Reliability of lateral bending and axial rotation with validity of a new method to determine axial rotation on anteroposterior cervical radiographs.

OBJECTIVE: To investigate the reliability of a new radiographic measurement of axial rotation and lateral bending on anterior-posterior cervical views by using a computer and sonic digitizer. DESIGN: A blind, repeated-measure design was used. Anteroposterior cervicothoracic radiographs were presented to each of 3 examiners in random order. Each film was digitized, and 1 week later the films were randomized for a second run. SETTING: Private, primary-care chiropractic clinic. MAIN OUTCOME MEASURES: The interclass and intraclass correlation coefficients (ICC) for intraexaminer and interexaminer reliability were calculated from measurements on radiographs for determining axial rotations (Ry) and lateral bending (Rz) of C3 to T3. RESULTS: When the new axial rotation method was applied to small rotations of a C3 plastic model, the average error was less than 1 degrees. For the calculations of axial rotation (Ry), the ICC values were in the good to excellent range. For axial rotation, the intraclass correlation coefficients were ICCs > or =0.78, and the interclass correlation coefficients were ICCs > or =0.67. For lateral flexions (Rz) of C3 to T3, all intraclass and interclass correlation coefficients were in the excellent range (ICCs > 0.87). CONCLUSIONS: Methods of calculating axial rotations in the spine have been reported for large angles (5 degrees to 30 degrees ) but not for smaller angles. A new method for determining axial rotations of the cervical segments on AP views, based on the chord across the arc displaced by the spinous-lamina junction, had reliability (ICC values) in the good to excellent range. Compared with measured rotations of a C3 model (-5 degrees to +5 degrees ), the new method had an average error of less than 1 degrees and approximately 11.5%. The reliability for the axial rotation measurements was in the good to excellent range, and the lateral bending measurements were all in the excellent range.

Linkage and redox isomerism in ruthenium complexes of catecholate, semi-quinone, and o-acylphenolate ligands derived from tri- and tetrahydroxy-9,10-anthracenediones.

The complexes Ru(CO)(2)L(2)(PHAQ-2H) (PHAQ = 1,2,4-trihydroxy-9,10-anthracenedione (PUR), 1,2,3- trihydroxy-9,10-anthracenedione (AG), and 1,2,5,8-tetrahydroxy-9,10-anthracenedione (QAL); L = PPh(3), PCy(3), PBu(3)), and Ru(CO)(dppe)(PBu(3))(PHAQ-2H), containing catecholate-type ligands were prepared. The complex Ru(CO)(2)(PBu(3))(2)(AG-2H) crystallizes in the space group P2(1)/n (No. 14 var) with a = 13.317(2), b = 15.628(2), c = 21.076(3) A, beta = 101.660(10) degrees, Z = 4; the crystal structure shows it to contain a 2,3-catecholate ligand. The electrochemistry of these complexes was examined, and the semi-quinone complexes [Ru(CO)(2)L(2)(PHAQ-2H)](1+) and [Ru(CO)(dppe)(PBu(3))(PHAQ-2H)](1+) were generated by chemical oxidation. One example of an o-acylphenolate complex, HRu(CO)(PCy(3))(2)(PUR-H), is also reported.

Reliability of centroid, Cobb, and Harrison posterior tangent methods: which to choose for analysis of thoracic kyphosis.

STUDY DESIGN: Thirty lateral thoracic radiographs were digitized twice by each of the three examiners. OBJECTIVES: To determine the reliability of the centroid, Cobb, and Harrison posterior tangent methods when applied to analysis of thoracic kyphosis. BACKGROUND DATA: Reliability studies on measurements of thoracic kyphosis are rare. METHODS: Blind, repeated-measures design was used. Thirty lateral thoracic radiographs were digitized twice by each of three examiners. To evaluate reliability of determining global and segmental alignment, vertebral bodies of T1-T12 were digitized. Centroids at the intersection of vertebral body diagonals and tangents to posterior vertebral bodies were constructed by computer. Also the computer constructed global and segmental centroid angles, Cobb angles (two-line method), and posterior tangent intersection angles from T1 to T12. Interclass and Intraclass correlation coefficients for these data were calculated and interpreted. RESULTS: From the points selected by examiners, all three methods have similar high ICC values for the global angles (> 0.94). For the segmental angles, the interobserver and intraobserver reliability is also very similar for all three methods, with ICCs in the good and excellent ranges (0.59-0.75 and 0.75-1.0, respectively). The mean absolute differences of observers' measurements are low, similar, and in the range of 0.9 degrees to 2.5 degrees. CONCLUSIONS: The centroid, two-line Cobb, and Harrison posterior tangent methods, when applied to measurements of kyphosis, are all reliable and have similar small error ranges. The centroid method does not give an accurate segmental analysis, uses more points and more time in clinical applications, and results in smaller angles of total kyphosis than the Cobb or posterior tangent methods. The posterior tangents are the slopes along the curve.

