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Quantitative fluoroscopy and the mechanics of the lumbar spine

A report submitted as the examined component of the project module S810 within the Open University’s postgraduate awards in Science.

Alexander Breen, BSc (Hons) – PI: A4548242

30th of September 2011

Word count (Introduction to Conclusion) 13,643

Appendices 3,307

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Acknowledgements

I would like to say thank you to the IMRCI research group and the Anglo-European College of

Chiropractic for their support throughout this MSc in the form of the time, space and

training that has made this dissertation possible. Thanks also go to those people who proof

read this document and offered constructive criticism.

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Abstract

Study Design Validity and repeatability studies of an automated tracking system for

vertebral segments were undertaken to assess quantitative fluoroscopy (QF) for the

measurement of continuous motion of the lumbar spine utilising videofluoroscopy. Two

cadaveric models and 20 volunteer subjects where imaged while undergoing flexion-

extension motion.

Objectives To assess the validity and the repeatability of QF for measuring three types of

inter-vertebral movement in the lumbar spine in the sagittal plane.

Summary of Background Data Instability of the lumbar spine is thought to be associated

with low back pain, but the diagnosis remains difficult. Functional radiographs have been

used for diagnosis of spinal instability measured as a function of range of movement of a

subject’s full voluntary bending angle, but limitations exist. However, (QF) is an emerging

technology which provides continuous information throughout the range of motion. This

may shed light on the biomechanical definition of spinal instability by measuring changes of

inter-segmental movement throughout a subject;s motion. QF has been shown to

automatically track the rotational motion of a vertebral segment with high reproducibility.

Methods; Validity (In vitro) and repeatability (in vivo) of QF were evaluated for translation,

disc height change and positions of the Instantaneous axes of rotation (IAR). Intervertebral

flexion and extension images were assessed in two cadaveric calibration models and 20

randomly selected human volunteers. Accuracy was measured using the calibration models

which underwent video-fluoroscopy. Model 1 was rotated through 18° about a fixed point

and the superior vertebra of the calibration. Model 2 was translated through 17mm along

the plane of the vertebral disc space.

Repeatability in terms of agreement was calculated as the standard error or measurement

[SEM] along with the 95% limits of agreement. Reliability was expressed as intraclass

correlations (ICC) between observation sets from volunteer studies currently in progress.

These volunteers underwent video-fluoroscopy of their lumbar spines during passive,

recumbent flexion-extension motion through 80° using a motor-driven motion table .

Approximately 230 consecutive images of segments L2–S1 were captured per participant,

and the position of each vertebra was tracked throughout the sequence using automated

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frame-to-frame registration to find the range of translational range of motion, anterior disc

height change and IAR position in adjacent vertebral segments. Intra and Inter examiner

studies were carried out using 2 sets of observations.

Results Accuracy across the 2 models for translation ranged from 0.1 to 2.0mm, for disc

height less than 1.0mm and for IAR position less than 0.01mm and 0.4mm in the X and Y

directions respectively.

Intra and inter-examiner disagreement in the measurement of translation were found to be

less than 1mm, with 95% limits of agreement less than 3.5mm. Reliability was also high with

intraclass correlations above 0.7.

For disc height, the standard error or measurement was consistently below 1mm. However,

the 95% limits of agreement were sometimes over 6mm for extension sequences and the

ICC’s showed only moderate reliability. This suggests that further development is necessary

for the measurement of disc height at all vertebral levels of the low back.

This study also found very high accuracy for IAR position (error<0.5mm), but due to the low

number of segments with sufficient rotation to make them available for examination, SEM

and ICC could not be calculated. However, the root-mean-square difference between

observations by the same observer and between two observers for this parameter was

consistently less than 1mm.

Conclusions These studies indicate generally high accuracy and repeatability of this

technology for the measurement of these three indicators of lumbar spine stability in the

sagittal plane. Further development of the method for some levels, directions and indices is

needed as well as studies with larger numbers to replicate and increase the transferability of

this work.

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Objectives

Assess the validity and reliability of the diagnostic technique OSMIA (Objective

Spinal Motion Imaging Assessment) for measuring inter-vertebral movement of the

lumbar spine in the sagittal plane.

Express the measurement of anterior inter-vertebral disc height change,

translational range and instantaneous axes of rotation in 20 volunteers.

Describe the use of lumbar spine phantom calibration models for calculation of

validity.

Evaluate the benefits of this technology against the stochastic risks arising from the

ionising radiation delivered to the patient.

Review the role of quantitative fluoroscopy in the investigation of lower spine

mechanics.

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Introduction

There are a number of methods for measuring the spine in motion, and the objective of this

report is to assess the validity and repeatability of one such technique called OSMIA

(Objective Spinal Motion Imaging Assessment). This technique uses moving video x-rays

(fluoroscopy) to measure inter-vertebral movement of the lumbar spine in the sagittal plane.

The measures used were anterior inter-vertebral disc height change, translational range and

average Instantaneous Axes of Rotation (IAR). Repeatability was assessed from the lower

spine motion of 20 volunteers by two independent observers and validity by the use of two

lumbar spine phantom calibration models. The study endeavoured to evaluate the utility of

this technology to measure continuous inter-vertebral motion, in view of the stochastic risks

arising from the ionising radiation delivered to the patient as a contribution to the

understanding of the role of quantitative fluoroscopy in the investigation of lower spine

mechanics.

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Glossary of terms:

Orientation

Axial Plane: transverse section (green).

Sagittal Plane: Front to back (red)

Coronal Plane: Left and right (blue)

Anterior: Front

Posterior: Back

Superior: Towards the head

Inferior: Towards the feet

Weight-Bearing: The body is sitting or standing erect

Recumbent: The body is lying down

Supine: Lying face up

Prone: Lying face down

Figure 1: Planes of human anatomy. (Image from

http://en.wikipedia.org/wiki/File:Human_anatomy_planes.svg)

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Abbreviations

%VBD Percentage of superior Vertebra Body Depth2D Two dimensional3D Three dimensional6 degrees of

FreedomAECC Anglo-European College of ChiropracticCI Confidence intervalCLBP Chronic low back painCNSLBP Chronic non specific low back painCT-scan Computed tomography scanDJD Degenerative joint diseaseEqv mm Equivalent Millimetres. Where 100%VBD = 35 eqv mmEZ Elastic ZoneICC Intraclass correlation coefficient

IMRCIIVF Intervertebral foramenL1 Lumbar vertebrae 1L2 Lumbar vertebrae 2L3 Lumbar vertebrae 3L4 Lumbar vertebrae 4L5 Lumbar vertebrae 5LBP Low back painLOA limits of AgreementMATLAB MATrix LABoratorymm MillimetresMRI Magnetic resonance imagingn Number of subjectsNICE OSMIA Objective Spinal Motion Imaging AssessmentQF Quantitative fluoroscopyRMS Root Mean SquareRoM Range of motionS1 Sacral segment 1SAP superior articular processSD Standard deviationSEM Standard error of measurementSoP Standard operating procedureSPSS Statistical Package for the Social SciencesUK United KingdomVBU Vertebral body unitsWHO World Health Organisationx̄ Sample mean

The directions of motion of a spinal segment (figure

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Institute for Musculoskeletal Research and Clinical

Implementation

National Institute for Health and Clinical Excellence

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Movement between two vertebrae can be in multiple directions and either rotational or translational.

Translational movements are anterior/posterior, superior/inferior, and left/right. Rotation

includes axial rotation (twisting), flexion/extension (forwards backwards – sagittal plane),

and lateral bending (left right coronal plane).

When the spine is free to move in all these directions it is said to have 6 degrees of freedom

[1] (See Figure 2).

Figure 2: Degrees of freedom of motion for inter-vertebral segments

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Table of Contents

ACKNOWLEDGEMENTS ................................................................................................................... 2

ABSTRACT ............................................................................................................................................ 3

OBJECTIVES ......................................................................................................................................... 5

INTRODUCTION .................................................................................................................................. 6

GLOSSARY OF TERMS: ..................................................................................................................... 7

ORIENTATION ....................................................................................................................................... 7 ABBREVIATIONS ................................................................................................................................... 8

LIST OF FIGURES .............................................................................................................................. 12

LIST OF TABLES ................................................................................................................................ 13

METHODOLOGY OF THE LITERATURE REVIEW .................................................................. 14

METHODOLOGY OF THE LITERATURE REVIEW .................................................................. 14

BACKGROUND ................................................................................................................................... 15

IMAGING THE SPINE: ........................................................................................................................... 18 MEASUREMENT METHODS: ................................................................................................................. 18

Goniometry .................................................................................................................................... 20 Roentgen Stereophotogrammetric Analysis (RSA): ....................................................................... 21 Measurements from radiographs ................................................................................................... 22

Translation ............................................................................................................................... 22 Disc height ............................................................................................................................... 27 Instantaneous Axes of Rotation (IAR) ..................................................................................... 30

Video fluoroscopy & OSMIA (Quantitative Fluoroscopy) ............................................................. 32 REPEATABILITY AND VALIDITY: ......................................................................................................... 34

METHODS: .......................................................................................................................................... 35

MATERIALS: ....................................................................................................................................... 35 Validity: ......................................................................................................................................... 35

Fixed centre of rotation calibration model (model 1) ............................................................... 35 Translating calibration model (bespoke model 2) .................................................................... 36

PROCEDURES ...................................................................................................................................... 38 Validity: ......................................................................................................................................... 38

Image sequence acquisition ...................................................................................................... 38 Repeatability: ................................................................................................................................. 39

Subject imaging ........................................................................................................................ 39 IMAGE ANALYSIS; ............................................................................................................................... 40

Image enhancement ....................................................................................................................... 40 Analysis and image registration .................................................................................................... 41 Data analysis ................................................................................................................................. 42

Translation Calculations ........................................................................................................... 42 Disc height calculations ........................................................................................................... 43 IAR calculations ....................................................................................................................... 44

DATA EXTRACTION AND TRACKING VERIFICATION ............................................................................. 47 VALIDITY STUDY: ............................................................................................................................... 48 REPEATABILITY STUDIES: ................................................................................................................... 49

Intra-observer study; ..................................................................................................................... 49 Inter-observer study; ..................................................................................................................... 49

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STATISTICAL ANALYSIS ...................................................................................................................... 50 VALIDITY: ........................................................................................................................................... 51 REPEATABILITY: ................................................................................................................................. 54

Translation: ................................................................................................................................... 54 Disc height change: ....................................................................................................................... 57 IAR ................................................................................................................................................. 59

DISCUSSION; ...................................................................................................................................... 61

TRANSLATION ..................................................................................................................................... 61 DISC HEIGHT ....................................................................................................................................... 62 IAR ..................................................................................................................................................... 63

CONCLUSION ..................................................................................................................................... 66

REFERENCES ..................................................................................................................................... 67

APPENDIX 1 ........................................................................................................................................ 73

APPENDIX 2 ........................................................................................................................................ 75

APPENDIX 3 ........................................................................................................................................ 80

APPENDIX 4 ........................................................................................................................................ 89

INTRA-OBSERVER REPEATABILITY RESULTS........................................................................................ 89 Translation ..................................................................................................................................... 89 Disc height ..................................................................................................................................... 90 Instantaneous axes of rotation ....................................................................................................... 91

INTER-OBSERVER REPEATABILITY RESULTS ........................................................................................ 92 Translation ..................................................................................................................................... 92 Disc height ..................................................................................................................................... 93 Instantaneous axes of rotation ....................................................................................................... 94

APPENDIX 5 ........................................................................................................................................ 95

INTRA-OBSERVER REPEATABILITY 95% LOA BLAND-ALTMAN PLOTS ............................................... 95 Translation ..................................................................................................................................... 95 Disc height ................................................................................................................................... 101

INTER-OBSERVER REPEATABILITY 95% LOA BLAND-ALTMAN PLOTS ............................................. 107 Translation ................................................................................................................................... 107 Disc height ................................................................................................................................... 113

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List of Figures FIGURE 1: PLANES OF HUMAN ANATOMY. (IMAGE FROM

HTTP://EN.WIKIPEDIA.ORG/WIKI/FILE:HUMAN_ANATOMY_PLANES.SVG) .............................................. 7 FIGURE 2: DEGREES OF FREEDOM OF MOTION FOR INTER-VERTEBRAL SEGMENTS ........................................ 9 FIGURE 3: NEUTRAL ZONE AND ELASTIC ZONE THEORY, [30] ..................................................................... 17 FIGURE 4: STANDARD (UNIVERSAL GONIOMETER) [53] .............................................................................. 20 FIGURE 5: DUALER IQ INCLINOMETER [54] ............................................................................................. 20 FIGURE 6: REPRESENTATION OF INCLINOMETER SET UP ON SKIN OF PATIENT.............................................. 20 FIGURE 7: MEYERDING METHOD OF DEFINING GRADES OF SPONDYLOLISTHESIS [49] ................................. 22 FIGURE 8: GRAPHICAL REPRESENTATION TRANSLATION MEASUREMENT TECHNIQUES [47]. ......................... 23 FIGURE 9: GRAPHICAL REPRESENTATION OF TWO LUMBAR VERTEBRA UNDERGOING EXTENSION IN THE

LATERAL PLANE................................................................................................................................ 25 FIGURE 10: GRAPHICAL REPRESENTATION OF THE FROBIN METHOD OF MEASURING TRANSLATION ............. 25 FIGURE 11: DEPICTION OF 5 DISC HEIGHT MEASUREMENT METHODS EVALUATED BY POPE (1977) [50] ..... 27 FIGURE 12: GRAPHICAL REPRESENTATION OF THE FROBIN METHOD OF MEASURING DISC HEIGHT ............. 28 FIGURE 13: A) SIMPLIFIED OUTLINE OF A VERTEBRAL BODY PAIR USED TO CALCULATE IAR POSITION

BETWEEN TWO IMAGES B) GRAPHICAL REPRESENTATION OF IAR CALCULATIONS FROM SUPERIMPOSED

RADIOGRAPHIC FILMS. ..................................................................................................................... 30 FIGURE 14: GRAPHICAL REPRESENTATION OF SUBJECTS POSITIONING........................................................ 33 FIGURE 15: IMAGE SHOWING SUBJECTS POSITIONING ................................................................................ 33 FIGURE 16: FIXED ROTATION POINT CALIBRATION MODEL ......................................................................... 35 FIGURE 17: TRANSLATION CALIBRATION MODEL ........................................................................................ 36 FIGURE 18: EXPERIMENTAL SET UP ........................................................................................................... 37 FIGURE 19: A SIEMENS ARCADIS AVANTIC PORTABLE C-ARM FLUOROSCOPE, SIEMENS GMBH, GERMANY.[85]

....................................................................................................................................................... 38 FIGURE 20: IMAGE ENHANCEMENT GUI .................................................................................................... 40 FIGURE 21: GUI FOR MANUALLY IDENTIFYING VERTEBRAL BODIES IN THE FIRST IMAGE OF A SEQUENCE

....................................................................................................................................................... 41 FIGURE 22: VARIOUS DEPICTIONS OF IAR POSITIONS ................................................................................ 45 FIGURE 23: IAR POSITION ON THE FIRST IMAGE OF THE IMAGE PAIR USED ................................................. 46 FIGURE 24: IAR POSITION ON THE SECOND IMAGE OF THE IMAGE PAIR USED. ............................................ 46 FIGURE 25: GUI DISPLAYING THE IAR POSITIONS RELATIVE TO THE INFERIOR VERTEBRA IN A PAIR ............. 46 FIGURE 26: TRANSLATION AND DISC HEIGHT CHANGE OF AN INTER-VERTEBRAL SEGMENT UNDERGOING

MOTION. .......................................................................................................................................... 48 FIGURE 27: RADIOGRAPHIC IMAGES OF MODELS 1 AND 2 DISPLAYING THE COMPUTER GENERATED IAR,

ANTERIOR DISC HEIGHT AND TRANSLATION RESULTS .......................................................................... 53 FIGURE 28: COMPUTER GENERATED POSITIONS OF BISECTRIX OF L3/L4, L4/L5 & L5/S1. .......................... 64 FIGURE 29: MEASUREMENTS OF MODEL 1; THEORETICAL PLACEMENTS OF BISECTRIX AND MIDLINES FOR

