Fig. 47.1
Pelvic parameters: pelvic incidence (PI), sacral slope (SS), and pelvic tilt (PT) (From Barrey [18]; with permission)
The most commonly used pelvic parameters were described by Duval-Beaupère [19]. Pelvic incidence (PI) is a shape parameter that relates the sacral plateau with the bifemoral axis. Pelvis tilt (PT) is a positional parameter that gives the rotational position of the pelvis around the femoral heads. Sacral slope (SS) is a positional parameter that gives the angle between the sacral plateau direction and the horizontal.
PI angle consists of the angle between two lines, namely, the line drawn between the midpoint of bicoxofemoral axis (midpoint of the line joining the center of both femoral heads) and the middle of the sacral plateau and the line perpendicular to the middle of the sacral plateau (Fig. 47.1). PI is a morphological immutable angle in adulthood, being specific to each individual [18]. PI is anatomically determined by the shape of the sacrum: pelves with high PI have generally a short sacrum tending to horizontalization (sacral plate is far below and behind the top of iliac wings in lateral view) while those pelves with low PI have a long vertical sacrum in lateral view (sacral plate close to the top of iliac wings) (Fig.47.9). Definitive value of PI is acquired when final skeletal growth is achieved. There is some controversy concerning a possible variation of PI (increase) with aging by sacroiliac joint degeneration.
The second pelvic parameter is the sacral slope angle (SS), which is the angle formed by two lines: a horizontal line and the line passing through the sacral endplate (Fig. 47.1). The steeper the sacral plateau, the greater the SS. Thus, the more inclined anteriorly the sacrum (anteverted pelvis), the greater the SS; the more verticalized the sacrum (retroverted pelvis), the lower the SS. The longitudinal analysis of the flattening or the slope of the sacral plateau in a same patient may reflect a compensatory mechanism for an imbalanced spine. When there is a compensatory retroversion, the sacral plateau flattens and SS decreases. The horizontalization of SS may affect the forces acting on disks and facets.
The third pelvic parameter is the pelvic tilt angle (PT) (Fig. 47.1), the angle between two lines, namely, a vertical straight line and the line drawn from the midpoint between the two femoral heads’ centers to the midpoint of the sacral endplate. The PT sets the oscillating motion of the hips around the bicoxofemoral axis, the femoral heads. This is possible due to the spherical shape of coxofemorals. When the pelvis swings forward, anteversion, the PT is lower; when it swings backward, pelvis retroversion, the PT is higher. The retroversion of the pelvis, the first compensatory mechanism of sagittal imbalance, aims to bring back the spine to the balanced situation, with C7 plumb line behind the posterior part of the sacrum. Thus, PT and SS are positional parameters, variables [12].
Legaye et al. [20, 21] and Duval-Beaupère et al. [19] noted important correlations between pelvic parameters, linked by the geometrical relation PI = PT+ SS [19, 20, 21]. The algebraic equation is: A = x + y, where A is constant and x and y are variable. Even if many studies have described a strong correlation between PI and SS (R: 0.8, P < 0.001) and PI and PT (R: 0.65 p < 0.001), it is mathematically impossible to write a linear relation between PI and SS or PI and PT.
If A = x + y, then x = kA + b or y = k′A + c; but this is not totally true to PI = PT + SS. A direct extraction of PT or SS from PI is a statistical approximation but cannot be written under a mathematical equation.
Interpretation of PI = PT + SS could be done in two means:
For a same person, PI is constant: when PT increases, SS decreases (retroverted pelvis=smaller SS); when PT decreases, SS increases (anteverted pelvis=higher SS).
For different people, a marked pelvis retroversion (high PT) is possible with higher PI only. Even with a small PI, a high SS is possible when the pelvis is very anteverted (small PT or negative PT).
An increase of the PT is the earliest compensatory mechanism resulting from the loss of lordosis of natural aging or may be the result of lack of lordosis obtention after fusion surgery (flat back syndrome).