Radiographic analysis of lumbar lordosis: centroid, Cobb, TRALL, and Harrison posterior tangent methods.

STUDY DESIGN: Delayed, repeated measures, with three examiners each twice digitizing thirty lateral lumbar radiographs. OBJECTIVES: To determine the reliability and clinical utility of the centroid, Cobb, tangential radiologic assessment of lumbar lordosis (TRALL), and Harrison posterior tangent line-drawing methods for analysis of lumbar lordosis. BACKGROUND DATA: Cobb's method is commonly used for curvature analysis on lateral lumbar radiographs, whereas the centroid, TRALL, and Harrison posterior tangent methods are not widely used. METHODS: Thirty lateral lumbar radiographs were digitized twice by each of three examiners. To evaluate reliability of determining global and segmental alignment, all four vertebral body corners of T12-S1 and the superior margin of the femur head were digitized. Angles created were segmental and global centroid, (two-line) Cobb angles, and intersections of posterior tangents. A global TRALL angle was determined. Means, standard deviations, mean absolute differences, interclass and intraclass correlation coefficients (ICC), and confidence intervals were calculated. RESULTS: The interobserver and intraobserver reliabilities of measuring all segmental and global angles were in the high range (ICCs > 0.83). The mean absolute differences of observers' measurements were small (0.6 degrees -2.0 degrees ). Distal segmental (L4-S1) and global angles of lumbar curvature were dependent on the method of measurement. CONCLUSIONS: All four radiographic methods had high reliability and low mean absolute differences of observers' measurements. Because it lacks a segmental analysis, the TRALL method is not recommended. The centroid, Cobb, and Harrison posterior tangent methods provide global and segmental angles. However, the centroid segmental method requires three segments and is less useful for a stability analysis.

Slight head extension: does it change the sagittal cervical curve?

It is commonly believed that slight flexion/extension of the head will reverse the cervical lordosis. The goal of the present study was to determine whether slight head extension could result in a cervical kyphosis changing into a lordosis. Forty consecutive volunteer subjects with a cervical kyphosis and with flexion in their resting head position had a neutral lateral cervical radiograph followed immediately by a lateral cervical view taken in an extended head position to level the bite line. Subjects were patients at a spine clinic in Elko, Nevada. All radiographs were digitized. Global and segmental angles of the cervical curve were compared for any change in angle due to slight extension of the head. The average extension of the head required to level the bite line was 13.9 degrees. This head extension was not substantially correlated with any segmental or global angle of lordosis. Subjects were categorized into those requiring slight head extension (0 degree-13.9 degrees) and those requiring a significant head extension (> 13.9 degrees). In the slight head extension group, the average change in global angle between posterior tangents on C2 and C7 was 6.9 degrees, and 80% of this change occurred in C1-C4. In the significant head extension group, the average change in global angle between posterior tangents on C2 and C7 was 11.0 degrees, and the major portion of this change occurred in C1-C4. Out of 40 subjects, only one subject, who was in the significant head extension group and had only a minor segmental kyphosis, changed from kyphosis to lordosis. The results show that slight extension of the head does not change a reversed cervical curve into a cervical lordosis as measured on lateral cervical radiographs. Only small extension angle changes (mean sum = 4.8 degrees) in the upper cervical segments (C2-C4) occur in head extension of 14 degrees or less.

Comparison of axial and flexural stresses in lordosis and three buckled configurations of the cervical spine.

