Method for measuring vertebral kinematics from videofluoroscopy

Clinical Biomechanics

1991; 6: 73-78

Method for measuring vertebral kinematics from videofluoroscopy J Cholewicki MSc S M McGill PhD R P Wells PhD H Vernon DC’ Occupational Biomechanics Laboratory, Department of Kinesiology, University of Waterloo, Ontario and ’ Canadian Memorial Chiropractic College, Toronto, Ontario, Canada

Summary Optical distortions and digitizing errors must be minimized to obtain accurate measurements of spine kinematics from videofluoroscopic imaging. This study adapted and evaluated a method for reducing these errors. Image and signal processing techniques were applied to obtain lumbar spine kinematic measures from walking and trunk extension trials. Mean absolute error was conservatively estimated to be 0.69” (SD = 0.43”) for vertebral rotation, independent of angle, and 0.33 mm (SD = 0.25 mm) for linear measurements. Digital filtering was applied to further minimize random errors.

Relevance Understanding lumbar spine biomechanics together with clinical assessment of spine movement pathology requires the accurate measurement of spinal kinematics. This paper describes a relatively inexpensive method of reducing measurement errors in digital processing of videofluoroscopic images. Key words:

Lumbar kinematics,

spine, videofluoroscopy,

measurement

Introduction Direct measurement of spinal kinematics with non-invasive techniques is not possible due to the inaccessibility of the spine in the human body and the relatively small range of motion of individual vertebral units. Radiographic techniques remain the most widely used method for obtaining vertebral displacement data used in the study of spine biomechanics and in the evaluation of spinal deformities and mechanical disorders. However, subjects are exposed to relatively large dosages of radiation when obtaining conventional X-ray pictures, which limits this technique to mostly clinical use and prevents it from becoming a routine, Received: 17 April 1990 Accepted: 17 October 1990 Correspondence and reprint requests to: J Cholewicki, Occupational Biomechanics Laboratory, Department of Kinesiology, University of Waterloo, Waterloo, Ontario, Canada N2L 3Gl @ 1991 Butterworth-Heinemann 0268~0033/91/020073-06

Ltd

error

in-viva tool in the area of spine research. Further limitations include the collection of only static images and the very limited number of exposures that can be obtained from one subject. On the other hand, X-ray videofluoroscopy, incorporating an image intensifier and a video camera, has the potential to meet better the requirements of both researchers and clinicians. Dynamic images of spine motion are produced with significantly reduced radiation exposure. Despite these advantages, little work has been done using videofluoroscopy in biomechanics. Clementz and Magnusson’ estimated tibia1 torsion in human necropsy specimens, while Breen et al2 presented plane rotational movement of lumbar vertebrae for one subject. However, as a tool for obtaining accurate kinematic measurements, videofluoroscopy is not without problems as it suffers from optical distortions and errors associated with the digitizing process. Image distortions from videofluoroscopy originate from various sources. Wallace and Johnson3 pointed out that, in addition to perspective distortions (as in all

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Clin. Biomech. 1991; 6: No 2

radiological or photographic images), the curved image intensifier produces ‘pin-cushion’ distortions. Further, the video system may add barrel or trapezoidal or non-linear distortions or a combination of these errors. Although a mathematical method for correcting the radial distortions in X-ray instruments was described by of several types of Hallert4v5, the superimposition non-uniform distortions, as is the case in makes a choice of a suitable videofluoroscopy, analytical model difficult. The correction method devised by Wallace and Johnson3 circumvents this problem. They used a calibration grid composed of wire markers forming 2-cm squares. The grid was placed between the subject and image intensifier and its corners were digitized. Linear correction of object co-ordinates was then performed within each grid box. This method is simple to implement on a microcomputer and provides correction for all of the above-mentioned types of distortions. The second source of error stems from the digitizing process itself, where the quality of image and the ability of the observer to obtain repeatable measurements is critical. The pioneering work of Breen et a12*6*7 used a calibration model comprising two human lumbar vertebrae linked with a universal joint and equipped with a protractor to investigate this problem. After digitization at different protractor settings, they estimated mean absolute errors in measuring the coronal plane angular motion between vertebrae to be, 0.56” (SD = 0.37”) and in the lateral plane to be 0.84” (SD = 0.87”). These error estimates were obtained from static positions of the calibration model in front of the image intensifier and did not include errors due to optical distortions. However, real-life dynamic images of spine motion would appear in different places on the monitor screen producing non-uniform distortions, which subsequently must be addressed. Although a correction for aspect ratio was employed in the above study, errors due to other, non-linear distortions must be minimized if accurate measures of spine kinematics are sought. The aim of the present study was to develop and evaluate a method for obtaining accurate kinematic measures from videofluoroscopy using image and signal processing techniques to minimize both distortion and digitization errors.