47.4 Spinal Parameters
47.4.1 Spinal Segmentation and Length of Lumbar Lordosis (LL)
To assess the sagittal balance, the authors took into account the part of the spine between C7 and T1 and the sacral plateau, excluding the cervical spine. While in animals the thoracic and lumbar spine have only one kyphotic curvature, in humans, two successive curves are described: thoracic kyphosis and lumbar lordosis. Anatomically, the first, corresponding to the thoracic vertebrae, is limited by C7–T1 disk above and T12–L1 disk below, and the second by T12–L1 proximally and S1 plateau distally (Fig. 47.2a) [12, 19, 22]. However, if we consider that lordosis is composed by vertebrae in the part of the spine where the curve is in extension, the length of extension in lumbar area may be variable (Fig. 47.2b). This concept has brought Berthonnaud et al. to describe a segmentation model of the spine with two curves between vertebrae T1 and S1: thoracic kyphosis and lumbar lordosis, limited by an inflection point where kyphosis turns into lordosis [5]. Thus, lordosis may be defined as the segment of the spine between the sacral endplate and the inflection point, without any reference to a specific anatomical landmark. The inflection point may be at the level of T12–L1 disk, a little bit higher or a little bit lower. In Roussouly type 1 lordosis, a thoracic vertebra, T12, may be at least in part in the lordotic spine, as it has been demonstrated in previous studies [12, 23]. Thus, this concept may affect the planning of an arthrodesis. The same remark may be done when using Cobb measurement. As for frontal scoliosis measurements, sagittal Cobb method has to address the most tilted vertebrae to measure a curve angle.
Fig. 47.2
(a) Subdivision of the sagittal spinal curvatures. Cervical spine goes from C1 to C7. Thoracolumbar spine is limited by C7–T1 and the sacral plateau. Inflection point is the place where the lordosis curve turns into kyphosis. This is a variable limit between lordosis and kyphosis (From Roussouly and Pinheiro-Franco [17]; with permission). (b) There is a great variability of the length of lordosis. Note shorter and marked lordosis on the left (lower pelvic incidence) and long and more harmonious lordosis on the right (higher pelvic incidence)
Stagnara pointed out the relation between LL and SS [24], with a description of static and dynamic spinal curvatures. Statistically, a strong correlation between LL and SS was well established [20] and Duval-Beaupère has extracted a statistical equation: 
. More recently, Roussouly et al. [6] proposed a classification of LL according to SS (Fig. 47.3). This classification was fundamented by the lordosis concept from the aforementioned segmentation model [5], being lordosis defined from the inflection point to the sacral endplate. LL curvature is divided into two arcs of circle tangent on the horizontal line passing on the apex of LL.
. More recently, Roussouly et al. [6] proposed a classification of LL according to SS (Fig. 47.3). This classification was fundamented by the lordosis concept from the aforementioned segmentation model [5], being lordosis defined from the inflection point to the sacral endplate. LL curvature is divided into two arcs of circle tangent on the horizontal line passing on the apex of LL.Fig. 47.3
The shape of lumbar lordosis depends on SS orientation. Types 1 and 2 have SS <35°; type 3 has 35° < SS <45°; and type 4 has SS >45° (From Roussouly and Pinheiro-Franco [3]; with permission)
47.5 Lumbar Lordosis Geometrical Analysis [17]: Basis for Roussouly Classification
Lumbar lordosis is not homogeneous throughout its extension. The angle of lordosis is not evenly distributed from the sacrum endplate to the proximal limit in the inflection point where the spine bends into kyphosis. The contribution of each functional segment unit to the lordosis increases progressively from L1 to L5. Two-thirds of the total lordosis is depicted in the lower lumbar spine L4–S1 [18]. A meta-analysis demonstrated that 66 % of LL concentrates in L4–L5 and L5–S1 (n = 552) [25]. Geometrical constructions of the spine have been proposed to describe LL: arc of circle [5] and quadrant of an ellipse [26]. The ellipsoid design is very realistic but difficult to use in everyday clinical practice [18]. Berthonnaud et al. [5] described a mathematical construction of lumbar lordosis. These authors proposed that lumbar lordosis could be measured using the Cobb method between the upper plateau of the sacrum and the inflection point where lordosis turns into kyphosis. The point of tangency of a vertical line with the anteriormost part of the convex side of lordosis with the vertical is the apex of lordosis. A horizontal line is traced from the apex of lordosis and defines two arches (Fig. 47.4): a lower arch (from the apex horizontal line to the sacral plate line) and an upper arch (from the apex horizontal line to the inflection point into kyphosis). The angle of the lower arch and the SS are equal and vary together by definition [6] (Fig. 47.4). Roussouly et al. demonstrated that the mean value of the upper arch angle was 20° and was stable whatever the value of SS was [6]. This explains why the lordosis is linked to the value of the lower arch (and therefore to SS). This has important implications in lumbar spine fusions.