OBJECTIVE: To calculate and compare combined axial and flexural stresses in lordosis versus buckled configurations of the sagittal cervical curve. DESIGN: Digitized measurements from lateral cervical radiographs of four different shapes were used to calculate axial loads and bending moments on the vertebral bodies of C2-C7.Background. Osteoarthritis and spinal degeneration are factors in neck and back pain. Calculations of stress in clinically occurring configurations of the sagittal cervical spine are rare. METHODS: Center of gravity of the head (inferior-posterior sella turcica) and vertebral body margins were digitized on four different lateral cervical radiographs: lordosis, kyphosis, and two "S"-shapes. Polynomials (seventh degree) and stress concentrations on the concave and convex margins were derived for the shape of the sagittal cervical curvatures from C1 to T1. Moments of inertia were determined from digitizing and the use of an elliptical shell model of cross-section. Moment arms from a vertical line through the center of gravity of the head to the atlas and scaled neck extensor moment arms from the literature were used to compute the vertical component of extensor muscle effort. Segmental lever arms were calculated from a vertical line through C1 to each vertebra. RESULTS: In lordosis, anterior and posterior stresses in the vertebral body are nearly uniform and minimal. In kyphotic areas, combined stresses changed from tension to compression at the anterior vertebral margins and were very large (6-10 times as large in magnitude) compared to lordosis. In kyphotic areas at the posterior vertebral body, the combined stresses changed from compression (in lordosis) to tension. CONCLUSIONS: The stresses in kyphotic areas are very large and opposite in direction compared to a normal lordosis. This analysis provides the basis for the formation of osteophytes (Wolff's Law) on the anterior margins of vertebrae in kyphotic regions of the sagittal cervical curve. This indicates that any kyphosis is an undesirable configuration in the cervical spine. Relevance. Osteophytes and osteoarthritis are found at areas of altered stress and strain. Axial and flexural stresses at kyphotic areas in the sagittal cervical spine are abnormally high.

Chiropractic biophysics digitized radiographic mensuration analysis of the anteroposterior cervicothoracic view: a reliability study.

OBJECTIVE: To investigate the reliability of a radiographic measurement procedure that uses a computer and sonic digitizer to determine projected spinal displacements from an ideal, normal position. DESIGN: A blind, repeated-measure design was used. Anteroposterior cervicothoracic spine radiographs were presented in random order to each of 3 examiners. Each film was digitized, and the films were randomized for a second examination. SETTING: Private, primary care chiropractic clinic. MAIN OUTCOME MEASURES: Intraclass correlation coefficients for intraexaminer and interexaminer reliability for measures on radiographs comparing the perpendicular distance (T(x)) from a vertical axis line drawn through the center of T4 and the center of C2, the linear distance (vertebra(apex)) from the center of the vertebra most displaced from a line connecting the centers of C2 and T4, the angle (Rz) formed by the intersection of the vertical axis line and the upper thoracic line, and the angle of intersection (CDA) between the upper thoracic line and the cervical line. RESULTS: Intraexaminer reliability for T(x) distance was 0.99 to 1.00, with confidence intervals from 0.98-1.00; for vertebra(apex) was 0.96 to 0.97, with confidence intervals from 0.92-0.98; for Rz was 0.94 to 0.98, with confidence intervals from 0. 89-0.99; and for CDA was 0.92 to 0.95, with confidence intervals from 0.84-0.97. Interexaminer reliabilities for the 3 examiners ranged from 0.97 to 0.99. CONCLUSIONS: Measures similar to those described in this study are commonly used to quantify and categorize spinal displacements from true vertical alignment (i.e., scoliosis measurements). Intraclass correlation coefficient values >0.70 are considered accurate enough for use in clinical and research applications. The measures tested here would fit within these guidelines of reliability. Establishing reliability is an important first step in evaluating these measures so that future studies of validity may be undertaken.

Cobb method or Harrison posterior tangent method: which to choose for lateral cervical radiographic analysis.