CALCULATIONS ................................................................................................................................ 75 FIGURE 30: MEASURED INITIAL DISC HEIGHT AND THERE RELATIVE VALUES AS A FUNCTION OF MEAN

VERTEBRAL BODY DEPTH .................................................................................................................. 76 FIGURE 31: CALCULATED DISTANCES FROM FIXED CENTRE OF ROTATION TO VERTEBRAL BODY CORNERS .... 77 FIGURE 32: MEASURING MAXIMUM DISC HEIGHT CHANGE RELATIVE TO BISECTRIX ..................................... 78

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List of Tables TABLE 1: ACCURACY OF DETERMINATION OF INTER-VERTEBRAL DISPLACEMENTS FOR TRANSLATION AND DISC

HEIGHT MOTION AND X AND Y IAR LOCATIONS IN TWO CALIBRATION MODELS* .................................. 51 TABLE 2: CALIBRATION STUDY; RMS DIFFERENCE BETWEEN MEASURED VALUES AND THOSE CALCULATED IN

THE MATLAB ENVIRONMENT, EXPRESSED IN MM ................................................................................ 52 TABLE 3: CALIBRATION STUDY; RMS DIFFERENCE BETWEEN MEASURED VALUES AND THOSE CALCULATED IN

THE MATLAB ENVIRONMENT, EXPRESSED IN EQUIVALENT MM ............................................................ 52 TABLE 4: INTRA-OBSERVER REPEATABILITY OF TRANSLATIONAL MOTION MEASUREMENT FOR 4 INTER-

VERTEBRAL LEVELS (L2-L3, L3-L4, L4-L5, AND L5-S1) .................................................................... 56 TABLE 5: INTER-OBSERVER REPEATABILITY OF TRANSLATIONAL MOTION MEASUREMENT FOR 4 INTER-

VERTEBRAL LEVELS (L2-L3, L3-L4, L4-L5, AND L5-S1) .................................................................... 56 TABLE 6: INTRA-OBSERVER REPEATABILITY OF DISC HEIGHT MOTION MEASUREMENT FOR 4 INTER-VERTEBRAL

LEVELS (L2-L3, L3-L4, L4-L5, AND L5-S1) ...................................................................................... 58 TABLE 7: INTER-OBSERVER REPEATABILITY OF DISC HEIGHT MOTION MEASUREMENT FOR 4 INTER-VERTEBRAL

LEVELS (L2-L3, L3-L4, L4-L5, AND L5-S1) ...................................................................................... 58 TABLE 8: INTRA-OBSERVER REPEATABILITY OF DETERMINATION OF X AND Y IAR LOCATION FOR 4 INTER-

VERTEBRAL LEVELS (L2-L3, L3-L4, L4-L5, L5-S1)* (ROOT-MEAN SQUARE DIFFERENCE BETWEEN

OBSERVATIONS) ............................................................................................................................... 60 TABLE 9: INTER-OBSERVER REPEATABILITY OF DETERMINATION OF X AND Y IAR LOCATION FOR 4 INTER-

VERTEBRAL LEVELS (L2-L3, L3-L4, L4-L5, L5-S1)* (ROOT-MEAN SQUARE DIFFERENCE BETWEEN

OBSERVATIONS) ............................................................................................................................... 60 TABLE 10: INTRA-OBSERVER REPEATABILITY OF TRANSLATION IN EXTENSION OF THE LUMBAR SEGMENTS L2-

L3, L3-L4, L5-S1 USING QF EXPRESSED IN SEM, 95% LOA, ICC AND 95% CI ................................ 89 TABLE 11: INTRA-OBSERVER REPEATABILITY OF TRANSLATION IN FLEXION OF THE LUMBAR SEGMENTS L2-L3,

L3-L4, L5-S1 USING QF EXPRESSED IN SEM, 95% LOA, ICC AND 95% CI ...................................... 89 TABLE 12: INTRA-OBSERVER REPEATABILITY OF DISC HEIGHT CHANGE IN EXTENSION OF THE LUMBAR

SEGMENTS L2-L3, L3-L4, L5-S1USING QF EXPRESSED IN SEM, 95% LOA, ICC AND 95% CI .......... 90 TABLE 13: INTRA-OBSERVER REPEATABILITY OF DISC HEIGHT CHANGE IN FLEXION OF THE LUMBAR

SEGMENTS L2-L3, L3-L4, L5-S1USING QF EXPRESSED IN SEM, 95% LOA, ICC AND 95% CI .......... 90 TABLE 14: INTRA-OBSERVER REPEATABILITY OF IAR IN EXTENSION OF THE LUMBAR SEGMENTS L2-L3, L3-

L4, L5-S1USING QF EXPRESSED IN RMS. ......................................................................................... 91 TABLE 15: INTRA-OBSERVER REPEATABILITY OF IAR IN FLEXION OF THE LUMBAR SEGMENTS L2-L3, L3-L4,

L5-S1USING QF EXPRESSED IN RMS. ............................................................................................... 91 TABLE 16: INTER-OBSERVER REPEATABILITY OF TRANSLATION IN EXTENSION OF THE LUMBAR SEGMENTS L2-

L3, L3-L4, L5-S1USING QF EXPRESSED IN SEM, 95% LOA, ICC AND 95% CI ................................. 92 TABLE 17: INTER-OBSERVER REPEATABILITY OF TRANSLATION IN EXTENSION OF THE LUMBAR SEGMENTS L2-

L3, L3-L4, L5-S1USING QF EXPRESSED IN SEM, 95% LOA, ICC AND 95% CI ................................. 92 TABLE 18: INTER-OBSERVER REPEATABILITY OF DISC HEIGHT CHANGE IN FLEXION OF THE LUMBAR

SEGMENTS L2-L3, L3-L4, L5-S1USING QF EXPRESSED IN SEM, 95% LOA, ICC AND 95% CI S1USING

QF EXPRESSED IN SEM, 95% LOA, ICC AND 95% CI ...................................................................... 93 TABLE 19: INTER-OBSERVER REPEATABILITY OF DISC HEIGHT CHANGE IN FLEXION OF THE LUMBAR

SEGMENTS L2-L3, L3-L4, L5-S1USING QF EXPRESSED IN SEM, 95% LOA, ICC AND 95% CI .......... 93 TABLE 20: INTER-OBSERVER REPEATABILITY OF IAR IN EXTENSION OF THE LUMBAR SEGMENTS L2-L3, L3-

L4, L5-S1 USING QF EXPRESSED IN RMS. ........................................................................................ 94 TABLE 21: INTER-OBSERVER REPEATABILITY OF IAR IN FLEXION OF THE LUMBAR SEGMENTS L2-L3, L3-L4,

L5-S1 USING QF EXPRESSED IN RMS. .............................................................................................. 94

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Methodology of the literature review

Initial searches were performed using the website Medline/PubMed for articles relating to

“Lumbar vertebra motion diagnosis”. Many of these articles had the phrase ‘low back pain’

in the title so a MeSH term search for “low back pain” was undertaken. The sub headings

‘diagnosis’ & ‘radiography’ were selected and added to the PubMed search. Other Mesh

terms were used and expanded searches were used to gain further material. The low yield of

results revealed that this is a niche subject. These references were hand searched and

citations obtained if they were not already included. It was found that many had references

in common. These common references described methodologies for data collection,

calculation of inter-vertebral movement and references to cadaveric studies that gave

reference values for modelled inter-vertebral movement. Further refinements were added

to the first search separately; “translation” OR “sagittal plane displacement”, “disc height”

OR “disc space”, “centre of rotation” OR “axes of rotation”. Furthermore, accuracy and

validity methodologies were described or referred to [2-6]. Titles, authors and references

from these bibliographies were hand searched to gain further background understanding of

this niche subject.

Moreover, I have searched out Shareware Software/ User interface (UI) programs on the

internet were also searched using the search engine Google to help in my development of

MatLab interfaces and Arduino I/O board programs for measuring output and control of the

calibration model systems. There are many open source codes available from

www.Matlabcentral.comand www.arduino.cc which have proven useful in the development

of this project.

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Background

The spine is an extraordinary structure which maintains several vital functions such as

providing support for vital organs, freedom of movement and protection for the spinal cord,

all while absorbing shock and allowing motion in three planes (sagittal, coronal and axial see

Figure 2). This is achieved through the contribution of a series of individual joint linkages.

Each linkage is made up of three joints; an inter-vertebral disc and two facet joints.

It has long been suspected that abnormalities in the mechanics of spine may be linked to

pain related to ‘instability’. However, the meaning of spinal instability varies between

specialists such as clinicians, bioengineers and radiologists [7] [8].

Clinical instability has been defined as the loss of the ability of the spine under physiologic

loads to maintain its pattern of displacement so that there is no initial or additional

neurological dysfunction[9]. Measures such as palpation [10] and ‘instability tests’ [11-13]

are used in practice to check for instability in patients who exhibit signs and symptoms

during examination, however, the credibility of such tests remains uncertain [14].

Radiological instability is defined as excessive motion between segments, and is commonly

investigated with functional radiography (flexion extension x-rays taken at the extreme of

trunk bending). This remains the most common method of assessing instability within living

patients (in vivo) [15] but has low reliability and validity [16-18]. The relationship between

clinical and radiographic instability has been studied with functional radiography but the

agreement was poor.[19] However its accessibility explains its’ continued clinical and

research use.

A biomechanical definition states that instability is a lack of resistance to force whilst the

spine is at, or near, the neutral position [9]. This is known as the neutral zone (NZ) theory

and has been validated from cadaveric studies [20, 21]. However the neutral zone cannot be

demonstrated in human studies using functional radiography or other static imaging

methods such as MRI. This is due to the fact that these modalities take an anatomical

snapshot of a physiological problem. It follows that back pain which is made better or worse

by movement or position (known as mechanical back pain) [22] would be better assessed by

measuring function rather than anatomy. There is now a technique which can do this in vivo

using low dose video x-rays and automated measurement algorithms. This technique, known

as quantitative fluoroscopy (QF), can measure both rotation and translation (sliding)

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between vertebrae (known as inter-vertebral motion). This has allowed the NZ theory to be

tested in vivo with promising initial results [23-27]

As depicted in Figure 3 the total range of motion (ROM) of a joint is subdivided into the

neutral zone (NZ) and the elastic zone (EZ). The zone with minimal resistance to force is

called the Neutral-zone (NZ) and the elastic zone (EZ) follows the neutral zone, where the

passive restraints due to molecular bonds in ligaments, joint capsules and muscles impinges

upon segmental motion causing elastic restraint.

Panjabi (1992) [28] found in cadaveric studies that if a segment is unstable, the neutral zone

will be increased, this is known as ‘laxity’. Mellor et al. (2009) [29] express the laxity of an

inter-vertebral segment by directly comparing inter-vertebral motion per level to the whole

trunk motion of a subject undergoing coronal sequences while using QF. If an inter-

vertebral segment moves at a rate similar to the trunk, it therefore follows that there is a

lack of resistant forces acting upon that segment. Due to the non linear relationship

between segmental motion and trunk bending at large ranges of motion (greater than 10°of

trunk motion), the linear correlation between the first 10° of trunk motion (incorporating

the neutral zone) against that of inter-segmental was observed. The theory was (as

prescribed by Panjabi (1992)) that the less passive holding elements acting upon the

segment in question the higher the correlation between the segmental and trunk motion. It

was noted [29] that muscle contraction might lead to false positive about the quality of

inter-vertebral motion due to voluntary or involuntary contractions (guarding or muscle

spasm). The theory is that examining a patient in the recumbent position will reduce the

involvement of muscular and motor activity and will not limit the overall range of motion.

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Figure 3: Neutral zone and elastic zone theory, [30]

However, further work is needed to establish normal motion in vivo and to determine

whether spinal motion is related to chronic non specific low back pain (CNSLBP). The

importance of knowing this would lead to better diagnosis of CNSLBP and possible

identification of biomechanical patient subgroups which could better inform treatment [31].

For those who accept instability is definable, a classification of this system would be one of

the keys to gaining control of CNSLBP [32]. It is generally accepted that instability consists of

both mechanical derangement and clinical consequences [33] but the relationships between

these and pain are still unknown.

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Imaging the spine:

Vertebral motion in the lumbar spine is traditionally analysed using functional radiography -

for instance to check the outcome of surgical fusion. It is apparent from the literature that

some imaging modalities are good at depicting spinal anatomy (CT, MRI, plain film

radiographs) but these are unable to capture functional information relating to how the

spine moves at a rate which is meaningful in the assessment of patients with mechanical

back pain. Furthermore, measurements obtained by these methods have high variability

and poor sensitivity and specificity in relation to symptoms [34, 35]. Most studies that have

accurately measured motion using these techniques have been restricted to measurements

of end range positions[36-39] and some are associated with high radiation dosage ([40] i.e.

CT). With the establishment of continuous kinematic data a better understanding of spinal

motion and its relation to pain in vivo might be gained if the method is found to be reliable

and accurate. Attempts have also been made to do this using MRI [41, 42], but the time

needed to acquire an image, which extends for the open coil/upright scanners needed to

allow trunk motion, has prevented the collection of continuous motion data for now [43]. A

more accessible low dose alternative, if measurements were found to be repeatable and

valid, would be the use of fluoroscopy sequences. This is the topic of this study.

Measurement methods:

Many attempts have been made to establish the relationship between motion and LBP.

Some kinds of low back pain, such as mechanical LBP are thought to be related to abnormal

(or unstable) motion of the spine expressed as the range or pattern of the tilting (rotation)

or sliding (translation) between individual vertebrae [22]. Inter-vertebral motion is more

complicated than merely two vertebrae pivoting about a central point located at the centre

of the disc space. It is a complex motion combining rotation and translation of the vertebrae

relative to each other throughout the range of motion. Many previous studies relating to

spinal motion seem to have concentrated mainly on the documenting of rotational and

translational ranges of motion (RoM) separately [44] [45]. The rationale of these studies was

to provide a normative database to be used as a basis for detection of abnormalities, for

example an excessive or reduced range of motion at an inter-vertebral level. These studies

mainly concluded that overall rotational RoM was so highly variable it was impossible to

distinguish normal from abnormal. Thus other methods of measurement clearly need to be

investigated. Unfortunately, many of these studies did not state standard deviations of the

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ranges of motion collected or present inter- or intra observer errors. As such, their findings

can not be used for direct comparison with other studies, such as the present one.

One method of measurement that combines both translation and rotation would be to

identify the Instantaneous Axes of Rotation (IAR), a point (or a locus of points), usually found

to be in the posterior third of the inferior vertebra [46] [47] [48] in healthy spines and about

which the superior vertebra rotates and translates over the inferior one. (A diagrammatic

representation can be seen in Figure 13 b of this report.) While the position of the IAR shows

the axes around which one vertebra rotates with respect to another, its position will alter

superiorly (towards the head) and inferiorly (towards the base of the spine) with translation.

The construction of IAR’s may provide insight into the function of the spine and into the

deformation of the discs and ligaments resulting from motion.

Measurements of disc height are often used to evaluate degenerative changes in the disc,

which in turn may lead to treatment (on the assumption that loss in disc height is related to

pain [49]). Standard radiography is the most frequent method used for routine evaluation of

the lumbar spine despite known difficulties, both in interpretation and in the clinical

significance of findings [50]. There is wide variation in the interpretation of lumbar

radiographs and because of this various methods of measuring the inter-vertebral disc space

have been developed in order to improve the variability/reliability. Most methods focus on

the identification of the bony landmarks adjacent to the disc space in question [50] [51].

These landmarks are difficult to objectively identify if the direction of the radiation beam is

not orthogonal to the inter-vertebral disc space. This leads to poor superimposition of the

vertebral endplates if body position and vertebral position are not strictly controlled.

Pope (1977) [50] evaluated five methods of measuring inter-vertebral disc height in

experiments locating specific vertebral pairs in intact human cadavers, and in vivo. Frobin et

al. (1997) [52] described a precision measurement of disc height which has several

advantages over the five methods reviewed by Pope et al. (1977). Both Frobin and Pope

attempted to control for magnification and distortion of radiographic images. The methods

which were evaluated by Pope and Frobin are explained in greater detail in a later section

this report (Measurements from radiographs).

Until recently, the most common method used in clinical practice to assess inter-vertebral

motion was involved manually drawing lines on vertebral body images on plain radiographs.