Fig. 47.4
(a) Schematic representation of arc of a circle model for type 1 lordosis. Note that the lower arch of the lumbar lordosis (=SS) is too small and the apex of lordosis is very low. There is a backward displacement of the top of lordosis and a very positive weighbridge angle. (b) Schematic representation of arc of a circle model for type 2 lordosis. The lower arch (SS) is slightly larger than in type 1, and the lordosis is still very small. The angle of weighbridge is from positive to zero. (c) Schematic representation of arc of a circle model for type 3 lordosis. Lordosis is divided between the two arches and the apex is at the center of L4. (d) Schematic representation of arc of a circle model for type 4 lordosis. The inflection point may be at the lower thoracic region. The lordosis angle increases as the number of vertebrae increases in the lordosis. The apex rises above L4 (From Barrey [18]; with permission)
47.6 The Roussouly Classification
Based on the geometrical model aforementioned, Roussouly et al. developed a classification of spinopelvic morphotypes translated by four types of lumbar lordosis according to the angle of SS and PI. The variation of lordosis was defined by the extent of the lower arch, and thus the SS. The separation of the values of the SS, according to Gauss curve, allowed the SS values to be classified into three groups depending on their values: SS <35°, 35° < SS <45°, SS >45° (Fig. 47.3). The values 35° and 45° were previously established [6, 18].
When the SS is small (<35°), two spinopelvic morphotypes of lordosis could be demonstrated:
Type 1: short acute lordosis (concentrated in L4–L5 and L5–S1). The thoracic kyphosis extends slightly into the lumbar spine and therefore, the thoracolumbar (TL) junction is under the classic T12–L1 disk. The lower arch of the lumbar lordosis (=SS) is too small, and the apex of lordosis is very low. There is a backward displacement of the top of lordosis and a very positive weighbridge angle. As lordosis is short, the kyphosis is long and extends a little beyond the thoracolumbar spine (Fig. 47.4a);
Type 2: corresponds to “flat back.” The lumbar spine is usually quite flat. The lower arch (SS) is slightly larger than in type 1, and the lordosis is still very small. The angle of weighbridge is from positive to zero (Fig. 47.4b).
When SS has an average value (between 35 and 45°):
Type 3: the best balanced spine. The inflection point is at the thoracolumbar junction. Lordosis is divided between the two arches and the apex is at the center of L4. There are usually four to five vertebrae in the curvature. The angle of weighbridge is from positive to zero (Fig. 47.4c).
When the SS is high (>45°):
Type 4: The inflection point may be at the lower thoracic region. The lordosis angle increases as the number of vertebrae increases in the lordosis. The apex rises above L4. The toggle angle is generally from zero to negative. As lordosis is extended, the thoracic kyphosis is shortened (Fig. 47.4d).