STUDY DESIGN: Thirty lateral cervical radiographs were digitized twice by three examiners to compare reliability of the Cobb and posterior tangent methods. OBJECTIVES: To determine the reliability of the Cobb and Harrison posterior tangent methods and to compare and contrast these two methods. SUMMARY OF BACKGROUND DATA: Cobb's method is commonly used on both anteroposterior and lateral radiographs, whereas the posterior tangent method is not widely used. METHODS: A blind, repeated-measures design was used. Thirty lateral cervical radiographs were digitized twice by each of three examiners. To evaluate reliability of determining global and segmental alignment, vertebral bodies of C1-T1 were digitized. Angles created were two global two-line Cobb angles (C1-C7 and C2-C7), segmental Cobb angles from C2 to C7, and posterior tangents drawn at each posterior vertebral body margin. Cobb's method and the posterior tangent method are compared and contrasted with these data. RESULTS: Of 34 intraclass and interclass correlation coefficients, 28 were in the high range (>0.7), and 6 were in the good range (0.6-0.7). The Cobb method at C1-C7 overestimated the cervical curvature (-54 degrees ) and, at C2-C7 it underestimated the cervical curve (-17 degrees ), whereas the posterior tangents were the slopes along the curve (-26 degrees from C2 to C7). The inferior vertebral endplates and posterior body margins did not meet at 90 degrees (C2: 105 degrees +/- 5.2 degrees, C3: 99.7 degrees +/- 5.2 degrees, C4: 99.9 degrees +/- 5.8 degrees, C5: 96.1 degrees +/- 4.5 degrees, C6: 97.0 degrees +/- 3.8 degrees, C7: 95.4 degrees +/- 4.1 degrees ), which caused the segmental Cobb angles to underestimate lordosis at C2-C3, C4-C5, and C6-C7. CONCLUSIONS: Although both methods are reliable with the majority of correlation coefficients in the high range (ICC > 0.7), from the literature, the posterior tangent method has a smaller standard error of measurement than four-line Cobb methods. Global Cobb angles compare only the ends of the cervical curve and cannot delineate what happens to the curve internally. Posterior tangents are the slopes along the curve and can provide an analysis of any buckled areas of the cervical curve. The posterior tangent method is part of an engineering analysis (first derivative) and more accurately depicts cervical curvature than the Cobb method.

Cervical coupling during lateral head translations creates an S-configuration.

OBJECTIVE: To determine cervical coupling during the posture of lateral head translation relative to a fixed thoracic cage. DESIGN: Digitized measurements from anteroposterior cervical radiographs of 20 volunteers were obtained in neutral, left, and right lateral translation posture of the head compared to a fixed thorax. BACKGROUND DATA: Clinically, lateral translation of the head is a common posture. Ranges of motion and spinal coupling have not been reported for this movement. METHODS: Vertebral body corners, mid-lateral articular pillars and the superior spinous-lamina junction of C3-T4 were digitized on 60 radiographs. Using the orthogonal axis of positive x-direction to the left, vertical as positive y and anterior as positive z, digitized points were used to measure projected segmental z-axis rotation, y-axis rotation, and segmental lateral translations of each vertebra. RESULTS: Subjects translated their heads laterally a mean of 51 mm. The major coupled motion was lateral bending (z-axis rotation), which changed direction at the C4-C5 disc space creating an S-shape. Upper cervical (C3-C4) lateral bending was contralateral to the main motion of head translation direction. Lower cervical and upper thoracic lateral bending were ipsilateral. Other segmental motions averaged less than 1 mm and 1 degrees. CONCLUSIONS: Lateral head translations (x-axis) compared to a fixed thoracic cage can be large with a mean of 51 mm to one side. The major spinal coupling was lateral bending which changed direction at C4-C5 resulting in an S-configuration. This might have application in side impacts. All other segmental movements were small, less than 1 mm and 1 degrees. RELEVANCE: The clinically common posture of lateral head translation results in an S-shaped cervical spine and may occur in side impact trauma. This posture has not been studied for cervical coupling patterns or range of motion (ROM).

Lumbar coupling during lateral translations of the thoracic cage relative to a fixed pelvis.