Methods Znstrumentation The

manufactured by Apotex videofluoroscope, Imaging Inc. (Markham, Ontario), equipped with a 9-inch diameter image intensifier was used to record radiographic images of the lumbar vertebrae onto SVHS video tape. The radiation exposure rated for this unit was 4 mA per second at an intensity of 110 kVp (a routine static lumbar radiograph generally produces an exposure of 50 to 100 mA s). Therefore, approximately 12 s of exposure from the videofluoroscope is

b Figure 1. a: videofluoroscopic image of the calibration

grid (1 x 1 cm) where a number of superimposed optical distortions is visible. b: A photograph of a digitized, sagittal view dynamic image of the lumbar spine.

equivalent to the radiation dose experienced during a conventional X-ray picture. The SVHS records were then digitized using a standard TV monitor with a resolution of 512 x 480 pixels (‘Peak performance’ video digitizing system). Two sampling frequencies were used (60 and 30 Hz) to enable a residual analysis to estimate signal to noise ratio. Digitized data was stored for further analysis on an IBM-compatible microcomputer interfaced with the above video system.

Correction of optical distortions

Our method was modified from Wallace and Johnson3

Cholewicki et al.: Measuring

to correct the digitized co-ordinates for distortion errors. A smaller, l-cm copper wire grid (Figure la) was placed in the plane of subject movement after the data collection session was completed, rather than between the subject and an image intensifier as was the case in the Wallace and Johnson study. The point different character of X-rays produces source magnification errors at different distances from their source. For this reason, it was important that the calibration grid and the studied object were placed at the same distance from the X-ray source. The geometrical relation used for linear correction within the grid box was modified from Wallace and Johnson3 and is shown in Figure 2. Instead of the vectors AH and AE constituting X and Y co-ordinates of the point P, the vectors EP and HP were calculated for this purpose in the present study. Although these differences may by insignificant in view of the other errors, we feel that the modified relation is geometrically correct. The correction algorithm, presented in Figure 3, was written in QBASIC and implemented on a microcomputer.

Vertebral

kinematics

In contrast to Breen et a1.27677,all four corners of each vertebral body were digitized. This allowed for the calculation of relative angular and linear displacements separately, using different pairs of markers, and for the results to be averaged for each frame to reduce digitization error. This also allowed for establishing the vertebral position in a global axes system even if one or two corners of the vertebrae were absent from the screen view or perhaps were undigitizable due to soft tissue X-ray scatter. The changes in anterior annulus

Figure 2. Linear correction method for optical distortions within one box of a calibration grid. AB, BC, CD and DA originally formed a l-cm square. Geometrical relationships can be derived to calculate the Xand Y co-ordinates of the point P (where X is a fraction of a distance EP/EF, and Y = HP/HG). Since EF and HG were 1 cm, the co-ordinates were expressed in cm.

Dqltlzed

vertebral kinematics

I cmgrad

75

Row X Y coordmtes

Identify location of pJintPonthegrid

for Y coordinate

Output

I corrected

XY

Figure 3. Flow chart of the algorithm for correction of optical distortions in the videofluoroscopic images (refer to Figure 2).

fibrosus height (distance between corresponding corners of vertebrae) served as examples of a distance measurement for error analysis.

