.N. Kunz et al.: Posterior Lumbar Interbody Fusion, Špine, Vol. 22, (1997), pp [2] P.A. Glazer, O. Colliou, S.M. Klish et al.: Biomechanical Analysis of Multilever Fixation Methods in the Lumbar Spine, Špine, Vol. 22, (1997), pp [3] G.O. Saidi, N. Kimio, M.P. Manohar et al.: Transforaminal Posterior Decompressions of the Lumbar Spine, Špine, Vol. 22, (1997), pp [4] M. Deduchi, B.C. Chang, K. Sato et al.: Biomechanical Evaluation of Translaminar Facet Joint Fixation, Špine, Vol. 23, (1998), pp [5] Y. Shono, K. Kaneda, K. Abumi et al.: Stability of Posterior Spinal Instrumentation and Its Effects on Adjacent Motion Segments in the Lumbosacral Spine, Špine, Vol. 23, (1998), pp [6] K.A. Stenson: A Review of Speckle Photography and Interferometry, Opt. Rng., Vol. 14, (1975), pp [7] J. Keprt, L. Bartoněk: Measurement of Small Deformations by Laser Speckle Interferometry, Acta UP Fac. Rer. Nat., Vol. 38, (1999), pp [8] L. Bartoněk, J. Keprt: Computerized Evaluation Optical Measuring Thin Films by the Help of Michelson Interferometer, Materials Engineering, Vol. 9, (2002), pp [9] L. Jaroslavskij, I. Bajla: Metódy a systémy čislicového spracovania obrazov, Ǎlfa, Bratislava, (in Slovak) [10] B. Zaratian: Visual C++ 6.0, Computer Press, Praha, 1999.