Other methods of measuring motion of the human spine exist (Goniometry, Roentgen

20

Stereophotogrammetric Analysis (RSA)), however RSA is invasive (due to the need to implant

metal beads) and goniometry can only measure surface motion. Furthermore, these may

not be sensitive enough to measure inter-vertebral motion with any accuracy with the

exception of RSA, which, while it is currently considered the gold standard, can be

undesirable due to the need for surgical intervention.

Goniometry

Figure 4 (below): Standard (universal

goniometer) [53]

Figure 5 (below): Dualer IQ inclinometer [54]

Figure 6 (below): Representation of

inclinometer set up on skin of patient

A goniometer comprises of a moving arm,

stationary arm, and a fulcrum (Figure

4). The fulcrum is placed over the joint

being measured. The stationary arm is

aligned with a reference point while the

moving arm is positioned on the section

of the body which is moved.

Alternately, an inclinometer (Figure 5) can be used to the same effect positioned as shown in

Figure 6 to find the global range of motion. While this technique gives a fair description of

global motion, inter-vertebral motion is unclear as factors which include muscle, fat and skin

movement generate errors. A more accurate surgical option is a potentiometric goniometer

attached to pins which are surgically implanted into the spinous processes of the vertebrae.

This involves surgical intervention. Therefore, while the goniometric techniques that do not

21

penetrate the skin have been found to have poor repeatability, those that do are

undesirable because of their invasiveness [55-57]

Roentgen Stereophotogrammetric Analysis (RSA):

With this technique, metal balls are surgically implanted into the patient's vertebrae and

radiography or fluoroscopy is used to image and measure their motion. RSA is currently used

in the detection of loosening of surgical fusions of the lumbar spine and to evaluate joint

replacement implant designs. However, it cannot be used without breaking the skin, which

rules it out for research and for the majority of the population (i.e. pre-surgical patients,

non-surgical patients and healthy controls.[58])

22

Measurements from radiographs

Translation

Radiographs, otherwise called X-rays or ‘roentgenograms’ [45], have traditionally been used

as the main technique for measuring inter vertebral motion with varying rates of

repeatability dependent on the method used[59]. A common method of displaying gross

translation between two vertebra in a clinical setting is the ‘Meyerding’ method (see Figure

7, simply grades translation into one of 4 grades where each grade is a distance equal to a

quarter of the anterior-posterior depth of the superior border of the inferior vertebra. The

measures are taken between lines drawn on radiographs on the posterior borders of the two

adjacent vertebrae. This defines grades of severity of a spondylolisthesis (vertebral slippage).

However, due to its inherent lack of objectivity, more recent studies [60-62] have attempted

to define the range of translation between two vertebrae in more continuous, as opposed to

proportional terms.

Figure 7: Meyerding method of defining grades of spondylolisthesis [49]

23

With these methods, lines are drawn either through the vertebral end plates or through the

posterior aspects of the vertebral bodies, comparing the positions of vertebrae in two or

more radiographs [60-62].

Figure 8: Graphical representation translation measurement techniques [47].

Figure 8 shows seven methods of measuring inter-vertebral movement in lateral view

images of the lumbar spine;

1. Lines are drawn on the posterior borders of the adjacent vertebral bodies and a

third line is drawn on the inferior border of the superior vertebra. Translation is

calculated as the distance between the first two lines along the third line.

2. A line is drawn along the anterior border of the inferior vertebral body and

translation is calculated from a perpendicular line from this to the inferior anterior

corner if the superior vertebra.

3. As within method 1 a line is drawn on the posterior border of the vertebral body and

a third line drawn on the superior border of the inferior vertebra. Translation is

calculated as the distance between the first two lines along the third line. This is

transformed into dimensionless units to compensate for magnification by expressing

the distance found as a fraction of the superior vertebra’s posteroanterior depth.

24

4. Similar to methods 1 and 3 a line is drawn on the posterior border of the vertebral

body and a third line drawn on the inferior border of the superior vertebra.

Translation is calculated as the distance between the first two lines along the third

line. This is, as with method 3, transformed into dimensionless units to compensate

for magnification by expressing the distance found as a fraction of the superior

vertebra’s posteroanterior depth.

5. A line is drawn on the posterior border of the vertebral body and a third line drawn

on the superior border of the inferior vertebra. Translation is calculated as the

distance between the first two lines along the third line.

6. Calculates the angle between two vertebrae as the angle between the inferior

border of the superior vertebra and the superior border of the inferior vertebra.

7. Lines are drawn on the posterior border of the vertebral bodies and a third line is

drawn that bisects the inter-vertebral disc space. Translation is calculated as the

distance between the first two lines along the third line

Due to the irregularity of the vertebral borders and variations in image quality, positioning,

and magnification between images, these techniques are dependent on the ability of

observers to repeatedly select a series of landmarks in an image (intra observer and inter

observer reliability). However, the reliability of this process is said to be low[59]. Further

issues arise with visualisation of the bony anatomy due to out-of-plane effects, overlapping

tissues, or the presence of surgical implants that can cause degradation of image quality or

uncertainty of landmark positions. Frobins’ method for “Precision measurements from

lumbar radiographs” [4] describes a way to measure inter-vertebral joint displacements in a

fashion which compensates for radiographic distortion and magnification and is known as

‘Distortion-Compensated Radiographic Assessment’ (DCRA). As such, according to Frobin et

al. (1996) special control of patient alignment to the radiographic source and detector is not

required [51].

25

Figure 9: Graphical representation of two lumbar vertebra undergoing extension in the lateral plane

Graphical representation of two lumbar

vertebrae undergoing extension in the sagittal

plane with a four point reference template

marked on the corner of each vertebra to

calculate the bisectrix, which is to be used as a

basis of calculation of disc height and

translation changes (using the Frobin

Method).

This protocol (shown in Figure 9) is based

on landmarks identified on the vertebral

body ‘corners’ and the mean depth of the

vertebra as defined by the average

distances between corners 1,4 and 1,3.

Subsequent measurements are defined as

a function of this mean depth, and thus

are expressed as a dimensionless number

(known as Percentage Vertebral Body

Depth or %VBD). The vertebral midlines

shown in Figure 9 are defined as lines

running through the midpoints between

corners 1-2 and 3-4 respectively.

The average gradient and y axes crossover

of the two midlines calculated for a

vertebral pair is called the bisectrix. This

should pass through the inter-vertebral

disc space

Figure 10: Graphical representation of the Frobin method of measuring translation

Using the method described in

Figure 9 a line is drawn from the

centre of each vertebra to the

coinciding bisectrix. These lines

each cross the bisectrix at 90

degrees to the bisectors’ gradient.

Translation is calculated as the

distance between where these two

lines cross the bisectrix along the

bisectrix itself.

The methods defined by Frobin et al. and outlined here are used to tackle systematic errors

in measurements caused by coupled motion (the tendency for tilting vertebrae to also

rotate in the axial plane, causing out of plane distortion). As rotation and translation usually

happen at the same time in vivo but may not change at the same rate, this method is able to

26

measure both translation and disc height changes in a way which removes the effect of

rotation on translational motion measurements and translation on disc height change

measurements. The methods by which these measurements are calculated (illustrated in

Figure 10 and Figure 12) are outlined in detail in the “Data analysis” part of the “Methods”

section of this report. In previous techniques [45] translation was measured as a function of

the angle between the posterior borders of the vertebral bodies of adjacent levels and the

distances between them (see Figure 8). These methods outlined by Shaffer et al. (1990) [45]

were prone to high errors. For example; Wall et al (1995)[63] reports errors in displacement

at the L5/S1 joint between 3% and 11 % of vertebral body depth (VBD), Danielson et al

(1988) reported an error at the same level near 15% VBD, Nachemson (1981) found a

measurement error of 4mm and Kalebo et al (1989) reported a 2.5% VBD error in

repeatability when measuring two successive radiographs taken under standardised,

identical conditions. Frobins’ method however, makes use of a bisecting line (the “bisectrix”)

as a moving reference plane allowing the motion calculated to remain independent of

motion in other planes. By expressing the motion as a function of the vertebral depth of the

superior vertebra, it is able to adjust for magnification distortion errors. As such this method

is able to measure translation within an error of 1.5% VBD. For a vertebra of 35mm depth

this measurement corresponds to an error of 0.5mm.

27

Disc height

Disc height is classically measured using radiographs. As the inter-vertebral disc has such

relative low density it is difficult to delineate in a radiograph and is generally represented as

the distance between adjacent bone landmarks. Measures of disc height using radiographs

are therefore taken as the distance between the contours of the end plate of the two

adjoining vertebral bodies. However this method is rarely accurate because the incident

radiation beam must pass through the disc space parallel to the vertebral body endplates of

the adjoining discs. While this is difficult to achieve at one single level it is almost impossible

to achieve on multiple levels in the same image, because of the divergent nature of the x-ray

beam. The result of this is that the disc spaces at the extremes of the field of view are

imaged off centre and thus slightly distorted.

In addition to this, the subject’s positioning is rarely without associated axial rotation or

lateral tilt (coupled motion) of the vertebra within the field of view. Various methods have

been attempted to counteract these difficulties. In 1977 Pope et al [50] compared 5

methods of measuring inter-vertebral disc space height in experiments locating specific

vertebral pairs in intact human cadavers and living subjects. These measurement methods

are depicted in Figure 11 of this report.

Figure 11: Depiction of 5 Disc height measurement methods evaluated by Pope (1977) [50]

28

Pope et al. [50] concluded that only those methods which corrected for radiographic

distortion were reliable (methods C and D of Figure 11) and all were limited by subject

positioning. It was found impossible to measure disc height at levels where out of plane

rotation was excessive because superimposition of two vertebral bodies made identifying

anatomical landmarks untenable. It was concluded [50] that both the ‘Farfan’ method

(Figure 11 C) and the ‘R1,R2,’ method (Figure 11 D) generated results within 0.5mm of the

actual height of the inter-vertebral disc space. Dabbs and Dabbs (1990)[49] investigated the

correlation between disc height decrease and low back pain using the methods outlined by

Pope et al. and found no correlation between disc height decrease and symptoms of back

pain. However, whether this result is due to the limited accuracy of these measurement

techniques or that disc height decrease may only be one factor in the causes of back pain

has led some authors to think this result controversial [51] and it has been proposed that

tears in the annular rings of cartilage within the disc are more relevant to pain than loss of

height alone ([64], [65]).

Figure 12: Graphical representation of the Frobin method of measuring Disc height

Frobin et al. [51] attempts

to account for radiographic

magnification and distortion

in the same way as outlined

for their translation

measurements by relating

the radiographically

measured disc height to the

mean depth of the superior vertebra. Based on the method described in Figure 12 a line is

drawn from the anterior corner of each vertebra adjacent to the disc space to the coinciding

bisectrix, these lines each cross the bisectrix at 90 degrees to the bisectrixs’ gradient . Disc

height is calculated as the sum of the length of these two lines from their origin at the

vertebral body corner to where they cross the bisectrix.

Frobin et al. [51] argues that this method has several advantages over previous methods:

1. This method solely relies on the identification of vertebral body corners as reference

landmarks. These landmarks are more prominent on radiographic images than the

contours of the vertebral endplates.

29

2. These landmarks and subsequent geometric measures (midlines and their bisectrix)

are identifiable on the image virtually free from distortions which arise from

deviations from the ideal positioning of the vertebral body pair measured which may

derive from axial or lateral bending or incident beam divergence. It follows that

independence of distortion also holds for disc height. Allowing all on a lateral view

to be measured not only those discs close to the central beam.

3. The geometric measures are derived from these objectively located landmarks

(vertebral body corners) and as such minimises subjective influence on the

calculated results.

4. Generating disc height results as a function of the mean depth of a vertebral body

eliminates the influence of radiographic magnification and variation of subject

stature.

5. By finding the perpendicular distance from the bisectrix to the anterior corners of

the vertebrae rather than measuring the direct corner to corner distance removes

the effects of translation in spondolisthesis (forward slippage) or retrolisthesis

(backward slippage) so that these measures can be taken separately and exclusive of

each other.

6. Since this method accounts for deviations or out of plane rotation during positioning

of the patient and distortion due to beam/vertebral body alignment, no special

arrangements which would require additional training have to be made when taking

these images. Furthermore, this method will work retrospectively with existing

images where exposure geometry, posture, magnification and stature are generally

unknown

30

Instantaneous Axes of Rotation (IAR)

Figure 13: a) (left) simplified outline of a vertebral body pair used to calculate IAR position between

two images b) (Right) graphical representation of IAR calculations from superimposed radiographic

films.

Many peer reviewed papers have

been published in the subject of

Instantaneous Axis of Rotation

(IAR), although they are given

many names including, Centre Of

Rotation (COR), Finite Centre of

Rotation (FCR) and Instantaneous

Centre of Rotation (ICR). Studies have been performed in the cervical spine [47, 66-68] and

in the lumbar spine [46, 69, 70] using very similar techniques. However, most authors who

have researched IARs between vertebrae have not assessed repeatability or validity. Instead

they have presented average locations in populations, usually in the sagittal plane [69, 71-

73]. In each of these studies, with the exception of McCane et al. (2005/2006)[74] [70] and

Van Mameren et al. (1992)[68] IARs are manually calculated from radiograph films. The

standard method used goes as follows;

A minimum of two images are taken of a vertebral pair which have undergone

rotation using tracing paper or similar materials to register the vertebral body

positions of both vertebrae in one image.

The outlines are moved to the second image and the inferior vertebra of the pair is

superimposed to use as a reference.

The superior vertebra as shown on the second image is outlined in its new position

in relation to the superimposed outline of the inferior vertebra.

A minimum of two arbitrary points (usually vertebral body corners) are identified on

both outlines of the superior vertebra.

A line is drawn between each of these points and its counterpart from the

subsequent image.

The midpoint of each line is found and second line drawn at right angles to each line

passing though these midpoints.

31

The position where these lines meet is the centre/axes of rotation of these two

vertebrae as they have moved.

A graphic representation of this calculation method is shown in Figure 13 ‘a’ and ‘b’ above.

While Van Mameren et al. (1992)[68] uses the above method when investigating the IAR

location of cervical vertebra in a population, in this method the calculations are performed

across 20 images collected from cineradiographic images (fluoroscopy) where the inter-

vertebral angle is greater than 7 degrees. Van Mameren et al. presents the IAR results across

multiple images in two ways; “Averaged” IAR (aIAR), defined as the mean cluster of IARs,

and “standard” IARs (stIAR) deduced from only the two extreme frames of the

cineradiographic film. In conclusion Van Mameren et al. found that Averaged IARs are more

reproducible than standard IARs. With aIARs having an average of 0.3mm standard deviation

across a population and stIARs having an average of 0.5mm standard deviation across a

population. Although the present study will not be comparable to Van Mamerens’ method

due to the fact that we are comparing both different types of vertebra and the present study

is not looking at reproducibility across a population, this study will be using a similar method

to that of aIARs to establish the validity and repeatability of this technique.

McCane et al. (2005/2006)[70, 74], on the other hand, were able to identify vertebral body

positions automatically on digitised radiographs of the lumbar vertebra using edge detection

techniques. From these outlines they identified vertebral body corner positions to account

for distortion in the same way as described above (when discussing translation and disc

height change) using the Frobin et al. method [52]. Using Matlab, a least squares derivation

of the angle of rotation and the position of the IAR are calculated

In all studies a lower limit is placed on the intervertebral angle which a segmental pair must

rotate by to be considered for IAR calculations. This is because it is nearly impossible to

measure the overall changes in vertebral body position at small degrees of rotation. The

rotational limitation given by the authors reviewed here was between 5 and 7 degrees, in

this current study a lower limit was placed at 5 degrees of rotation to be consistent with the

literature, however, during this study it become apparent that the methods used in the

current study may be able to detect IAR position at an inter vertebral angle of only 3 degrees

if there is a significant translation component involved in the inter vertebral motion.