OBJECTIVE: To determine lumbar coupling during lateral postural translations (lumbosacral list) of the thoracic cage relative to a fixed pelvis. DESIGN: Digitized measurements from anteroposterior lumbar radiographs of 17 volunteers were obtained in neutral, maximal left lateral translation and maximal right lateral translation posture of the thoracic cage compared to a fixed pelvis. Subjects were constrained with two sets of clamps at the lateral borders of the pelvis and lower ribs. BACKGROUND: Data. Clinically, lumbosacral list is a common posture. Range of motion and spinal coupling results have not been reported for the lumbosacral list movement. METHODS: Four vertebral body corners, mid narrow-waisted body margins, superior and inferior pedicle margins, and spinous-lamina junction of T12-L5 were digitized on 51 anterior-posterior lumbar radiographs. Using the orthogonal axes of positive x-direction to the left, vertical as positive y, and anterior as positive z, digitized points were used to measure projected segmental z-axis rotation, y-axis rotation, and segmental lateral translations of each vertebra. RESULTS: Using the displacement of T12, subjects could translate 35-70 mm left or right along the x-axis with an average of 53.2 mm to the left and 52.1 mm to the right. Using superior endplates to superior sacral base, lateral flexion was largest at L1 and decreased from L1 to L5, but the segmental rotation angles for lateral flexion were largest at L2-L3 (3.9 degrees ), L3-L4 (6.2 degrees ) and L4-L5 (5.7 degrees ) and were in the same direction as the main motion translation. The relative z-axis rotation of T12 was opposite to the direction of L1-L5. The coupled y-axis rotations were less than 1 degrees and coupled segmental lateral translations were averaging less than 1 mm. CONCLUSIONS: Thoracic cage x-axis translations compared to a fixed pelvis are significant, between 35 and 70 mm. The z-axis lumbar coupled rotation was largest at L2-L3, L3-L4 and L4-L5 and to the same side of the main motion translation in L1-L5, but opposite the main motion direction for T12. All other movements were small, averaging less than 1 degrees or 1 mm. RELEVANCE: The clinically common posture of lateral translation of the thoracic cage (lumbosacral list) is often associated with disc herniation. Yet normal lumbar coupling patterns and total range of motion of this movement have not been established in the literature. Normal values for lumbar segmental coupling on anterior-posterior lumbo-pelvic radiographs during trunk list might be important for an analysis of segmental instability since segmental translations were determined to be 1 mm or less.

Chiropractic biophysics digitized radiographic mensuration analysis of the anteroposterior lumbopelvic view: a reliability study.

OBJECTIVE: To investigate the reliability of a radiographic measurement procedure that uses a computer and sonic digitizer to determine projected spinal displacements from an ideal normal position. DESIGN: A blind, repeated-measure design was used. Anteroposterior lumbopelvic radiographs were presented to each of 3 examiners in random order. Each film was digitized, and the films were randomized for a second run. SETTING: Private, primary-care chiropractic clinic. MAIN OUTCOME MEASURES: The angle of the sacral base in comparison to a true horizontal line (horizontal base angle), lumbodorsal angle, lumbosacral angle, and the thoracic translational displacement from true vertical determined as the perpendicular distance from the center of T12 to a vertical axis line drawn from the center of the S1 spinous process cephalad and parallel to the lateral edge of the x-ray film. RESULTS: Intraexaminer reliability for the (a) horizontal base angle was .72 to .94, with confidence intervals included in the range of .52 to .97; (b) lumbodorsal angle was .90 to .96, with confidence intervals in the range of .82 to .98; (c) lumbosacral angle was .84 to .96, with confidence intervals in the range of .72 to .98, and (d) thoracic translational displacement from vertical was .95 to.97, with confidence intervals included in the range of .91 to .99. Interexaminer reliability for the three examiners ranged from .71 to .97. CONCLUSIONS: Measures similar to those described in this study are commonly used to measure and categorize spinal displacements from true vertical alignment (ie, scoliosis measurements). Most patient assessment methods used in chiropractic have poor or unknown reliability. The one possible exception to this rule is spinal displacement analysis performed on radiographs. In chiropractic, intraclass correlation coefficients values greater than .70 are considered accurate enough for use in clinical and research applications. The measures tested here would fit within these guidelines of reliability. Establishing reliability is an important first step in evaluating these measures so that future studies of validity may be undertaken.

Elliptical modeling of the sagittal lumbar lordosis and segmental rotation angles as a method to discriminate between normal and low back pain subjects.