Data collection

Three sets of data were collected for this study. The first set incorporated a model of a human L4/L5 motion segment in the sagittal plane, cut out of a copper sheet and attached to a long handle. Holes, 1.2 mm in diameter, were drilled in each corner of each vertebra to establish clear markers for digitizing. The model was moved and rotated in the field of view and its image was recorded on the videofluoroscope. Object-to-intensifier distance was identical to the distance at which a subject would be placed for the study. The model was positioned in all possible places in front of the image intensifier. Since the physical model did not allow for movement between the two vertebrae, any calculated relative displacements could be attributed to distortion error; digitizing errors being minor, due to the clearly identifiable markers. These errors, expressed as the mean and standard deviations (SD) of distances from the true values, were evaluated before and after correction for distortions. A total of 25 different frames (positions) were digitized and assessed. The second data set consisted of a vertebral model of Ld and Ls constructed from dry human vertebrae (Figure 4), similar to the one used by Breen et a1.2,6p7. It was designed to allow rotational movement in the sagittal plane, which could be measured from an attached protractor. Three rotated positions were

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Clin. Biomech. 1991; 6: No 2 Table 1. Mean absolute errors due to optical distortions before and after correction (copper model), and digitizing error arising from poor quality image after multiple digitization (dry bones model) Optical distortions Measure

Digitizing error

Uncorrected

Corrected

Angle (deg)

0.870

0.465

0.506

SD

(0.842)

(0.288)

(0.324)

Distance (mm)

0.44

0.22

0.24

SD

(0.43)

(0.17)

(0.18)

difference calculated. The low-pass filter cutoff frequency was incremented from 0.5 Hz to 15 Hz in steps of 0.5 Hz and the process repeated. Assuming that the noise is ‘white’, the frequency at which the curve deviates from linearity is considered optimal for signal-to-noise enhancement using low-pass filtering. Figure4. Photograph of the vertebral model used to assess digitizing error.

selected for assessment: O“, Y, and 10” of relative rotation. A plastic jar (14 cm diameter), filled with water was placed in front of the model to simulate scatter from soft tissue. Multiple digitizing of video frames was employed, and the errors were plotted against the number of averaged frames to determine the optimum number of repeated digitizations to intensity was then minimize error. Radiographic reduced to mimic the image quality of the worst possible case, yet remain eligible for analysis. The digitizing errors were estimated using an established number (4) of multiple digitizations, assuming that the optical distortion had a minimal effect due to the model being stationary in a small area of the image intensifier view. The third data set involved the collection of videofluoroscopic images of the lumbar spines of five volunteer subjects. Two walked on a treadmill, which produced a coronal view, while three subjects performed trunk extension starting from full flexion in Image and data processing the sagittal plane. incorporated all of the above-mentioned techniques for error reduction. Digitizing was carried out at sample rates of 60 Hz and 30 Hz to facilitate a residual analysis to estimate signal to noise ratio and the best low-pass Relative angular displacements cutoff frequency. between lumbar vertebrae were then calculated and digitally filtered (Butterworth dual pass, with a cutoff frequency of 3 Hz). The cutoff frequency was chosen from a residual analysis of the raw and filtered data (after Wells and Winter’). Rriefly, the filtered signal was compared with the raw signal and the RMS

Results

A summary of errors in angle (rotation) and distance (translation) arising from different sources, obtained from the vertebral models, is presented in Table 1. The optical distortions correction algorithm attenuated the mean absolute error in the relative vertebral angle measurement by 0.41” (47%) and in the distance measurement by 0.22 mm (50%). The standard deviation of the error decreased by 0.55” and 0.26 mm for the angle and distance measures respectively. Analysis of the effects of multiple digitizing of a single image (Figure 5) revealed that repeating the digitizing four times seemed to produce an optimum between the amount of error reduction and a laborious amount of digitizing. Compared to a single digitization, mean error and its SD decreased by more than a half.