32

Video fluoroscopy & OSMIA (Quantitative Fluoroscopy)

With quantitative fluoroscopy (QF), low dose video x-ray images are acquired of the area of

interest at a steady frame rate as the subject undergoes motion of the lumbar spine. (Due to

the shadows caused by the subjects’ ribs, images of the thoracic spine cannot be used, so

this method is limited to lumbar and cervical motion.) The motion captured in these images

is tracked either manually by a user recalculating vertebral orientations in each image, or by

an automated method which is able to follow individual vertebrae throughout the image

sequence which gives an objective output of the motion [70, 75-80].

The Anglo European College of Chiropractic (AECC)’s Institute for Musculoskeletal Research

and Clinical Implementation (IMRCI) developed a fluoroscopic method for quantifying inter-

vertebral motion called OSMIA (an Objective Spinal Motion Imaging Assessment). This can

be used to measure continuous inter-vertebral motion during trunk bending using low dose

pulsed fluoroscopy combined with automated tracking algorithms. While the literature on

spinal mechanics contains many studies of the measurement of inter-vertebral movement

from trunk end-range images, continuous motion is suggested to be a better way of

measuring spinal stability [9] due its ability to objectively display the motion patterns of

inter-vertebral joints at different stages . Furthermore, QF gives the operator access to

when the maximum range of motion of an intervertebral segment is achieved which may not

occur at the same time as maximum trunk bending.

In 2006 the Institute for Musculoskeletal Research and Clinical Implementation published a

study [81] describing the repeatability and validity of inter-vertebral motion measurement

using OSMIA in a passive recumbent protocol in the coronal plane. Figure 14 and Figure 15)

this allows the subject’s muscles to be relaxed and inactive. In this study, both inter-observer

and intra-subject repeatability were determined. At the time of this study, the outputs of

this process were the range of motion (ROM) expressed as inter-vertebral angles (IVA) in

side bending. It was found that this method for measuring inter-vertebral range of rotation

was accurate to within 1 degree, with inter-observer and intra-subject errors of fewer than 3

degrees in the coronal plane. But limitations in the imaging and processing at the time

meant that sagittal plane images could not be analysed.

33

Figure 14: Graphical representation of subjects positioning

Figure 15: Image showing subjects positioning

These images were provided

courtesy of Ortho Kinematics Inc [82]

QF uses low-dose fluoroscopy (around 0.4 mSv per single plane, i.e. sagittal) to acquire

images which makes it a relatively low-risk tool for its use in live subjects [81]. These image

sequences are post-processed for better recognition of the bones by a set of tracking

algorithms that have been developed to follow and record the positions of individual

vertebral images, then calculate their continuous displacements.

The average dose across 53 subjects who have undergone this examination protocol (20 of

which are analysed in the present study); undergoing fluoroscopic imaging in the sagittal

plane during passive motion is 404cGy.cm2 (SD 108cGy.cm2) which converts to 0.4 mSv (SD

0.11mSv) using the tissue weighting factors from the ICRP publication 36 [83]. This is

equivalent to approximately nine weeks of UK average background radiation [40]. (Where

the UK average is 2.2mSv per year: regional averages range from 1.5 - 7.5 mSv per year[40]).

As a comparison, the typical dose received during an x-ray examination of the Hip is 0.3mSv,

equivalent to 7 weeks background radiation or additional lifetime risk of 1 in 67,000 fatal

cancer per examination. An x-ray examination of the thoracic spine is 0.7mSv (4 months

background radiation or 1 in 30,000 lifetime risk of fatal cancer per examination) and an

examination of the lumbar spine is 1.3mSv (7 months background radiation, 1 in 15,000

lifetime risk) [40].

The fluoroscope captures X-rays pulsed at 15 frames per second. These pass through the

patient as they undergo controlled motion of around 15 seconds duration. Flexion and

34

extension are imaged as separate sequences, and each sequence contains approximately

230 individual frames.

Since IMRCIs’ 2006 publication both the method of acquisition and the algorithms used to

calculate inter-vertebral movement have been improved (a significant proportion of the

algorithms by myself) to increase the automation, speed and resolution of the motion

calculations. This present project breaks new ground by calculating the validity and intra and

inter-observer repeatability of this improved method to measure commonly used indices of

spine stability (translation, disc height, plus the positions of the IARs) between adjacent

vertebrae, at sub-second intervals using patented tracking programs in the Matlab

environment, and Frobins’ method of landmark identification outlined in the Measurements

from radiographs and Data analysis sections of this report.

Repeatability and validity:

There is little material to be found when searching the literature for ‘repeatability’ and

‘validity’ studies of spinal motion measurement. There is also little uniformity. Inter and

intra observer repeatability have been expressed in a variety of units and ‘repeatability’,

‘agreement’ and ‘reliability’ although different concepts, [84] are often used

interchangeably.

‘Validity’ refers to accuracy against a reference, or ‘gold’ standard. This is generally reported

as the root-mean square of the differences between observed and reference values [2-6].

Both ‘reliability’ and ‘agreement’ relate to measurements which are reproducible or not in

test-retest situations. ‘Agreement’ gives the measurement error, expressed as the standard

deviation (SD) of test-retest measurement differences, while ‘reliability’ measurements are

related to the variability between subjects[4, 5] and are expressed as intra-class correlation

coefficients (ICC).

This study used the OSMIA technology to assess the inter-vertebral motion of subjects in the

same recumbent positions[29]. The exclusion of muscle activity makes it possible to assess

the visco-elastic behaviour of the passive holding elements which has been a problem in

previous studies.

35

Methods:

For this study validity and reliability of the OSMIA (Objective Spinal Motion Imaging

Assessment) system were measured using data collected from two phantom calibration

models as well as data collected from 20 volunteer subjects. The validity study used one of

the calibration models from the 2006 study which allowed rotation only [81] and a second

bespoke model provided the reference standard for anterior-posterior translation.

Materials:

Validity:

Two calibration models consisting each of a pair of human lumbar vertebrae were imaged

using a Siemens Avantic C-arm fluoroscope during known motion both in the sagittal and

coronal planes. The reference data from the models were compared to the motion

calculated from processing the images

Fixed centre of rotation calibration model (model 1)

Figure 16: Fixed rotation point calibration model

A calibration model built for a

previous study [81] was used as it has a fixed

centre of rotation at the centre of the disc

space between the two vertebrae (Figure 16).

Eighteen degrees of rotational motion was

induced in this model using a rotating disk on

a vertical X-ray bucky (Atlas Clinical Ltd -

Lichfield, UK).

Due to the known centre of rotation we know the translation of the vertebra is zero. The

disc height change was mathematically calculated (outlined in Appendix 2) from the angles

acquired from the motion and vertebral body dimension measurements (the latter taken

using electronic callipers (Axminster Instruments Ltd.)). The centre of rotation, visible as a

fixed point on the fluoroscopic images, was used along with the measured distance (using

electronic callipers (Axminster Instruments Ltd.)) of the joint from the superior-posterior

corner of the inferior vertebra verify the IAR.

36

Translating calibration model (bespoke model 2)

Figure 17: Translation calibration model

Translation calibration model positioned in front of the motion control apparatus

The second model is depicted above in Figure 17 and also comprises of two human lumbar

vertebrae. The inferior vertebra was fixed to an acrylic block and unlike the first model a

groove was cut into the inferior vertebral body which allowed a remote controlled arm to

slide the superior vertebra over the inferior vertebrae from anterior to posterior and back

again. This motion was controlled by a servo motor which controls translational motion

concurrently with measured angular rotation.

The superior vertebra of the pair was fixed by a universal joint allowing both translation and

rotation to occur at the same time, or to control these individually. The translation arm was

driven by a motor and sensor apparatus connected to a laptop computer to deliver and

measure translation with a measurement precision of 0.01mm (Arduino Software Ltd.). The

algorithms writhen in the Arduino environment can be seen in Appendix 3.

The reference translation of this model was determined as the percentage of the anterior-

posterior depth of the upper vertebral body, by measuring the mean depth of the upper and

lower end-plates with an electronic calliper (Axminster instruments – spatial resolution +/-

Tilt sensor

Vertebra connected

by universal joint and

translator arm

Rotating beam and

connector rod

Actuator motor

37

0.02mm). This was used as the denominator to divide the translation obtained during the

testing to obtain this percentage.

Figure 18: Experimental set up

The models were mounted on a rigid base

with their vertebral centres positioned

approximately 15cm from a rotating disk on

a vertical X-ray bucky (Atlas Clinical Ltd -

Lichfield ,UK) driven by a controller using

bespoke software (Daqfactory V5C –

Heatherose Electronics Ltd – Newark, UK).

To rotate the model at a standard rate and

range, the rotating disc was connected to

the upper vertebra via a transverse arm

from which a rod projected downward and connected to the superior vertebra (Figure 18).

This apparatus could deliver precise translation and rotation in flexion-extension.

Experimental set up of the fixed centre of

rotation calibration model With C-arm in place

38

Procedures

Validity:

Image sequence acquisition

Figure 19: A Siemens Arcadis Avantic portable C-arm fluoroscope, Siemens Gmbh, Germany.[85]

A Siemens Arcadis Avantic portable C-arm fluoroscope (Siemens Gmbh, Germany Figure

19[85]) was used to acquire the images, with a soft tissue substitute (a sample of ground

bovine meat for the translation model and bag of porcine sausages on the fixed centre of

rotation model ) interposed between the X-ray source, the model and the image intensifier

to impose image degradation due to soft tissue scatter. Each model in turn was aligned with

the primary X-ray beam passing through the universal joint.

The calibration models were placed at an object detector distance to so that the images

acquired displayed a vertebral body size approximately the same size as those seen when

imaging in vivo. When imaging volunteer subjects, the detector is placed as close as possible

to the volunteer without impinging on subjects’ movement, this reduces magnification and

increases the number of vertebrae in the field of view which allows positional data to be

calculated for as many vertebral bodies as possible throughout the motion sequence.

However the use of the Frobin method of ‘Distortion-Compensated Radiographic

Assessment’ (DCRA) means it is not necessary to account for deviations in exposure

geometry and, magnification so there is no need to measure the source to object neither

(SOD) distance nor the object to image receptor (OID) distance.

Images were transferred from the fluoroscope via a USB Flash drive to a server ready for

analysis.

39

Repeatability:

Subject imaging

Image sequences from subjects were obtained from an ongoing research studies in which I

participated. This study received favourable ethical opinion from the National Research

Ethics Service approval (REC number 09/H0502/99). 20 subjects were randomly sampled (by

drawing lots from a hat) from a population of 53.

In this protocol subjects’ are positioned on the table lying on their side with their torso

stabilised while their hips and pelvis are on the lower part of the table which moves through

a controlled arc of up to 40degrees each way. The superior anterior corner of the 4th lumbar

vertebra was aligned with the fulcrum of the table and the fluoroscopic C-arm was

positioned so the 2nd lumbar vertebrae through to the sacral-lumber vertebra (L2-S1) would

be in the field of view throughout the image sequence as the subject was moved. The

subject was taken to the full range of the motion table (40°) in a practice run to ensure

comfort and compliance, and to also relax the muscles and thus prevent any tensing. During

this run, a low dose image (fluoro-grab) at the end of range was obtained to ensure out of

plane rotation had not occurred and L2-S1 remains in the field of view. Once the range of

table motion had been set the QF began. Images were acquired at 15 frames per second on

the passive motion table which was designed to move the subjects’ legs and hips in a 40

degree arc in each direction of flexion-extension which were imaged separately. There were

typically 230 individual DICOM images in each fluoroscopy sequence.

The patients were positioned with their knees and hips bent - effectively placing them into

partial flexion by flattening the lumbar lordosis, to allow stability during the passive motion.

(Figure 14 and Figure 15)

40

Image analysis;

Image enhancement

The Images were enhanced using graphic user interfaces (GUIs) written or adapted

by the author within the MatLab environment during the OSMIA development at IMRCI. The

initial enhancement GUI shown in Figure 20 gives the user a choice of 5 standard

enhancement stacks which can be altered further to gain the best possible edge

enhancement of the images to improve tracking quality.

Figure 20: Image enhancement GUI

These enhancements allow for easier

identification of the vertebral bodies,

which are outlined in the first image of

the sequence by a skilled observer.

Further enhancements which highlight

the vertebral body edges facilitate the

algorithms to identify the vertebral

body positions in subsequent images.

Manual registration of vertebral bodies

in the first image is then followed by automatic vertebral tracking in the subsequent frames

[25].

41

Analysis and image registration

Following edge enhancement of the images, individual vertebrae in each image

sequence were tracked by patented pixel recognition and cross correlation software written

in the MatLab environment. This involves an observer marking the borders of each vertebra

with two templates (see Figure 21).

Figure 21: GUI for manually identifying vertebral bodies in the first image of a sequence

The first template is a snug outline of the vertebral body. This is used to track the position of

the vertebra as it moves through each image. Values for the angular rotation of the vertebra

are taken from the positions of these templates. The second template is a four point

template which marks the four corners of the vertebra. These templates are called the

reference templates and are used in the calculation of other vertebral motion parameters.

This is done using the ‘Frobin method’ [52] which describes translation, disc height and IARs

as a function of the four corner positions of each vertebrae in measurement units as defined

by the average vertebral body depth of the superior vertebra.

42

Data analysis

Frobins’ method shown in Figure 9, a four point reference template positioned on each

vertebra; these “reference templates” model the dimensions of the vertebral body. How this

is done is outlined in the “Measurements from radiographs” –“Translation” section of this

reports Background. An example of this can be seen in Following edge enhancement of the

images, individual vertebrae in each image sequence were tracked by patented pixel

recognition and cross correlation software written in the MatLab environment. This involves

an observer marking the borders of each vertebra with two templates (see Figure 21).

Figure 21.

Translation Calculations

Figure 10 (Background) describes the method in which translation is calculated; by finding

the mean of the 4 corner positions of each vertebra it is possible to derive the centre

position of each vertebral body. A line is then calculated which passes perpendicular to the

bisectrix from these centre positions of adjacent vertebrae. As the gradient of the bisector is

known (mB), any line which lies perpendicular to it must have a gradient equal to its

negative inverse

Equation 1

.

Knowing the equation of a straight line in Cartesian co-ordinates;

Equation 2

When two lines cross perpendicular to each other, co-ordinates of this crossover position

can be calculated when the gradient and crossover of one line is known and a co-ordinate

that the second line passes through is also known. This can be expressed by the following

equations (See Appendix 1 for Derivation)

Equation 3 Equation 4

&

43

This method can be performed to find the co-ordinates at which lines from each vertebral

centre meets the bisectrix at 90 degrees. The distance between these two points represents

translation in this study.

44

Equation 5 Equation 6

Disc height calculations

Figure 12 (Background) describes the method by which anterior disc height is calculated.

Lines are drawn between the anterior corners closest to the disc space for each vertebra and

the bisectrix. These lines as before pass through the bisectrix perpendicular to it, using the

equations derived above the points at which theses lines intersect the bisectrix can be

calculated. Where x1 and y1 are the coordinates for the corner used x' and y' are the

corresponding coordinates where this line passes through the bisectrix at 90 degrees.

Frobins’ method describes anterior disc height as the sum of the lengths of these two lines.

This method is used as it removes the effects of translation on the disc height change when

compared to a direct corner to corner measurement.

45

IAR calculations

Figure 13 (Background) demonstrates how IAR positions can be drawn on a plain x-ray

image. Previous studies using plain films use two images of a vertebral pair which have

undergone rotation using tracing paper or some other medium to register the vertebral

body positions of both vertebrae in one image. Then the outlines are moved to the second

image and the inferior vertebra of the pair is superimposed to use as a reference. Then the

superior vertebra is outlined in its new relative position.

Within the Matlab environment the four corner reference template positions for two

adjacent vertebrae are taken and re-positioned so that the inferior vertebras position is

superimposed. From these coordinate positions, the axis of rotation between the two

images is calculated by finding the least squares solution between each of the four corners

and their partners from the second image. The positions at which each of these least

squares solutions meet is taken as the IAR for those two vertebrae between those two

images. The axis of rotation can then be displayed in one of three ways;

IAR position on the first image of the image pair used

IAR position on the second image of the image pair used.

Graphical user interface displaying the IAR positions relative to the inferior vertebra

in a pair

46

Figure 22: Various depictions of IAR positions

a (top left), represents the IAR

position on the first image of the

image pair used.

b (top right), represents the IAR

position on the second image of the

image pair used.

c (bottom left) & d (bottom right),

represents the IAR the position is

relative to the inferior vertebra in a

pair.