Clinical significance of lumbar lordosis has not been agreed on. Our purpose is to compare lordotic measurements of normal and pain subjects and to test the validity of a new anthropometric model of lumbar curvatures. Digitized radiographic points (body corners) from standing lateral lumbar radiographs were modeled with ellipses in a least-squares method and were used to create segmental angles, a global angle at L1-L5, a Cobb angle from T12 to S1, Ferguson's sacral base angle, and an angle of pelvic tilt. Fifty normal subjects were matched in age, sex, weight, and height with 50 acute pain subjects, 50 chronic pain subjects, and 24 pain subjects with radiographic abnormalities. Of 11 angles, 2 distances, and 2 ratios, statistical analysis was significantly different across groups for 12 of these measurements, with the alternative hypotheses accepted for the other 3 measurements. The lordosis of both normal and low back pain subjects can be successfully modeled with a portion (approximately 86 degrees) of an ellipse, but with different major and minor axis ratios. The normal group's average elliptic lordosis has the smallest least-squares error, approximately 1 mm per digitized point, with (minor axis)/(major axis) ratio = 0.39, L1-L5 global angle = 40 degrees, and Cobb angle = 65 degrees. The chronic and radiographic abnormalities pain groups have an elongated ellipse with hypolordosis, reduced L1-L5 global angle = 29.6-35 degrees, reduced Cobb angle = 57-58 degrees, and elliptic axis ratio = 0.27-0.30. The acute pain group is hyperlordotic with the largest L1-L5 global angle, largest Cobb angle = 70 degrees, largest Ferguson's angle, and largest pelvic tilt angle.

Further analysis of the reliability of the posterior tangent lateral lumbar radiographic mensuration procedure: concurrent validity of computer-aided X-ray digitization.

OBJECTIVE: To investigate the reliability of a specific method of radiographic analysis of the geometric configuration of the lumbopelvic spine in the sagittal plane, and to investigate the concurrent validity of a computer-aided digitization procedure designed to replace the more tedious and time-consuming manual measurement process. DESIGN: A blind, repeated-measures design was used. The results of radiographic measures derived through the traditional manual marking method were compared with measures derived by computer-aided digitization of lateral lumbopelvic radiographs. SETTING: Private chiropractic clinic. MAIN OUTCOME MEASURES: Pearson's product-moment correlation coefficients, paired sample t tests and intraclass correlation co-efficients (ICC) were used to examine intraexaminer reliability, and repeated measures of analysis of variance were used to examine interexaminer reliability for relative rotation angles for T12-L1, L1-L2, L2-L3, L3-L4, L4-L5, L5-S1, overall lordosis measurement [absolute rotation angle (ARA)] from L1-L5 and Cobb angle of overall lordosis measured from the inferior surface of T12 to the superior surface of S1, Ferguson's sacral base angle to horizontal, angle of pelvic tilt (arcuate angle) to horizontal and anteroposterior thoracic translation (Sz) in millimeters. RESULTS: ICC estimates for intraexaminer reliability were in the range of 0.96-0.98 for the L1-L5 ARA, a range of 0.87-0.99 for the arcuate angle measurement, 0.83-0.94 for the Ferguson's angle measurement, 0.88-0.95 for the Cobb angle measurement from the inferior surface of T12 compared with the superior surface of S1 and 0.98-1.00 for the translation measurement of the lower thoracic spine to S1 (Sz). The intersegmental measurement's (T12-L1, L1-L2, L2-L3, L3-L4, L4-L5, L5-S1) correlations ranged from a low of 0.55 to a high of 0.97. Examination of these findings suggests that the reliability for the three doctors is acceptable with only the T12-L1 intersegmental measure falling below 0.70 for the least experienced examiner. Average ICC of interexaminer reliability for manual and computer-aided digitizing examiners were the following: 0.96 for the L1-L5 ARA; 0.84 for the arcuate angle measurement; 0.82 for the Ferguson's angle measurement; 0.88 for the Cobb angle measurement; 1.00 for the Sz translation measurement; and values of 0.65, 0.73, 0.74, 0.75, 0.89 and 0.81 for relative rotation angle measurements T12-L1, L1-L2, L2-L3, L3-L4, L4-L5 and L5-S1, respectively. CONCLUSION: The data tend to support the reliability of this method of radiographic analysis of the geometric configuration of the lumbopelvic spine as viewed on lateral lumbopelvic radiographs. The additional data presented here tend to support the concurrent validity of the computer-aided digitization method of analysis inasmuch as the measures determined by the digitizing examiners are essentially identical to those determined by the manual method plus or minus the average standard error of measure of each value.