I

2

3

4

5 6 7 6 9 IO II Number of digitimtiors per frame

12

13

I4

15

Figure 6. Effects of multiple digitizing of a single image on error reduction expressed as a mean (Cl) and standard deviation (@.

Cholewicki

0

I

I

2

4

I

I

I

6 6 IO Filter frequency cutoff (Hz)

1

I

12

14

,

Figure 6. The residual plotted against low-pass filter cutoff frequency for angular rotation data, where the residual is the RMS difference between the raw and filtered signal in degrees.

In order to estimate the total remaining error (E,,,), due to distortions (Edist) and digitizing process (Edisit), the sum of the two component errors, which were assumed to be independent, was calculated in the following manner:

When the remaining digitizing error obtained from the worst quality image case was used in this equation, the total mean error was 0.69”, SD = 0.43” (Edigit = 0.506”, Edist = 0.465”) for angular and 0.33 mm SD = 0.25 mm (Edigit = 0.24 mm, Edisr = 0.22 mm) for linear measurements. This is a conservative estimate, since the worst case was used, and because both distortion and digitizing error values overlap to some extent. There was no difference between results obtained from the data sampled at 60 or 30 Hz, indicating 30 Hz as being sufficient, although lower sampling rates may The residual analysis (Figure 6) be appropriate. resulted in the selection of 3 Hz for the low-pass filter cutoff frequency for trunk extension trials. Although

‘r

-121 0

I 0.2

1 0.4

I 0.6

I 0.8 Time(s)

I

I

I 1.2

I 1.4

1.6

Figure 7. Relative sag&al plane rotation between L3 and h during extension of the spine starting from a full flexion for subject 1, W; subject 2, +; subject 3, Cl.

et al.: Measuring vertebral kinematics

77

there was some signal present in the vicinity of 4 Hz, the relatively large proportion of noise makes it worthless to recover. The cutoff frequency of 3 Hz may not be appropriate for other high acceleration movements, but it is physiologically justifiable for slow trunk extensions. Figure 7 presents the results from the extension of a lumbar spine of three volunteer subjects. The average relative rotation between L3 and L4 vertebrae was 8.9”. It was not possible to digitize the walking trial continuously because the fast lateral translations produced a blurred image of the spine due to screen persistence within the videofluoroscope monitor. However, the frames corresponding to the extreme lateral oscillations of the trunk (late swing phase) were good quality, since the movement paused at those phases of the gait cycle to reverse direction. The coronal plane rotation between L3 and L4 (average of 15 right and left steps) was 0.55” and between L3 and Ls was 1.21” for one subject and 0.4” between L3 and L5 for the other subject (bending occurred in the direction of support limb).

Discussion

Correction for optical distortions and the use of a multiple digitizing technique resulted in a substantial reduction of measurement errors. The accuracy of measurement of relative angles from this study appears satisfactory for many applications and is an improvement on others. Breen et a1.2q6 reported digitizing errors of 0.56” (SD 0.37”) for movements in coronal plane and 0.84” (SD 0.87”) for movements in sagittal plane. When compared to Breen et a1.2*6our improved estimate of digitizing error (0.5”; SD 0.32”) was probably due to repeating the digitizing of a single image four times. While our error estimates are lower when only digitizing error sources were considered, we felt that a better estimate of total error must also include geometrical distortion error. Clementz and Magnusson’ reported much larger errors when measuring tibia1 torsion directly from the unprocessed image (1.3”). The 3D X-ray movement analysis of the lumbar spine conducted by Pearcy and Whittle’ produced RMS errors of less than 2 mm for translations and less than 1.5” for rotations. However, our results were obtained only from a single plane. Distance from measurement videofluoroscopic imaging appeared to be very accurate, as indicated by the relatively small mean error and its variance. It was interesting to note that there was more than a two-fold increase in error when the quality of the radiographic image deteriorated, despite digitizing a frame four times (when compared with a clear image (Figure 5)). This suggests that the clarity of imaging and careful digitizing are crucial for obtaining accurate measures. Unfortunately, videofluoroscopy produces unacceptable blurring of rapid movements due to the persistence of the phosphorous screen. These problems, however, are not relevant to the analysis of