Results for this report are given in terms of the IAR position relative to the inferior vertebra

in a pair. As in Figure 22 c, the position of the IAR can be identified as a function of the four-

corner template on the inferior vertebra. The superior-posterior corner of the inferior

vertebra is taken as the origin (O) for this reference field where the X-axis is along the

template points on the vertebras’ superior border and the Y-axis is perpendicular to the X-

axis and passes though the origin. Figure 22 d, shows the IAR position in terms of the

reference field shown in Figure 22 c. The unit of distance used is the proportion of the

average vertebral body depth of superior vertebra (due to the non uniform shape of the

sacral template) where the origin of this co-ordinate system is the anterior-superior corner

of the inferior vertebra.

For example, in Figure 22d, the IAR position is depicted at co ordinates (15% X,-10% Y) as a

percentage of vertebral body depth (%VBD). An example of how these types of results may

be depicted using one of the subjects from the present study is shown in the following three

figures, where the IAR position for this level L2-L3 is 39%VBD in the X direction and 10%VBD

in the Y direction from the origin (superior-posterior corner of the inferior vertebra) .

47

Figure 23: IAR position on the first image of the image pair used

Figure 24: IAR position on the second image of the image pair used.

Figure 25: GUI displaying the IAR positions relative to the inferior vertebra in a pair

48

IAR positional data are calculated between any two template positions where the inter-

vertebral angle is greater than 5 degrees. (As IVA (inter vertebral angle) decreases the

variation in IAR position increases. This is a systematic error due to the way in which the IAR

positions are calculated.)

As IAR positional data can be found between any image frames if the 5 degree rotation

condition is met, it was decided to measure IAR between the first frame of the image

sequence and the image frame where angular rotation was at its maximum (+/- 0.5 degrees)

and then calculate the average IAR position found in all subsequent frame pairs. The limit of

+/- 0.5 degrees was selected as this is the increment through which the tracking templates

rotate when calculating vertebral body position within each image. These results are

presented as the average position of the IAR in X and Y co ordinates [68].

Data extraction and tracking verification

As these image sequences contain on average over 200 images, statistical analysis of the

whole motion pattern made by each segment for each subject is unfeasible. Therefore, the

translation and disc height results for this study are presented in terms of their end-ranges

of motion (ROM) expressed as a percentage of average vertebral body depth of the superior

vertebra (%VBD).

Inter-vertebral range of motion data from these studies were displayed graphically as the

change in translation or disc height from the initially marked image. In

49

Figure 26 are two graphs which demonstrate how these data may be viewed. The X-axis of

each graph refers to the image numbers at which each range result was acquired. The Y axis

is the change in position described as a fraction of the superior vertebral depth (VBU).

Each vertebra was marked 5 times (Test A-E). The scatter shown in each line contains the

positions found for all vertebral pair tests. (For example L2’s test A to L3’s Test A, L2’s test A

to L3’s Test B, etc ...). In total, as each vertebra was marked 5 times. This generated 25

positional values for each inter-vertebral motion type for each level as is shown in

50

Figure 26 as the scatter about the average position. As described in the Analysis and section

of this report, these results are reviewed by the user and any aberrant results were

removed.

51

Figure 26: Translation (left) and Disc Height change (right) of an inter-vertebral segment undergoing

motion.

(Left) Translation of L2 over L3 during extension. Where posterior translation of the superior vertebra

over the inferior is expressed as the negative change in position.

(Right) Disc Height change of the L2-L3 inter vertebral disc during extension of the lumbar spine. An

increase of anterior disc height is shown here as positive movement.

IAR was expressed in terms of X and Y positional data (as defined in the

52

IAR calculations section of this methodology Figure 22) between end range of rotation

images and the first image in a sequence. End range of rotation images were defined as the

images/reference template positions where the relevant inter-vertebral segment reached its

end range of rotation ±0.5 degrees. (Repeatability and validity of rotational motion of inter-

vertebral pairs have been verified for this technology in previous studies [81] which found an

RMS difference between reference and computed inter-vertebral angles in the same model

as used in this study (model 1) of 0.52 degrees for flexion-extension and an RMS inter-

observer variation of 1.94 degrees.)

Validity Study:

This procedure was repeated 10 times for each calibration model. The fixed axis of rotation

of the first calibration model meant that translation was zero thus the IAR calculated was in

a fixed position throughout the motion sequence. Furthermore, the disc height ranges can

be calculated as a function of the range of rotation that the model was put through and of

the dimensions of the model (these calculations are outlined in Appendix 2). By measuring

these ranges and dimensions with electronic callipers and the average body depth of the

superior vertebra in the pair these values can be expressed as vertebral body units (VBUs)

where 1 VBU is the average vertebral body depth of the superior vertebra in a pair (or %VBD

where 1VBU = 100%VBD). The second translating calibration model’s dimensions were also

measured with electronic callipers and the distance by which the superior vertebra moved

was known as a function of how far the translation control motor arm moved. The known

ranges of movement for each model was compared those calculated from the fluoroscopic

images within the Matlab environment.

Repeatability studies:

Two observers separately analysed the 40 image sequences (2 sequences per subject for 20

subjects). One observer (Observer A) performed this analysis twice to generate data used in

the intra-observer study. Data collected from each analysed sequence and verified by the

observer who originally performed that analysis. If more than 2 tests were deemed to not

have tracked properly a re-test was performed per vertebra. These retests would constitute

re-enhancements and/or remarking of tracking templates from greater than 5 images before

tracking failed. It is impossible to bias results between observations, partially due to the

large amount of data produced. This would make it impracticable to match results mainly

53

due to the observer having no control over how the positioning the initial templates would

influence the results. Due to the time constraints of this project only one retest was

performed per sequence when needed. This unfortunately meant that some results were

unobtainable and thus could not be used in the reliability studies. A greater time frame

would have allowed each observer to re-place templates which had initially failed gaining

more results.

Intra-observer study;

One observer (Observer A) generated a set of results for each fluoroscopy sequence. Once

completed these sequences were tracked a second time by the same observer. The results

of the two analyses were compared using the statistical method described in the ‘Statistical

analysis’ section of this report to calculate intra-observer repeatability in terms of

agreement and reliability [84].

Inter-observer study;

A second observer (Observer B) generated a set of results for the same sequences as

Observer A. These were compared to the first of the two result sets that were marked up in

the Intra-observer study. The results were compared using the statistical analysis methods

described in the ‘Statistical analysis’ section of this report.

Statistical analysis

The validity for all parameters was expressed as the root-mean-squares (RMS) of the

differences between reference and observed values over 10 measurements per parameter.

Reliability was expressed as agreement within and between observers by the standard error

of measurement (SEM) [84] and the 95% limits of agreement (LOA) between observation

sets [6]. Reliability between data sets was expressed as the intra-class correlation

coefficients of test-retest data and their 95% confidence intervals [86, 87], [88].

SEM = SD difference/ √2 to 95% limits of agreement

95% LOA = x ̄± 1.96 x SD difference (Bland-Altman-Plot)

ICC = SD1/ (SD1 + SD difference)

intra-observer: 1-way random effect

inter-observer: 2-way random effect

54

95% CI = x ̄± 1.96 x SD/√n (x ̄= sample mean, SD=Standard deviation n= number of subjects)

55

Results:

Validity:

Table 1 shows the root-mean--square (RMS) difference between the reference and

computed inter-vertebral translation and disc height range. The average vertebral body

depth was 28.77mm for the fixed centre of rotation model (model 1) and 34.66mm for the

translating model (model 2). Results were standardised by expressing them as a percentage

of the superior vertebra’s average body depth. These values are also displayed as equivalent

millimetres (eqv mm). Equivalent millimetres are derived from an average lumbar vertebral

body depth of 35mm [51]

For translation, the RMS difference between the computed and reference values was around

0.1 mm (0.358%VBD) for the model with a fixed centre of rotation (Model 1). For the

translating model (Model 2), where the upper vertebra was moved though half the depth of

the lower one, this discrepancy was of the order of 2 mm (6.237 %VBD).

For disc height, the discrepancy between computed and reference values was less than 1mm

for both models, also indicating acceptable accuracy given that an average disc height is in

the region of 10mm.

Table 1: Accuracy of determination of inter-vertebral displacements for translation and disc height

motion and X and Y IAR locations in two calibration models*

Root mean Square differences between reference and computed measures - 10 observations

Model 1 Model 2

measure RMS (%VBU) RMS (%VBU)

Translation 0.358 6.237

Disc Height 2.282 0.051

xIAR 0.021 N/A

yIAR 1.13 N/A

* All units are expressing in % vertebral body depth

56

For IAR position using the fixed centre of rotation model (Model 1), the x IAR discrepancy

was very small and the y IAR discrepancy only around 0.3mm (derived from its measured

average vertebral body depth of 28.77mm), indicating excellent accuracy (Table 2) with the

greatest RMS difference being 0.66mm in disc height change.

Table 2: Calibration study; RMS difference between measured values and those calculated in the

Matlab environment, expressed in mm

Model 1 Model 2

measure RMS (mm) RMS (mm)

Translation 0.103 2.162

Disc Height 0.657 0.018

xIAR 0.006 N/A

yIAR 0.325 N/A

Model 2 demonstrates a lower accuracy in translation than its fixed centre of rotation

counterpart. This may be due to the input motion of the motor controlled translation arm

not being in line with the plane in which translation is measured. By way of explanation,

there is a known 4%VBD decrease in disc height though the motion (measured using

electronic callipers) due to the construction of the Model not being sufficiently aligned.

Table 3 expresses the same results as Table 1 and Table 2 in terms of equivalent millimetre

(eqv mm) derived from the assumed average vertebral body depth of 35 mm. This contrasts

the values derived from true range (in millimetres) to those expressed in equivalent

millimetres.

Table 3: Calibration study; RMS difference between measured values and those calculated in the

Matlab environment, expressed in equivalent mm

Model 1 Model 2

measure RMS (eqv mm) RMS (eqv mm)

Translation 0.125 2.183

Disc Height 0.799 0.018

xIAR 0.007 N/A

yIAR 0.396 N/A

57

Figure 27: Radiographic images of models 1 and 2 displaying the computer generated IAR, anterior

disc height and translation results

58

Repeatability:

Inter-observer and intra-observer agreement was determined using; Standard Error of

Measurement (SEM), Bland-Altman plots,, 95% limits of Agreement (95% LOA) expressed as

%VBD., The reliability of measurements was expressed as intraclass Correlation Coefficients

(ICC), which are dimensionless numbers, and their 95% CIs The Intra-observer results for

pooled intervertebral levels for translation and disc height change are shown in Reliability

(ICC) analysis can be graded as; slight (0.0-0.20), fair (0.21-0.40), moderate (0.41-0.60),

substantial (0.61-0.80), and almost perfect (0.81-1.00) [89]. The average ICC of intra-

observer flexion and extension translation indicated excellent reliability (ICC=0.803) and all

results acquired for all levels in both bending modes achieved a moderate, good or excellent

grade ranging between 0.533 and 0.988 (Appendix 4 Table 10 and Table 11). The best result

for ICC was achieved in flexion at L2-L3 (0.988) and the least favourable result was also

achieved in flexion at L3-L4 (moderate) (0.533).

The overall 95% CI range shows good agreement for both inter and intra observer. However,

when compared by inter-vertebral level, as shown in Appendix 4 Table 10 and Table 11, the

agreement decreases with relation to the number of mutual observations (n) the worst

results appearing at Intra-observer L5-S1 for extension (-0.344 - 0.910). The confidence

interval width for L5-S1 extension, despite the small sample, may indicate a problem with

reliability due to image quality at this level.

59

Table 4 to Table 7.

The results below are given in terms of SEM 95%, LOA and ICC (95% CI) for all levels. Results

per level are also displayed in Appendix 4.

Translation:

Standard Error of Measurement (SEM) for translation results in both the flexion and

extension bending directions. Reliability (ICC) analysis can be graded as; slight (0.0-0.20), fair

(0.21-0.40), moderate (0.41-0.60), substantial (0.61-0.80), and almost perfect (0.81-1.00)

[89]. The average ICC of intra-observer flexion and extension translation indicated excellent

reliability (ICC=0.803) and all results acquired for all levels in both bending modes achieved a

moderate, good or excellent grade ranging between 0.533 and 0.988 (Appendix 4 Table 10

and Table 11). The best result for ICC was achieved in flexion at L2-L3 (0.988) and the least

favourable result was also achieved in flexion at L3-L4 (moderate) (0.533).

The overall 95% CI range shows good agreement for both inter and intra observer. However,

when compared by inter-vertebral level, as shown in Appendix 4 Table 10 and Table 11, the

agreement decreases with relation to the number of mutual observations (n) the worst

results appearing at Intra-observer L5-S1 for extension (-0.344 - 0.910). The confidence

interval width for L5-S1 extension, despite the small sample, may indicate a problem with

reliability due to image quality at this level.

60

Table 4 and Table 5 suggest good agreement, with the greatest measurement error being

1.958%VBD (0.69eqv mm). The largest error found per level was found at L5-S1 in extension

with an intra-observer error of 3.260%VBD (1.14eqv mm) (Appendix 4 Table 10). In both

flexion and extension, L5-S1 produces the greatest SEM.

The best agreement (the smallest 95% LOA range) for all levels was achieved in the Intra-

observer study of flexion -3.943 to 3.967 %VBU (-1.38 to 1.39eqv mm) and the least

agreement (the biggest 95% LOA range) in the Intra-observer extension study -5.855 to

4.998 %VBU (-2.05 to 1.75eqv mm) (Reliability (ICC) analysis can be graded as; slight (0.0-

0.20), fair (0.21-0.40), moderate (0.41-0.60), substantial (0.61-0.80), and almost perfect

(0.81-1.00) [89]. The average ICC of intra-observer flexion and extension translation

indicated excellent reliability (ICC=0.803) and all results acquired for all levels in both

bending modes achieved a moderate, good or excellent grade ranging between 0.533 and

0.988 (Appendix 4 Table 10 and Table 11). The best result for ICC was achieved in flexion at

L2-L3 (0.988) and the least favourable result was also achieved in flexion at L3-L4 (moderate)

(0.533).

The overall 95% CI range shows good agreement for both inter and intra observer. However,

when compared by inter-vertebral level, as shown in Appendix 4 Table 10 and Table 11, the

agreement decreases with relation to the number of mutual observations (n) the worst

results appearing at Intra-observer L5-S1 for extension (-0.344 - 0.910). The confidence

interval width for L5-S1 extension, despite the small sample, may indicate a problem with

reliability due to image quality at this level.

61

Table 4 and Table 5). However, per inter-vertebral level, the best agreement (the smallest

95% LOA range) was achieved in inter-observer L2-L3 extension (-1.5973 to 1.151%VBU) and

the least agreement (the biggest 95% LOA range) was obtained in L5-S1 intra-observer

extension (-10.791 to 7.282 %VBU) (Appendix 4 Table 10 and Table 11). The L5-S1

disagreement between observations could therefore reach 17% of VBD, which is in the

region of the cut-off for abnormality. This indicates that improvement is necessary in

measurement at this level, where in the lateral view, super imposition of the pelvis impede

the tracking of L5-S1. The Bland-Altman plots used to calculate 95% LOA can be seen in

Appendix 5.

Reliability (ICC) analysis can be graded as; slight (0.0-0.20), fair (0.21-0.40), moderate (0.41-

0.60), substantial (0.61-0.80), and almost perfect (0.81-1.00) [89]. The average ICC of intra-

observer flexion and extension translation indicated excellent reliability (ICC=0.803) and all

results acquired for all levels in both bending modes achieved a moderate, good or excellent

grade ranging between 0.533 and 0.988 (Appendix 4 Table 10 and Table 11). The best result

for ICC was achieved in flexion at L2-L3 (0.988) and the least favourable result was also

achieved in flexion at L3-L4 (moderate) (0.533).

The overall 95% CI range shows good agreement for both inter and intra observer. However,

when compared by inter-vertebral level, as shown in Appendix 4 Table 10 and Table 11, the

agreement decreases with relation to the number of mutual observations (n) the worst

results appearing at Intra-observer L5-S1 for extension (-0.344 - 0.910). The confidence

interval width for L5-S1 extension, despite the small sample, may indicate a problem with

reliability due to image quality at this level.