Can the sagittal lumbar curvature be closely approximated by an ellipse?

For the sagittal lumbar curvature, existing spinal models are based only on the anthropomorphic radiographic characteristics of one individual, or, at best, of only a few individuals. This raises questions of applicability of the modeling results to clinical situations. Because spinal coupling and loads on spinal tissues have been shown to be functions of the initial static posture, a rigorously derived neutral lumbar lordosis would be important for clinicians and spine researchers. This study presents modeling of the sagittal lumbar spine in the shape of an ellipse. Vertebral body and disc heights, derived from digitized lateral lumbar radiographs of 50 normal subjects, were used to create an ellipse along the posterior body margins from the inferior of T12 to the superior sacral base. Additional data to create an elliptical lumbar model were determined from a least-squares analysis of passing ellipses through the digitized posterior body points. This confirmed that an elliptical model closely fit the lumbar curvature with a least-squares error of 1.2 mm per digitized point. The elliptical model is approximately an 85 degrees portion of a quadrant. The semi-major and semi-minor axes, a and b, are parallel to the posterior body margin of T12 and parallel to the inferior body endplate of T12, respectively, with a semi-minor to semi-major radio of b/a=0.39. The elliptic model has a height-to-length ratio of H/L=0.963, where height is the vertical distance from inferior T12 to superior S1 and length is the arc length along George's line (along the posterior longitudinal ligament) from T12 to S1.

Radiographic mensuration characteristics of the sagittal lumbar spine from a normal population with a method to synthesize prior studies of lordosis.

Standing lateral lumbar radiographs of 50 normal healthy subjects were retrospectively selected for evaluation of lumbar lordosis. The objective was to evaluate, in a normal population, global and segmental contributions to lordosis in the standing position, and to devise a method to compare the seemingly unrelated multitude of lordotic values in the literature. Because of a variety of positioning and measurement methods of lordosis in live subjects and cadavers, correlation of results is difficult. While often relying on simple pain questionnaires, studies of normal subjects rarely have complete medical history, physical, neurological, and orthopedic examinations. Standing lateral lumbar radiographs of 50 subjects, who had complete histories and normal examinations, were analyzed to determine overall lordosis, segmental contributions, and vertical sagittal alignment. Using posterior body tangents, the mean L1-L5 angle was -39.7 degrees, CobbT12-S1 = -65 degrees, Ferguson's sacral angle = 39 degrees, pelvic tilt angle was 49 degrees, and average RRAs (segmental angles) were RRAT12-L1 = -3.6 degrees, RRAL1-L2 = -4.1 degrees, RRAL2-L3 = -7.6 degrees, RRAL3-L4 = -11.7 degrees, RRAL4-L5 = -16.8 degrees, and RRAL5-S1 = -32.4 degrees. Using segmental rotation angles as a method to compare past and current literature, a normal standing lumbar lordosis of CobbT12-S1 = -61 degrees, range -55 degrees to -65 degrees, was determined with specific segmental angles.

Evaluation of the assumptions used to derive an ideal normal cervical spine model.

OBJECTIVES: To evaluate the accuracy of anatomical assumptions made to derive a geometrical, ideal, normal model of the upright, static, sagittal cervical spine, to make comparisons with other spinal models and to discuss the implications of a normal cervical model. BACKGROUND: Anatomical assumptions were made based on observations to assist in the development of a computerized geometrical model of the ideal upright, static, sagittal cervical spine. These assumptions address the magnitudes of the contribution made by the vertebral bodies and intervertebral discs to the overall magnitude and geometric shape of the cervical lordosis. STUDY DESIGN: (a) Data were collected from 400 lordotic lateral cervical radiographs and compared with the predictions of a geometric normal cervical lordotic model. Angels of intersecting tangent lines, drawn at posterior vertebral body margins, were measured at each disc space and between C2 and C7. Height-to-length ratios and an anterior weight-bearing distance were measured. (b) LITERATURE REVIEWs were obtained through Medline and Chirolars. RESULTS: (a) Modeling: the 400 sample subjects varied from the geometric model by approximately 5%. Subgroup averages, from partitioning the C2-C7 angle into 5 degrees intervals, were less than 8% in error to model predictions. (b) LITERATURE REVIEW: lordosis is the normal configuration for the cervical spine and many chiropractic empirical models are similar. CONCLUSIONS: The anatomical assumptions used to derive our normal geometric model of the cervical lordosis seem to be supported by the average values and literature reviewed. Two typical geometric configurations of the cervical spine were identified as a normal circular lordotic arc of 34 degrees and an ideal normal of 42 degrees. LITERATURE REVIEWed establishes cervical lordosis as a desirable clinical outcome of care.