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relatively slow movements. such as in trunk extension/flexion or lateral bending. If the screen persistence could be reduced, the accuracy of measures under dynamic conditions should be expected to improve greatly. The errors due to the digitizing process arise from two sources - one being the ability of the observer to recognize and place the cross-hair accurately on the given bony landmark; and the other relates to the landmark itself changing its shape or clarity slightly, between frames, from blurring and soft tissue scatter. While the first error is reduced through multiple digitizing, the second source of error remains as noise in the resultant signal, which can be further reduced by Although theoretically the raw digital filtering. co-ordinates or their linear transformations should be filtered, in this study, the final angles were filtered. Because the individual vertebral corners sometimes disappeared from the screen or were blurred, the raw co-ordinates often had missing values. However, the angular displacement of a vertebra can be still calculated if any two of its corners are visible. Therefore, it was more numerically convenient to filter the continuous angular data. Much work is currently being done in the area of digital enhancement of X-ray images, such as contrast stretching or edge finding’. Unfortunately, the present quality of videofluoroscopic images remains insufficient for accurate automatization of measurements, therefore requiring exhaustive manual interaction. It appears that both correction for image distortions and digitizing error are necessary to obtain accurate kinematic measures of spinal motion. However, both walking and extension experiments demonstrated that the relatively inexpensive technique of image and signal processing of videofluoroscopic images, described in this paper, reduces errors and can facilitate the study of relative vertebral motion during the performance of dynamic tasks.

Conclusions

1. Both correction for image distortions and digitizing error are necessary to obtain accurate kinematic measures of spinal motion via videofluoroscopy. 2. A l-cm grid (or smaller) is recommended for

correcting optical distortions. The four averaged digitizations per frame and a filter cutoff frequency of 3 Hz appear adequate to minimize random digitizing error. should be directed towards 3. Further efforts shortening the persistence times of the videofluoroscopic screens in order to improve the image quality of fast-moving objects.

Acknowledgments

This study was financially supported by the Natural Sciences and Engineering Research Council, Canada. The usage of the videofluoroscope and video data acquisition system was donated by Apotex Imaging Inc., Markham, Ontario, Canada.

References Clementz BG. Magnusson A. Assessment of tibia1 torsion employing fluoroscopy. computed tomography and the cryosectioning technique. Acta Radiologica 1989: 30: 75-80

Breen A. Allen R. Morris A. Spine kinematics: a digital videofluoroscopic technique. J Biomed Eng 1989: 11: 224-28 Wallace WA, Johnson F. Detection and correction of geometrical distortion in X-ray fluoroscopic images. J Biomech

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Hallert B. A new method for the determination

of the distortion and the inner orientation of cameras and projectors. Photogrammetria 1955; 11: 107- 15 Hallert B. Determination of the inner orientation of cameras for non-topographic photogrammetry, microscopes. X-ray instruments and television images. Photogrammetric Eng. 1960; 26: 748-54 Breen A, Allen R, Morris A. An image processing methoc for spine kinematics - preliminary studies. Clin Biomech 1988; 3: 5-10

Breen A, Allen R, Morris A. An image processing technique for the radiographic assessment of vertebral derangements. J Photogr Sci 1989; 37: 131-33 Wells RP, Winter DA. Assessment of signal and noise in the kinematics of normal, pathological and sporting gaits. Proc Canad Sot Biomech, London, Ontario. Oct. 27-28 1980: 92-93

Pearcy MJ. Whittle MW. Movements of the lumbar spine measured by three-dimensional X-ray analysis. J Biomed Eng 1982; 4: 107- 12