62

Table 4: Intra-observer repeatability of translational motion measurement for 4 inter-vertebral levels

(L2-L3, L3-L4, L4-L5, and L5-S1)

Within Observers

Direction n Agreement (% Vertebral Body Depth Reliability

SEM 95% Limits of Agreement Intra Class Correlation

Flexion 49 1.427 -3.943 to 3.967 0.859 (0.751 - 0.920)

Extension 40 1.958 -5.855 to 4.998 0.782 (0.589 - 0.884)

Table 5: Inter-observer repeatability of translational motion measurement for 4 inter-vertebral levels

(L2-L3, L3-L4, L4-L5, and L5-S1)

Between Observers

Direction n Agreement (% Vertebral Body Depth Reliability

SEM 95% Limits of Agreement Intra Class Correlation

Flexion 48 1.674 -4.297 to 4.985 0.806 (0.654 - 0.891)

Extension 33 1.736 -5.575 to 4.051 0.861 (0.718 - 0.931)

63

Disc height change:

Standard error of measurement (SEM for disc height motion results in both the flexion and

extension bending directions for intra- and inter-observer studies (Table 6 and Table 7) seem

to suggest good repeatability with a greatest error being 3.907%VBD (0.69eqv mm).

While repeatability is good both when displayed overall and by inter-vertebral level there is

a general decrease of agreement when results are compared by inter-vertebral levels where

the number of mutual observations (n) is low. The overall agreement for Inter-observer

(Table 7) extension is quite large (-12.380 to 9.277) due to low agreement at L5-S1 of -23.53

to 13.50 %VBD (Appendix 4 Table 12) while the next lowest agreement for inter observer

Extension is 2.15 to 1.671 %VBD at L4-L5.

This is also reflected in the ICC (95% CI) results where, while repeatability remains good or

better, the agreement (95% CI) is low due to very large ranges at singular levels. The

reliability of intra-observer flexion disc height change was poor at some inter-vertebral

levels. Where 2 levels (L2-L3 and L4-L5) produced low ICCs and large confidence intervals

this may also be due to the low number of available results for each level (n=4 and 5

respectively).

Overall, these results depict good-excellent agreement and reasonable reliability at most

levels and directions for disc height change.

64

Table 6: Intra-observer repeatability of disc height motion measurement for 4 inter-vertebral levels

(L2-L3, L3-L4, L4-L5, and L5-S1)

Within Observers

Direction n Agreement (% Vertebral Body Depth Reliability

SEM 95% Limits of Agreement Intra Class Correlation

Flexion 21 0.755 -1.982 to 2.202 0.531(-0.138 - 0.808)

Extension 46 1.113 -3.167 to 3.006 0.895 (0.811 - 0.942)

Table 7: Inter-observer repeatability of disc height motion measurement for 4 inter-vertebral levels

(L2-L3, L3-L4, L4-L5, and L5-S1)

Between Observers

Direction n Agreement (% Vertebral Body Depth Reliability

SEM 95% Limits of Agreement Intra Class Correlation

Flexion 15 0.361 -0.979 to 1.024 0.866 (0.600 - 0.955)

Extension 44 3.907 -12.380 to 9.277 0.609 (0.284 - 0.787)

65

IAR

Due to the low number of mutual trackings of individual vertebral pairs between observers

that reached a rotational range of greater than 5 degrees (the lowered limit cut off defined

for this study) the use of the statistical calculation used in translation and disc height motion

would not be representative here. Therefore, RMS difference between average IAR locations

in the x and y co-ordinates of the reference field have been displayed below in Table 8 and

Table 9 (by level in Appendix 4 Instantaneous axes of rotation

Table 20 and Table 21).

Table 8 and Table 9 below show that overall, both inter and intra observer agreement is

very good with a greatest variance at Inter- observer extension of 2.08 %VBD giving a sub

millimetre accuracy of 0.728eqv mm.

A substantial displacement of the IAR from its normal position in the posterior 1/2 of the

disc space ([90] [91] [46]) would begin at around 17.5mm, placing the reaction force of

weight-bearing (if IAR is found posteriorly) close to the facet joints and if IAR is found to

move inferiorly, (in the inferior vertebral body) this denotes a combination of translation

with rotation. These results indicate repeatability that could detect this and can therefore

be considered acceptable.

66

Table 8: Intra-observer repeatability of determination of X and Y IAR location for 4 inter-vertebral

levels (L2-L3, L3-L4, L4-L5, L5-S1)* (Root-Mean Square difference between observations)

Within Observers

Direction n IARx (%VBD) IARy (%VBD)

Flexion 30 1.09 0.15

Extension 21 1.63 1.75

* Expressed as the distance from the posterior- superior corner of the inferior vertebra in

each pair in percentage units of vertebral body depth

Table 9: Inter-observer repeatability of determination of X and Y IAR location for 4 inter-vertebral

levels (L2-L3, L3-L4, L4-L5, L5-S1)* (Root-Mean Square difference between observations)

Between Observers

Direction n IARx (%VBD) IARy (%VBD)

Flexion 24 2.08 0.85

Extension 20 0.55 1.63

* Expressed as the distance from the posterior- superior corner of the inferior vertebra in

each pair in percentage units of vertebral body depth

67

Discussion;

This study shows that it is feasible to make accurate and reliable measurements of

translation, disc height motion and Instantaneous axis of rotation with quantitative

fluoroscopy (QF) of the lumbar spine in flexion and extension using the OSMIA technique.

No prior studies have measured continuous motion in vivo using these parameters, nor have

they assessed the accuracy or observer repeatability of continuous motion sequences.

Translation

Shaffer et al (1990) [45] measured the consistency and accuracy of 7 different methods for

measuring sagittal translation using plain film x-rays. It was found that using plain film x-rays

as a basis for diagnosing instability can often lead to errors in classification due to

magnification or distortion within the image field. Morgan and King [92] described the most

accurate and repeatable of the seven methods outlined by Shaffer et al., (Figure 8.2,) finding

the translation between two vertebra using plane film x-rays by drawing a line along the

anterior border of the inferior vertebra and finding the perpendicular distance from this line

to the inferior-anterior corner of the superior vertebra. While this was shown to produce the

fewest classification errors it is the reverse where the posterior border contains the

reference line that seems to be recommended most frequently (Figure 8.4) [93-96].

In this study, with the exception of L5-S1, the measurement error for translation (SEM) was

generally below 2%VBD (0.7eqv mm) for all levels and directions and is comparable to that

of static in vivo methods of measuring translation. The maximum SEM is found with inter-

observer extension L5-S1 of 3.26%VBD (1.14eqv mm). Abbott et al, (2006) [97] using the

Frobin method [51] , reports a repeatability coefficient of 0.046 vertebral body units

(4.6%VBD or 1.61eqvmm) which is comparable to Frobins results of 0.034 vertebral body

units (3.4%VBD or 1.19eqvmm). The level of repeatability of this study has been improved by

averaging. The tracking of inter-vertebral motion is typically repeated 5 times, with 5

separate templates which makes it adequate for normative and clinical studies. The error

found in this study while measuring translation against a reference standard (models 1 and

2) was 0.36 to 6.237%VBD (0.13 to 2.18eqv mm) respectively.

Clinically the most widely used method for expressing translation is the traditional

Meyerding Method [98], using a calculation of the anterior posterior body depth of the

superior vertebra (%VBD) or describing the distances in millimetres. These values are usually

68

gained from direct manual measurements from radiographic films using pencils and rulers

[97] [51] [46].

The present study generally indicates high reliability (ICC) in translation above 0.80 for most

the levels with few exceptions; intra-observer extension at L5-S1 and inter-observer

extension L2-L3 and L5-S1 where the ICC’s for these sequences show moderate (L5-S1 and

L2-L3 inter-observer extension) and fair (L5-S1 intra-observer extension) reliability.

With these exceptions there seems to be no great difference between the repeatability

parameters of inter- vs. intra –observer studies, this may be due to the small number of

levels available for analysis or an indicator that once an observer is sufficiently trained the

results produced by the methods used are reliable. Repeating this study with a bigger

sample size would provide the answer.

Disc height

Few papers addressing the reliability of measuring inter-vertebral disc height were found

and of those that were, few papers both expressed their results in terms of measurement

errors (SEM) or described how these measurements were mathematically obtained. Frobin

[52, 99] whose method was the basis of this study’s vertebral measurements, in his 1997

paper [52] explains the method for a “precision measurement of disc height, vertebral

height and sagittal plane displacement (translation) from lateral radiographic views of the

lumbar spine” and finds an overall error, averaged across all inter-vertebral (L2-S1) levels, of

4.15%VBD with greatest error reported was 4.61% VBD at L5-S1. In comparison to the

present study which reported an overall SEM ranging from 0.76 to 3.91%VBD and greatest of

SEM of 6.68% VBD at L5-S1 of its Inter observer, extension sequences. Thus, applying a

method originally intended for plain film radiography is comparable when applied to

fluoroscopic sequences with the exception of the L5-S1.

Frobin also performs the same calculations for accuracy on a phantom model and achieves

an error of 2.80%VBD, compared to 2.28% VBD for the present study.

Boos et al. 1996 used two methods to calculate disc height from images acquired from

magnetic resonance imaging. Boos et al. found an intra observer error of 0.27mm

(0.77%VBD) and 0.34mm (0.97%VBD) for their two methods and 0.36mm (1.03%VBD) in

their inter-observer study. Comparing this to Frobins 4.15% error encountered when

measuring disc height from lateral radiographic views and the present study’s 0.76-

69

3.91%VBD (0.27eqvmm–1.37eqv mm) we find that measurement precision from magnetic

resonance images is superior to QF and Frobin studies. Furthermore, it is pointed out that,

magnetic resonance imaging induces no radiation hazard. However, the MRI is currently

unable to produce dynamic motion information.

IAR

It has been difficult to compare validity and repeatability of IAR locations with other studies

in this field. This is mainly due to method in which IAR has been measured by drawing the

lines tracing paper with a pencil and ruler by superimposing the traced outlines on each of

the radiographic images (similar to method shown in Figure 15). Furthermore, most people

who have researched IARs between vertebrae have not presented any data on reliability or

validity. Instead they have presented average locations in populations, usually in the sagittal

plane [69, 71-73]. Exceptions to this are Amevo et al. (1991) [66] [67] and McCane [70].

Amevo presented an inter and Intra observer study of the measurement of IARs in a

population measured both by hand and using digitisation techniques. McCane (2006) [70],

in addition to calculating standard IAR locations (called ‘Finite Centres of Rotation’ (FCR))

using radiographs, also performed a calibration study using their method of automatically

detecting vertebral body positions.

Amevo 1991 [67], found for the entire process of plotting IARs, inter- and intra-observer

differences, an average variation of less than 0.5mm Although McCane [70] presented an

average error of ±8.5mm when measuring IAR in a calibration study and ±7.4mm in an inter

operator repeatability study, he describes this to be a superior method of calculating IAR

positions using the automated vertebral body finding technique. This result seems

contradictory as this error (±8.5mm) equates to almost a quarter of a standard vertebral

body depth (35mm). The calculations used for both McCane [70] and the present study are

the same and come from McCane’s 2005 paper “On calculating the finite centre of rotation

for rigid planar motion” [74]. When McCane’s results are compared to the findings of the

present study it appears that the technique utilised here is far superior for calculating IAR

positions.

The error (RMS) in the present validity study was 0.396eqv mm (y axis IAR co ordinate

position) and 0.007eqv mm (x axis IAR), the greatest error (RMS) in the intra-observer

repeatability study equated to 0.613eqv mm (y axis IAR), and 0.728eqv mm (x axis IAR) in

the inter-observer study.

70

Overall, the lower translation and disc height repeatability values for extension may be due

to lower quality images which are more difficult to track or as may well be the case for L5-

S1, difficulty in tracking can be caused by interposed bone from the Ilium degrading the

images at this level. It has been noted that in lateral views using low dose x-rays, it is

sometimes difficult for the observer or tracking software to identify L5 and S1 landmarks as

they move between the ilia. These erroneous results at the S1 level however, maybe due to

the difficulty in positioning the S1 template caused in part by difficulty identifying the

inferior border of S1.

In Figure 28 (below) the bisectrix between adjacent vertebrae as calculated in the Matlab

environment is shown for 4 adjacent intervertebral segments (From the top down L3 (mainly

off screen), L4, L5 and S1). While the bisectrix calculated for L3/L4 and L4/L5 pass between

the two vertebrae in the disc space as is expected, the bisectrix for L5/S1 passes through S1

its self. This may be the cause of some of the large errors in the disc height results. Future

methodologies may need to account for this issue.

Figure 28: Computer generated positions of bisectrix of L3/L4, L4/L5 & L5/S1.

Previous authors [46] using functional radiography was able to identify the S1/S2 vestigial

disc when placing template corner points. However, due to the lower quality images of QF,

this vestigial joint is rarely identifiable in the fluoroscopic images. One solution may be

similar to Frobin et als’ 2002 [52, 99] method of finding the generating a bisectrix for

71

another non uniform vertebral segment, C2 (The second cervical body in the neck). In this

method the translation and disc height of C2/C3 is measured across a line called “parallel to

bisectrix”. This bisectrix is generated from the mid line of C3 (similarly to what is calculated

in the present study) and only two points from C2 (across the inferior border) the gradient is

calculated as the average of these two lines and the bisectrix is drawn I the disc space.

While other repeatability and accuracy studies may be comparable to the method used in

the present study, the static film, end range of voluntary bending angle methods fail to take

the dynamic aspect of inter-vertebral motion into account. In previous studies, spinal

instability was measured with end-range radiographic neutral, flexion and extension views

(Abbott et al, 2006) [97], however important information about segmental motion such as in

the neutral zone (Figure 3) might be missed out.

Further study using these techniques with greater subject numbers and less time restrictions

would help to gain a greater number of inter-vertebral level results and therefore assist in

developing a greater understanding of the limitations of these techniques and also how the

neutral zone may be applied in vivo to increase our understanding of what instability of the

spine really means and how it can be accurately measured.

Due to the nature of the continuous motion data available in the OSMIA technique, much

more data is available for analysis. Future studies should therefore concentrate on which

measurements are of value to clinicians, researchers and patients. It is already clear that end

of range measurements are of little value (ref back to the introduction). Suggestions for

measurements which should be investigated include assessing the rate of change and

regularity of spinal motion patterns and an appreciation of how the spine behaves as a

multi-directional series of joints which are influenced by each other and work together

rather than simply the range of motion of individual, inter-vertebral segments.

Spinal motion measurements from QF need to be standardised, particularly in terms of

defining the normal parameters of angulations, translation, disc height and IAR’s. This can

only be achieved with a wide normative study of video-fluoroscopy sequences undertaken

on healthy subjects; such a study is currently underway at the IMRCI.

72

Conclusion

Low back pain (LBP) is a costly economic problem. The majority of it will resolve in 6 weeks

but that which continues or becomes episodic has the highest societal impact [100]. The

issue appears to be centred around accurate diagnosis, with most of chronic low back pain

(CLBP) labelled non specific because no correlation can be found between results from

objective examination findings, such as from imaging, and the symptoms. However, most

chronic non-specific low back pain (CNSLBP) is thought to be mechanical because it is made

better or worse by movement or position [22].

One problem however is that the methods used for measuring back mechanics use static

images to address what is a dynamic, functional problem. This study found high repeatability

and accuracy for a quantitative fluoroscopy (QF) technology used in the objective

measurement of three indicators of lumbar spine inter-vertebral function in the sagittal

plane: translation, disc height and the location of the instantaneous axis of rotation. This

information was derived dynamically, throughout the motion under study.

The levels of repeatability and accuracy found suggest that continuous measurement of

inter-vertebral motion using QF technology represents new possibilities for assessment and

insight into suspected spinal dysfunction and the effects of joint degeneration. This can be

used for diagnosis and monitoring, for example before and after surgical or physical therapy

interventions.

This area of work in spine kinematics research may provide useful measures against which

treatment goals and methods could be developed and assessed. Such dynamic studies, if

found to be repeatable and accurate, may provide better and more objective evidence with

which to improve our understanding of CNSLBP. However, further work is needed to assess

the repeatability and accuracy of a range of other kinematic measures that can be assessed

by QF technology. These might include motion pattern analysis, neutral zone laxity

assessment and other data transformations that describe the functional integrity of the

spine.