Chiropractic biophysics technique: a linear algebra approach to posture in chiropractic.

OBJECTIVE: This paper discusses linear algebra as applied to human posture in chiropractic, specifically chiropractic biophysics technique (CBP). MATHEMATICAL ANALYSIS: Rotations, reflections and translations are geometric functions studied in vector spaces in linear algebra. These mathematical functions are termed rigid body transformations and are applied to segmental spinal movement in the literature. Review of the literature indicates that these linear algebra concepts have been used to describe vertebral motion. However, these rigid body movers are presented here as applying to the global postural movements of the head, thoracic cage and pelvis. CONCLUSION: The unique inverse functions of rotations, reflections and translations provide a theoretical basis for making postural corrections in neutral static resting posture. Chiropractic biophysics technique (CBP) uses these concepts in examination procedures, manual spinal manipulation, instrument assisted spinal manipulation, postural exercises, extension traction and clinical outcome measures.

A normal sagittal spinal configuration: a desirable clinical outcome.

OBJECTIVE: Traditional forms of chiropractic treatment methods have attempted to restore alignment of vertebrae to proposed "normal" positions. Although this approach has existed throughout chiropractic's 100-yr history, little has been written in the scientific literature in support of this approach. The objective of this review is to study further the rationale behind this approach and evaluate some of the mechanical, anatomical and physiological evidence upon which this chiropractic approach is based. STUDY SELECTION: Articles and studies were selected that discuss analysis of stress and strains in spinal tissues from gravitational loading and experimental deformation in human and animal models. Studies that included radiographic measurements and classifications of spinal configuration in the sagittal plane were reviewed for their relevance to the chiropractic concept of a typical, usual or normal spinal configuration against which to compare patients. CONCLUSION: The usual, typical or normal configuration of the cervical spine in the sagittal dimension is a lordosis with a range of 16.5-66 degrees when measured as tangent lines along the cervical curve of the posterior vertebral body margins of C2 and C7. An analysis of stresses and strains supports this claim, as do studies from the scientific literature that attempt to measure and classify average cervical configuration from large population bases. The use of normative data as a gauge against which to measure patients' structural health and as an outcome of the degree of success or failure of chiropractic interventions seem to be logical consequences of these findings.

Comparisons of lordotic cervical spine curvatures to a theoretical ideal model of the static sagittal cervical spine.

STUDY DESIGN: Measurements from lateral cervical radiographs of randomly selected patients are compared with two proposed ideal models. OBJECTIVES: To evaluate lordotic cervical curvatures from a large population base, to provide a geometric sagittal cervical spine model, and to test the validity of the model to predict measured angles and distances. Averages of ranges and normal values for cervical lordosis under conditions of static equilibrium are sought. SUMMARY OF BACKGROUND DATA: Seven angles and three distances were taken from 400 randomly selected lateral cervical radiographs of patients at a private clinic. METHODS: The radiographic measurements are compared with predicted values from our geometric sagittal cervical spine model and the Delmas ideal cervical model. RESULTS: Values were predicted successfully by the geometric model with an average error of 5% compared with the radiographic measurements. The range of lordosis, measured at the posterior of C2 and C7, was 16.5-66 degrees, with a mean of 34 degrees. The average height-to-length ratio for the cervical spine was 0.97. CONCLUSIONS: Predicted values from the geometric model were comparable with the measurements of the relative rotation angles at each vertebral interspace, absolute rotation angles from C2 to C7, and height-to-length ratios. A cervical lordosis of 34 degrees and a height-to-length ratio of 0.97 are suggested for clinical and theoretical outcomes.