47.6.1 LL and PI Relations
In asymptomatic volunteers, there is a strong correlation between LL and PI but less than between LL and SS. The authors have seen that due to the relation PI = PT + SS, there is a strong correlation between PI and SS but without concluding to a linear relation. Generally for a small PI, SS is smaller and this situation is represented mainly by types 1 or 2 lordosis. On contrary, for high-grade PI, SS is generally higher, with more type 3 or 4 lordosis. Occasionally, the authors have seen that PT may be small (<10°) or even negative in very anteverted pelvis. This situation may allow SS >40° even with a small PI and conducts to type 3 or 4 lordosis with a small PI. The value of PI may bring to a tendency of LL morphotypes, but to extract LL value from PI is an inexact extrapolation.
47.6.2 LL and Thoracic Kyphosis Angle (TK)
LL and TK are linked by their length and angles. Spinal parameters LL and TK are interdependent (Fig. 47.2). Jackson and McManus [13] found a significant correlation between LL and TK [27]. One change in one segment induces a change in the reciprocal segment according to the flexibility of the spine. If the TK increases, LL increases in order to maintain C7 in the balanced position. Reversely, when LL decreases, TK decreases, flattening the back.
Following the inflection point, the distribution of both LL and TK is variable. In case of short LL, TK may reach the thoracolumbar area. With long LL, TK may be shortened in the more proximal thoracic area. Sometimes, both LL and TK curves are separated by a straight segment of a variable number of vertebrae (Fig. 47.2). The importance of this disposition is not well validated but requires further study.
If we consider the tangent arcs of circle segmentation, there is a direct relation between the upper arc of LL and the lower arc of TK. An increased TK may induce an increased LL. This is more relevant in type 1 (too small lower arch of LL) where the total LL depends mostly on the upper arch of LL that has to compensate the higher lower arc of TK in the thoracolumbar area.
47.7 Global Balance of the Spine
47.7.1 The Global Balance [17]
To the analysis of the global balance of the spine, several points have been proposed. One of them, the external ear conducts, is useful to indicate the head positioning. The T9 tilt was described by Duval-Beaupère et al. as an indicator of the spine balance at the body mass center level [19, 27]. Historically, a vertical [4] plumb line originating in the center of the C7 vertebral body was deemed to be in approximately the same place in the sagittal plane as a vertical line passing through the patient’s center of gravity (Fig. 47.5). Easy to be read on sagittal X-rays, C7 plumb line is the most commonly used index of the global balance. Kuntz et al. [28] noted in a review of the literature that global parameter as C7 plumb line was a stable, reliable index of the sagittal balance, being maintained in narrow ranges for alignment of the spine over the pelvis and femoral heads. This parameter has been historically quantified by measuring the position of a vertical line originating in the center of the C7 vertebral body with respect to the posterior superior corner of S1.
Fig. 47.5
Mechanism of compensation of a progressive kyphosis. (a) Balanced spine – C7 PL over the sacral endplate. (b) With progressive loss of lordosis, pelvis retroversion permits maintaining C7 PL behind the femoral heads. (c) Severe unbalance, retroversion reaches its limits, knees flexed in attempt to “put backwards C7 PL”; note the Pelvifemoral angle (PFA) (From Roussouly and Pinheiro-Franco [3]; with permission)
The center of the vertebral body of C7 may be considered as the upper limit of the thoracic spine and, indeed, of the whole spine below the cervical area. Before recent radiograph quality advances, C7 was considered easier to be identified rather than T1 that was hidden by the shoulder superposition.
The positioning of C7 has been widely studied and its implication in sagittal balance well established. Three ways of evaluation are possible:
Distance measurement: sagittal vertical axis (SVA) is the distance between the posterior edge of the sacral plateau and the C7 plumb line projection. Schwab et al. [29] considered that a value superior to 5 cm is an evidence of imbalance. Radiograph distance measurement is controversial. It is necessary to have a precise calibration of the radiographies as comparison between the radiographies may lead to potential errors. On another way, if SVA >5 cm is certainly an imbalanced situation, SVA <5 cm does not depict obvious balance.
The authors prefer to use angles or distance ratio, as these are not subject to calibration variations typical of radiographs.
Angles measurement: using the line from the center of C7 to the center of the sacral plateau, two angles are designed:
C7 tilt is a positional parameter with the vertical direction. This angle is very stable in a normal population around 3–5° backward.