73

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90. Gertzbein, S.D., Holtby, R., Tile, M., Kapasouri, A., Chan, K.W., Cruickshank, B., Determination of a locus of instantaneous centres of rotation of the lumbar disc by Moire fringes: a new technique. Spine, 1984. 9(4): p. 409-413.

91. Haher, T.R., Obrien, M., Felmly, W.T., Welin, D., Perrier, G., Choueka, J., Devlin, V., Vassiliou, A., Chow, G., Instantaneous axis of rotation as a function of the three columns of the spine. Spine, 1992. 17: p. S149-154.

78

92. Morgan, F.P., King, I., Primary instability of lumbar vetebrae as a common cause of low back pain. Journal of Bone and Joint Surgery, 1957. 39B(1): p. 6-22.

93. Dupuis, P.R., Yong-Hing, K., Cassidy, J.D., Kirkaldy-Willis, W.H., Radiologic diagnosis of degenerative lumbar spinal instability. Spine, 1985. 10(3): p. 262-276.

94. Stokes, I.A.F., Frymoyer, J.W., Segmental motion and instability. Spine, 1987. 12(7): p. 688-691.

95. Boden, S.D., Wiesel, S.W., Lumbosacral segmental motion in normal individuals - have we been measuring instability properly? Spine, 1990. 15: p. 571-576.

96. Dvorak, J., Panjabi, M.M., Chang, D.G., Theiler, R., Grob, D., Functional radiographic diagnosis of the lumbar spine: flexion-extension and lateral bending. Spine, 1991. 16(5): p. 562-571.

97. Abbott, J., Fritz, J., McCane, B., Shultz, B., Herbison, P., Lyons, B., Stefanko, G., Walsh, R., Lumbar segmental mobility disorders: comparison of two methods of defining abnormal displacement kinematics in a cohort of patients with non-specific mechanical low back pain. BMC Musculoskeletal Disorders, 2006. 7(1): p. 45.

98. Meyerding, H.W., Spondylolisthesis. Surgery, Gynecology and Obstetrics, 1932. 54: p. 371-377.

99. Frobin, W., Leivseth, G., Biggemann, M., Brinckmann, P., Vertebral height, disc height, posteroanterior displacement and dens-atlas gap in the cervical spine: precision measurement protocol and normal data. Clincial Biomechanics, 2002. 17: p. 423-431.

100. C.S.A.G., Epidemiology Review: The epidemiology and cost of back pain. 1994, Department of Health: London.

79

Appendix 1

As the gradient of the bisector is known (mB), and any line which lies perpendicular to it

must have a gradient equal to its negative inverse .

Knowing the equation of a straight line in Cartesian co-ordinates;

We can combine these two equations to represent the line which passes perpendicular to

the bisectrix and though the canter point of one of the vertebra.

As centre point co-ordinates & ) are known this lines y-axis crossover point ( ) can

be calculated.

The point in which the line from the centre point intersects the bisectrix both equations

& can be said to be true.

As intersect co-ordinates ( & ) are true for both equations is the same for both

equations so they can be merged.

80

Or, as

As is known, can be found by;

This method can be repeated using the centre point co-ordinates of the other vertebra in

the pair giving the co-ordinates at which both lines meet the bisectrix. The distance between

these two points is what is used to describe translation in this study.

Or

81

Appendix 2

Measurement of Fixed centre of rotation models change in disc height is achieved by

measuring (with electronic callipers in millimetres) the dimensions of the calibration model

10 times.

The Mean vertebral body depth is found to be 28.77mm.

The position of the universal joint is found to be 5.35mm from the superior border of the

inferior vertebra 14.54mm along the superior border of the inferior vertebra from the

posterior corner.

The initial direct corner to corner distance between the anterior corners close to the disc

space between the two vertebrae was 6.11mm.

Figure 29: Measurements of model 1; theoretical placements of bisectrix and midlines for calculations

Bisectrix line is assumed to pass through the centre of rotation and have half the gradient

that the superior vertebras midline would as inferior vertebra is fixed at horizontal.

The dimensional measurement values where converted to fractions of superior vertebral

body depth.

82

Figure 30: Measured initial disc height and there relative values as a function of mean vertebral body

depth

So;

IAR X position= 14.54mm

IAR Y position= -5.35mm

Initial Disc height= 6.11mm

Therefore centre of rotation to inferior vertebra corner vertical distance = IAR Y position

= -5.35mm

Therefore centre of rotation to superior vertebra corner vertical distance = Initial Disc height

- IAR Y position = 0.76mm

Distance from centre of rotation to anterior corner of inferior vertebra horizontally

= 28.77- 14.54mm = 14.24mm

Therefore the direct distance from centre of rotation to anterior-inferior corner of superior

vertebra ‘Hyp1’ = ((14.54mm *14.54mm) + (14.24mm *14.24mm)) = 14.26

Therefore the direct distance from centre of rotation to anterior-superior corner of the

inferior vertebra ‘Hyp2’ = ((-5.35mm *-5.35mm) + (14.24mm *14.24mm)) = 15.21mm

As the distance form the centre of rotation to vertebral corners remains constant and we

know the change in angle from initial position to last position is 16 degrees. (Or -13 degrees

from horizontal to 3 degrees horizontal) as read off the attached protractor.

83

Figure 31: Calculated distances from fixed centre of rotation to vertebral body corners

At initial;

Initial angle ‘θ1’ = -13 degrees / -0.227 radians (rads)

Gradient of superior body midline (m1) = tan (angle of vertebra from horizontal) = -0.231

Gradient of inferior body midline ‘m2’= 0

Bisector gradient ‘mB’= average of superior and inferior midline gradients = (-0.231+0) ÷ 2 =

-0.115

Bisector angle ‘θB’ = Tan-1(mB) = Tan-1(-0.115) = -0.1149

Angle of Hyp1 from horizontal ‘θ (Hyp1)’ = Tan-1(0.76÷ 14.24) = 0.0532

Angle of Hyp2 from horizontal ‘θ (Hyp2)’ = Tan-1(-5.35÷ 14.24) = -0.3594

Angle between Bisectrix and Hyp1 ‘θ (Hyp1 - mB)’ = 0.1682

Angle between Bisectrix and Hyp1 ‘θ (Hyp2 - mB)’ = -0.2444

Perpendicular distance between bisectrix and Superior corner = Sin (θ (Hyp1 - mB)) x Hyp1

= 2.39mm

Perpendicular distance between bisectrix and inferior corner = Sin (θ (Hyp2 - mB)) x Hyp2

= --3.68mm

Total distance = 6.07mm

84

Figure 32: Measuring maximum disc height change relative to bisectrix

Final position;

Initial angle ‘θ1’ = 3 degrees / 0.0524 rads

Gradient of superior body midline (m1) = tan (angle of vertebra from horizontal) = 0.0524

Gradient of inferior body midline ‘m2’= 0

Bisector gradient ‘mB’= average of superior and inferior midline gradients = 0.0524

+0) ÷ 2 = 0.0262

Bisector angle ‘θB’ = Tan-1(mB) = Tan-1(0.0262) = 0.0262

Angle of Hyp1 from horizontal ‘θ (Hyp1)’ = Δ θ1+‘θ (Hyp1)’ = 0.3325

Angle of Hyp2 from horizontal ‘θ (Hyp2)’ = Tan-1(-14.24÷ 0.76) = -0.3594

Angle between Bisectrix and Hyp1 ‘θ (Hyp1 - mB)’ = 0.3063

Angle between Bisectrix and Hyp1 ‘θ (Hyp2 - mB)’ -0.3856

Perpendicular distance between bisectrix and Superior corner = Sin (θ (Hyp1 - mB)) x Hyp1

= 4.30mm

Perpendicular distance between bisectrix and inferior corner = Sin (θ (Hyp2 - mB)) x Hyp2

85

= --5.72

Total distance = 10.02

Change in disc height=3.95mm

(Disc height change ÷ average vertebral body depth) *100

= (3.95mm÷28.77mm.)*100= 13.73 percent vertebral body depth (%VBD)

86

Appendix 3

Calibration Model motor control software

int pwm_a = 3; //PWM control for motor outputs 1 and 2 is on digital pin 3

int pwm_b = 11; //PWM control for motor outputs 3 and 4 is on digital pin 11

int dir_a = 12; //dir control for motor outputs 1 and 2 is on digital pin 12

int dir_b = 13; //dir control for motor outputs 3 and 4 is on digital pin 13

const int numReadings = 10;

int var = 0;

int var2 = 0;

int readings[numReadings]; // the readings from the analog input

int index = 0; // the index of the current reading

int total = 0; // the running total

int average = 0; // the average

int average2 = 0; // the average

int average3 = 0; // the average

int motorout = 0;

//variables in limits

// speed of motor movement 50-255 (less than 50 will not move)

int speed1 = 50; // speed =50 (slowest consistant value)

// Motor distance 0-1023 (realisticaly 50- 1022)

int ExtLim=1000; // full reach (to ensure no motor twist)

int FlexLim=150; // full retraction (to ensure no motor twist)

int VarLim=0; // variable motor limit to be based of tilt sensor

int motorout1=0;

const int inputPin = A0; //inputpin A0 for sensor

const int motor = 9; //ditigal pin9

int inByte = 0;

void setup() {

// initialize serial communication with computer:

Serial.begin(9600);

for (int thisReading = 0; thisReading < numReadings; thisReading++)

readings[thisReading] = 0;

87

pinMode(pwm_a, OUTPUT); //Set control pins to be outputs

pinMode(pwm_b, OUTPUT);

pinMode(dir_a, OUTPUT);

pinMode(dir_b, OUTPUT);

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

void loop()

{

if (Serial.available() > 0) {

int inByte = Serial.read();

var = 0;

var2 = 0;

switch (inByte){

while (var < 1) {

case 'e'://extension translation only

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, LOW); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, LOW); //Set motor direction, 3 high, 4 low

while (var2 < 1000) {

motorout = analogRead(motor);

Serial.println(motorout, DEC);

Serial.print("");

delay(10);

var2++;

if (motorout>ExtLim){

var2=1000;

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

}

88

var2=0;

delay(1000);

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, HIGH); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, HIGH); //Set motor direction, 3 high, 4 low

while (var2 < 1000) {

motorout = analogRead(motor);

Serial.println(motorout, DEC);

Serial.print("");

delay(10);

var2++;

if (motorout<FlexLim){

var2=1000;

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

}

var=10;

}

break;

while (var < 1) {

case 'f':////flexion translation onlyy

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, HIGH); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, HIGH); //Set motor direction, 3 high, 4 low

while (var2 < 1000) {

motorout = analogRead(motor);

Serial.println(motorout, DEC);

Serial.print("");

delay(10);

var2++;

if (motorout<FlexLim){

var2=1000;

89

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

}

var2=0;

delay(1000);

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, LOW); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, LOW); //Set motor direction, 3 high, 4 low

while (var2 < 1000) {

motorout = analogRead(motor);

Serial.println(motorout, DEC);

Serial.print("");

delay(10);

var2++;

if (motorout>ExtLim){

var2=1000;

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

}

var=10;

}

break;

while (var < 1) {

case 'q'://Move to the opposite extreem of translation motion

motorout = analogRead(motor);

motorout1=motorout;

if (motorout1>FlexLim){

while (motorout>FlexLim){

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, HIGH); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, HIGH); //Set motor direction, 3 high, 4 low

90

motorout = analogRead(motor);

}

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

if (motorout1<ExtLim){

while (motorout<ExtLim){

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, LOW); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, LOW); //Set motor direction, 3 high, 4 low

motorout = analogRead(motor);

}

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

var=10;

}

break;

while (var < 1000) {

case 'v'://variable translation based on rotation

// subtract the last reading:

total= total - readings[index];

// read from the sensor:

readings[index] = analogRead(inputPin);

// add the reading to the total:

total= total + readings[index];

// advance to the next position in the array:

index = index + 1;

// if we're at the end of the array...

if (index >= numReadings)

// ...wrap around to the beginning:

index = 0;

// calculate the average:

average = total / numReadings;

91

// send it to the computer (as ASCII digits)

average = map(average, 0, 1023, 60, 121);

Serial.println(average, DEC);

Serial.print("");

average = map(average, 60, 121, FlexLim, ExtLim); //change back for motor

Serial.print("");

motorout = analogRead(motor);

Serial.print(motorout, DEC);

Serial.print("\t");

average2=average+round((ExtLim-FlexLim)/(121-60));

average3=average-round((ExtLim-FlexLim)/(121-60));

motorout1 = motorout;

if (motorout1>average2){

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, HIGH); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, HIGH); //Set motor direction, 3 high, 4 low

delay(50);

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

else if (motorout1<average3){

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, LOW); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, LOW); //Set motor direction, 3 high, 4 low

delay(50);

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

else if (average3<motorout1<average2){

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

else if (motorout1>ExtLim){

analogWrite(pwm_a, speed1);

92

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, LOW); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, LOW); //Set motor direction, 3 high, 4 low

}

else if (motorout1<FlexLim){

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, HIGH); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, HIGH); //Set motor direction, 3 high, 4 low

}

var++;

}

break;

case 's':// sensor only

var2=0;

while (var <500){

// subtract the last reading:

total= total - readings[index];

// read from the sensor:

readings[index] = analogRead(inputPin);

// add the reading to the total:

total= total + readings[index];

// advance to the next position in the array:

index = index + 1;

// if we're at the end of the array...

if (index >= numReadings) {

// ...wrap around to the beginning:

index = 0;

}

// calculate the average:

average = total / numReadings;

// send it to the computer (as ASCII digits)

average = map(average, 0, 1023, 60, 121);

Serial.println(average, DEC);

Serial.print(" ");

93

delay(50);

var++;

}

break;

while (var < 1) {

case 'c'://go the other way

motorout = analogRead(motor);

motorout1=motorout;

Serial.print("initial: ");

Serial.println(motorout, DEC);

Serial.print("\t");

if (motorout1>FlexLim){

while (motorout>FlexLim){

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, HIGH); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, HIGH); //Set motor direction, 3 high, 4 low

motorout = analogRead(motor);

}

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

if (motorout1<ExtLim){

while (motorout<ExtLim){

analogWrite(pwm_a, speed1);

analogWrite(pwm_b, speed1);

digitalWrite(dir_a, LOW); //Set motor direction, 1 low, 2 high

digitalWrite(dir_b, LOW); //Set motor direction, 3 high, 4 low

motorout = analogRead(motor);

}

analogWrite(pwm_a, 0);

analogWrite(pwm_b, 0);

}

motorout = analogRead(motor);

Serial.print("final: ");

94

Serial.println(motorout, DEC);

Serial.print(" ");

var=10;

}

break;

}

}

}

95

Appendix 4

Intra-observer repeatability results

Translation

Table 10: Intra-observer repeatability of translation in extension of the Lumbar segments L2-L3, L3-L4,

L5-S1 using QF expressed in SEM, 95% LOA, ICC and 95% CI

Extension Translation

SEM1 95% LOA2 ICC3 (95% CI4)

n (%VBD) (%VBD) ICC

7 L2-L3 0.593 -1.896 to 1.392 0.935 (0.671 - 0.989)

13 L3-L4 1.156 -2.958 to 3.448 0.742 (0.185 - 0.920)

10 L4-L5 1.610 -4.563 to 4.359 0.899 (0.619 - 0.975)

10 L5-S1 3.260 -10.791 to 7.282 0.644 (-0.344 - 0.910)

40 Overall 1.958 -5.855 to 4.998 0.782 (0.589 - 0.884)

Table 11: Intra-observer repeatability of translation in flexion of the Lumbar segments L2-L3, L3-L4,

L5-S1 using QF expressed in SEM, 95% LOA, ICC and 95% CI

Flexion Translation

SEM1 95% LOA2 ICC3 (95% CI4)

n (%VBD) (%VBD) ICC

11 L2-L3 0.517 -1.365 to 1.410 0.988 (0.958 - 0.997)

14 L3-L4 1.234 -3.716 to 3.123 0.533 (0.406 - 0.849)

11 L4-L5 1.109 -2.322 to 3.825 0.853 (0.483 - 0.960)

13 L5-S1 2.209 -6.450 to 5.794 0.828 (0.456 - 0.947)

49 Overall 1.427 -3.943 to 3.967 0.859 (0.751 - 0.920)

96

Disc height

Table 12: Intra-observer repeatability of disc height change in extension of the Lumbar segments L2-

L3, L3-L4, L5-S1using QF expressed in SEM, 95% LOA, ICC and 95% CI

Extension Disc Height change

SEM1 95% LOA2 ICC3 (95% CI4)

n (%VBD) (%VBD) ICC

6 L2-L3 1.504 -3.094 to 5.242 0.650 (-1.099 - 0.950)

12 L3-L4 0.252 -0.791 to 0.603 0.965 (0.895 - 0.991)

15 L4-L5 0.717 -1.883 to 2.091 0.971 (0.915 - 0.990)

13 L5-S1 1.550 -5.111 to 3.483 0.829 (0.462 - 0.947)

46 Overall 1.113 -3.167 to 3.006 0.895 (0.811 - 0.942)

Table 13: Intra-observer repeatability of disc height change in flexion of the Lumbar segments L2-L3,

L3-L4, L5-S1using QF expressed in SEM, 95% LOA, ICC and 95% CI

Flexion Disc Height change

SEM1 95% LOA2 ICC3 (95% CI4)

n (%VBD) (%VBD) ICC

4 L2-L3 1.059 -1.729 to 4.143 0.236 (-6.630 - 0.950)

3 L3-L4 0.518 -1.448 to 1.424 0.651 (-4.600 - 0.991)

5 L4-L5 0.858 -2.636 to 2.123 -5.37 (-46.046 - 0.320)

9 L5-S1 0.435 -1.338 to 1.071 0.879 (0.503 - 0.972)

21 Overall 0.755 -1.982 to 2.202 0.531(-0.138 - 0.808)

97

Instantaneous axes of rotation

Table 14: Intra-observer repeatability of IAR in extension of the Lumbar segments L2-L3, L3-L4, L5-S1using QF expressed in RMS.

Table 15: Intra-observer repeatability of IAR in flexion of the Lumbar segments L2-L3, L3-L4, L5-S1using QF expressed in RMS.

Extension Instantaneous Axis of Rotation (IAR) RMS difference in position Intra-observer described as percentage

of superior vertebral body depth (%VBD)

L2-L3 L3-L4 L4-L5 L5-S1 Overall

n 4 1 10 6 21

X( %VBU) 1.38 3.80 1.61 6.84 1.63

y (%VBU) 3.06 11.93 4.34 5.14 1.75

Flexion Instantaneous Axis of Rotation (IAR) RMS difference in position Intra-observer described as

percentage of superior vertebral body depth (%VBD)

L2-L3 L3-L4 L4-L5 L5-S1 Overall

n 1 9 12 8 30

X( %VBU) 2.93 1.09 0.35 5.46 1.09

y (%VBU) 0.22 2.59 3.72 2.13 0.15

98

Inter-observer repeatability results

Translation

Table 16: Inter-observer repeatability of translation in extension of the Lumbar segments L2-L3, L3-L4,

L5-S1using QF expressed in SEM, 95% LOA, ICC and 95% CI

Extension Translation

SEM1 95% LOA2 ICC3 (95% CI4)

n (%VBD) (%VBD) ICC

6 L2-L3 0.496 -1.5973 to 1.151 0.932 (0.514- 0.990)

12 L3-L4 0.999 -3.426 to 2.112 0.809 (0.337 - 0.945)

7 L4-L5 1.871 -3.843 to 6.531 0.916 (0.512 - 0.986)

8 L5-S1 1.839 -8.264 to 1.931 0.910 (0.553 - 0.982)

33 Overall 1.736 -5.575 to 4.051 0.861 (0.718 - 0.931)

Table 17: Inter-observer repeatability of translation in extension of the Lumbar segments L2-L3, L3-L4,

L5-S1using QF expressed in SEM, 95% LOA, ICC and 95% CI

Flexion Translation

SEM1 95% LOA2 ICC3 (95% CI4)

n (%VBD) (%VBD) ICC

11 L2-L3 1.468 -4.357 to 3.783 0.865 (0.499 - 0.964)

14 L3-L4 1.302 -3.561 to 3.654 0.570 (-0.339 - 0.862)

11 L4-L5 1.766 -4.299 to 5.491 0.700 (-0.115 - 0.919)

12 L5-S1 2.152 -4.929 to 7.002 0.844 (0.458 - 0.955)

48 Overall 1.674 -4.297 to 4.985 0.806 (0.654 - 0.891)

99

Disc height

Table 18: Inter-observer repeatability of disc height change in flexion of the Lumbar segments L2-L3,

L3-L4, L5-S1using QF expressed in SEM, 95% LOA, ICC and 95% CI S1using QF expressed in SEM, 95%

LOA, ICC and 95% CI

Table 19: Inter-observer repeatability of disc height change in flexion of the Lumbar segments L2-L3,

L3-L4, L5-S1using QF expressed in SEM, 95% LOA, ICC and 95% CI

Flexion Disc Height change

SEM1 95% LOA2 ICC3 (95% CI4)

N (%VBD) (%VBD) ICC

4 L2-L3 0.287 -1.115 to 0.474 0.953 (0.271 - 0.997)

2 L3-L4 0.131 -0.238 to 0.488 0.852 (-95.175 – 1.000)

3 L4-L5 0.032 0.164t o 0.343 0.995 (0.792 – 1.000)

6 L5-S1 0.493 -1.266 to 1.469 0.639 (-1.583 - 0.949)

15 Overall 0.361 -0.979 to 1.024 0.866 (0.600 - 0.955)

Extension Disc Height change

SEM1 95% LOA2 ICC3 (95% CI4)

N (%VBD) (%VBD) ICC

6 L2-L3 0.618 -1.597 to 1.832 0.968 (0.773 - 0.996)

11 L3-L4 0.427 -1.223 to 1.142 0.918 (0.695 - 0.978)

14 L4-L5 0.691 -2.152 to 1.679 0.957 (0.865- 0.986)

13 L5-S1 6.679 -23.529 to 13.496 0.487 (-0.683 - 0.843)

44 Overall 3.907 -12.380 to 9.277 0.609 (0.284 - 0.787)

100

Instantaneous axes of rotation

Table 20: Inter-observer repeatability of IAR in extension of the Lumbar segments L2-L3, L3-L4, L5-S1

using QF expressed in RMS.

Table 21: Inter-observer repeatability of IAR in flexion of the Lumbar segments L2-L3, L3-L4, L5-S1

using QF expressed in RMS.

SEM = SD difference/ √2 to 95% limits of agreement

2 95% LOA = x ̄± 1.96 x SD difference (Bland-Altman-Plot)

3 ICC = SD1/ (SD1 + SD difference) intra-observer: 1-way random effect inter-observer: 2-way random effect 4 95% CI = x ̄± 1.96 x SD/√n (x ̄= sample mean, SD=Standard deviation n= number of subjects)

Extension Instantaneous Axis of Rotation (IAR) RMS difference in position Inter-observer described as

percentage of superior vertebral body depth (%VBD)

L2-L3 L3-L4 L4-L5 L5-S1 Overall

n 5 1 9 5 20

X( %VBU) 2.80 5.23 0.19 0.77 0.55

y (%VBU) 4.03 0.41 4.16 3.13 1.63

Flexion Instantaneous Axis of Rotation (IAR) RMS difference in position Inter-observer described as

percentage of superior vertebral body depth (%VBD)

L2-L3 L3-L4 L4-L5 L5-S1 Overall

n 1 7 10 6 24

X( %VBU) 1.69 0.21 1.58 10.90 2.08

y (%VBU) 2.47 1.05 2.59 7.11 0.85

101

Appendix 5

Intra-observer repeatability 95% LOA Bland-Altman plots

Translation

Flexion L2-L3;

95% LOA (%VBD) = -1.365 to 1.410

-6 -4 -2 0 2 4-8.0

-5.5

-3.0

-0.5

2.0

4.5

Mean ((Flexion + Flexion) / 2)

Difference (Flexion - Flexion) mean difference ± 95% limits of agreement

Flexion L3-L4;

95% LOA (%VBD) =-3.716 to 3.123

-2 0 2 4 6-4.0

-2.4

-0.8

0.8

2.4

4.0

5.6

Mean ((M + N) / 2)

Difference (M - N) mean difference ± 95% limits of agreement

102

Flexion L4-L5;

95% LOA (%VBD) =-2.322 to 3.825

-4.0 -2.4 -0.8 0.8 2.4 4.0 5.6-5.0

-2.5

0.0

2.5

5.0

7.5

Mean ((M + N) / 2)

Difference (M - N) mean difference ± 95% limits of agreement

Flexion L5-S1;

95% LOA (%VBD)= -6.450 to 5.794

-6 -1 4 9-5

0

5

10

Mean ((M + N) / 2)

Difference (M - N) mean difference ± 95% limits of agreement

103

Flexion Overall;

95% LOA (%VBD) =-3.943 to 3.967

-6 -1 4 9-7

-2

3

8

Mean ((M + N) / 2)

Difference (M - N) mean difference ± 95% limits of agreement

104

Extension L2-L3;

95% LOA (%VBD) = -1.896 to 1.392

-6 -5 -4 -3 -2 -1-2

-1

0

1

2

Mean ((Extension + Extension) / 2)

Difference (Extension - Extension) mean difference ± 95% limits of agreement

Extension L3-L4;

95% LOA (%VBD) = -2.958 to 3.448

-4 -2 0 2 4-5.0

-2.5

0.0

2.5

5.0

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

105

Extension L4-L5;

95% LOA (%VBD) = -4.563 to 4.359

-9.0 -6.5 -4.0 -1.5 1.0 3.5-8.0

-5.5

-3.0

-0.5

2.0

4.5

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

Extension L5-S1;

95% LOA (%VBD) = -10.791 to 7.282

-10.0 -7.5 -5.0 -2.5 0.0 2.5-15

-10

-5

0

5

10

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

106

Extension Overall;

95% LOA (%VBD) = -5.855 to 4.998

-10 -5 0 5-20

-15

-10

-5

0

5

Mean ((Extension + Extension) / 2)

Difference (Extension - Extension) mean difference ± 95% limits of agreement

107

Disc height

Flexion L2-L3;

95% LOA (%VBD) =-1.729 to 4.143

-2.2 -1.7 -1.2 -0.7 -0.2 0.3-2

0

2

4

6

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

Flexion L3-L4;

95% LOA (%VBD) = -1.448 to 1.424

-0.20 0.05 0.30 0.55 0.80 1.05-2

-1

0

1

2

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

108

Flexion L4-L5;

95% LOA (%VBD) = -2.636 to 2.123

-0.2 0.0 0.2 0.4-3

-2

-1

0

1

2

3

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

Flexion L5-S1;

95% LOA (%VBD) = -1.338 to 1.071

-1.5 -0.5 0.5 1.5-2.0

-1.2

-0.4

0.4

1.2

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

109

Flexion Overall;

95% LOA (%VBD) = -1.982 to 2.202

-2.5 -1.5 -0.5 0.5 1.5-2

0

2

4

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

110

Extension L2-L3;

95% LOA (%VBD) = -3.094 to 5.242

0 2 4 6 8-4

-2

0

2

4

6

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

Extension L3-L4;

95% LOA (%VBD) = -0.791 to 0.603

2 3 4 5 6 7-1.0

-0.6

-0.2

0.2

0.6

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

111

Extension L4-L5;

95% LOA (%VBD) = -1.883 to 2.091

-2 0 2 4 6 8-2

0

2

4

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

Extension L5-S1;

95% LOA (%VBD) = -5.111 to 3.483

2 4 6 8 10 12-6

-4

-2

0

2

4

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

112

Extension Overall;

95% LOA (%VBD) = -3.167 to 3.006

-2 3 8 13-6

-3

0

3

6

Mean ((A + B) / 2)

Difference (A - B) mean difference ± 95% limits of agreement

113

Inter-observer repeatability 95% LOA Bland-Altman plots

Translation

Flexion L2-L3;

95% LOA (%VBD) =-4.357 to 3.783

-6 -4 -2 0 2 4-8.0

-5.5

-3.0

-0.5

2.0

4.5

Mean ((Flexion + Flexion) / 2)

Difference (Flexion - Flexion) mean difference ± 95% limits of agreement

Flexion L3-L4;

95% LOA (%VBD) =-3.561 to 3.654

-2 0 2 4 6-4.0

-2.4

-0.8

0.8

2.4

4.0

5.6

Mean ((M + N) / 2)

Difference (M - N) mean difference ± 95% limits of agreement

114

Flexion L4-L5;

95% LOA (%VBD)= -4.299 to 5.491

-4.0 -2.4 -0.8 0.8 2.4 4.0 5.6-5.0

-2.5

0.0

2.5

5.0

7.5

Mean ((M + N) / 2)

Difference (M - N) mean difference ± 95% limits of agreement

Flexion L5-S1;

95% LOA (%VBD)= -4.929 to 7.002

-6 -1 4 9-5

0

5

10

Mean ((M + N) / 2)

Difference (M - N) mean difference ± 95% limits of agreement

115

Flexion Overall ;

95% LOA (%VBD)= -4.297 to 4.985

-6 -1 4 9-7

-2

3

8

Mean ((M + N) / 2)

Difference (M - N) mean difference ± 95% limits of agreement

116

Extension L2-L3;

95% LOA (%VBD) = -1.5973 to 1.151

-6 -5 -4 -3 -2 -1-2.0

-1.2

-0.4

0.4

1.2

Mean ((Extension + Extension) / 2)

Difference (Extension - Extension) mean difference ± 95% limits of agreement

Extension L3-L4;

95% LOA (%VBD) = -3.426 to 2.112

-3 -2 -1 0 1 2 3-5.0

-2.5

0.0

2.5

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

117

Extension L4-L5;

95% LOA (%VBD) = -3.843 to 6.531

-9.0 -6.5 -4.0 -1.5 1.0 3.5-5.0

-2.5

0.0

2.5

5.0

7.5

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

Extension L5-S1;

95% LOA (%VBD) = -8.264 to 1.931

-10 -5 0 5 10-10.0

-7.5

-5.0

-2.5

0.0

2.5

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

118

Extension Overall;

95% LOA (%VBD) = -5.575 to 4.051

-10 -5 0 5 10-8

-3

2

7

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

119

Disc height

Flexion L2-L3;

95% LOA (%VBD) = -1.115 to 0.474

-2.1 -1.6 -1.1 -0.6 -0.1 0.4-1.50

-0.75

0.00

0.75

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

Flexion L3-L4;

95% LOA (%VBD) = -0.238 to 0.488

-0.11 -0.01 0.09 0.19 0.29-0.50

-0.25

0.00

0.25

0.50

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

120

Flexion L4-L5;

95% LOA (%VBD) = 0.164t o 0.343

0.0 0.2 0.4 0.6 0.80.16

0.21

0.26

0.31

0.36

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

Flexion L5-S1;

95% LOA (%VBD) = -1.266 to 1.469

-0.8 -0.3 0.2 0.7 1.2-1.5

-0.5

0.5

1.5

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

121

Flexion Overall;

95% LOA (%VBD) = -0.979 to 1.024

-2.5 -1.5 -0.5 0.5 1.5-1.0

-0.5

0.0

0.5

1.0

1.5

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

122

Extension L2-L3;

95% LOA (%VBD) = -1.597 to 1.832

0 2 4 6 8-2

-1

0

1

2

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

Extension L3-L4;

95% LOA (%VBD) = -1.223 to 1.142

2 3 4 5 6 7-2.0

-1.2

-0.4

0.4

1.2

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

123

Extension L4-L5;

95% LOA (%VBD) = -2.152 to 1.679

0 3 6 9-4

-2

0

2

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

Extension L5-S1;

95% LOA (%VBD) = -23.529 to 13.496

1 6 11 16 21 26-30

-20

-10

0

10

20

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement

124

Extension Overall;

95% LOA (%VBD) =-12.380 to 9.277

0 5 10 15 20 25-30

-20

-10

0

10

Mean ((E + F) / 2)

Difference (E - F) mean difference ± 95% limits of agreement