Spinosacral angle, SSA, is a shape parameter drawn with the sacral plateau line (angle between the line from the center of C7 to the center of the sacral plate and the sacral plate line itself). It is representative of the total kyphosis of the whole thoracolumbar spine (cervical spine excluded). Its very high correlation (R > 0.9) with SS in an asymptomatic population demonstrates the stability of positioning C7 plumb line over the sacrum in normal conditions.
Distance ratio: described by Barrey [18], the ratio between the distance of the C7 plumb line and the posterior edge of the sacrum, and the distance of the C7 plumb line and center of femoral heads, allows the positioning of C7 plumb line relative to these two anatomical landmarks.
C7 plumb line must be related to an anatomical pelvic landmark as the center of the femoral heads (CFH) or the posterior point of the sacral plate (PP-S1). Usually, the horizontal distance between C7 PL and an anatomical landmark is calculated. It is not recommended to use distance to characterize this position. Barrey proposed a ratio between the horizontal distances from C7 PL to CFH and between CFH and PP-S1 (Fig. 47.6). This ratio provides an adimensional value concerning the position of C7 PL in relation to the vertical lines passing through CFH and through PP-S1 (Fig. 47.6):
Fig. 47.6
In order to avoid errors with distance magnification C. Barrey proposed a ratio between horizontal distances from the center of the femoral heads (FH) and C7PL (R1) and the distance from FH and the posterior edge of the sacral plate (R2). R1/R2 is negative when C7 PL is forward FH, 0 < R1/R2 < 1 when C7PL is between FH and the sacrum, and R1/R2 > 1 when C7PL is behind the sacrum (From Roussouly and Pinheiro-Franco [17]; with permission)
When C7 PL is behind the PP-S1 (ideal, balanced situation), the ratio value is superior to 1.
When C7 PL is between CFH and PP-S1, the ratio is between 0 and 1 (balance is compromised).
When C7 PL is forward CFH, the ratio value is negative (noncompensated severe imbalance).
47.7.2 Method of Measurement [27]
The analysis of the sagittal balance of the spine requires radiographs in a standardized fashion. The Cobb method may be used. A lateral radiograph of the spine must be made with vertical 30- to 90-cm film with a constant distance from the radiographic source. The knees must be fully extended and the arms flexed forward to 45° and resting on supports. According to Vedantam et al. [30], positioning the arms at 90° rather than 30° resulted in a negative shift of the sagittal vertical axis. Marks et al. [31] affirmed that shoulder flexion of 45° is the best position to use when a lateral radiograph is made, in order to repeatedly measure the sagittal vertical axis.
The radiograph must show the femoral heads caudally and C7 cranially. Radiographs should be digitized, and all measurements may be performed by specialized softwares. The present authors use KEOPS (SMAIO, Lyon, France) (Fig. 47.7). The software permits rapid and precise measurement of all angular parameters on digitized radiographs. Other authors [32] demonstrated in a similar software that the intraobserver and interobserver reliability is very high and that the results obtained by the numerical process are similar to those obtained by manual measurement. Recently, the EOS system was developed allowing full-spine standing imaging with minimal irradiation.
Fig. 47.7
Analysis of the sagittal balance using digitized imaging and software KEOPS (SMAIO, Lyon, France)
The KEOPS sagittal balance analyzer is a Web-based software aimed to measure key spinopelvic parameters on long-standing sagittal X-rays from femoral heads to center of ears; compare measured parameters to those of asymptomatic populations using specific cursors and simulate surgical correction on sagittal spinopelvic reconstruction. Accuracy and repeatability were validated with multiple users performing two times 30 measurements [33]. It was observed that the measurements were more reliable than manual measurements performed by the same users. The software proposes a global acquisition mode in which femoral heads, S1 plate, center of C7, and a b-spleen line passing through the middle of each vertebral body are acquired in less than 2 min. A synthesis allows users to compare patient spinopelvic morphology and positioning parameters with those of an asymptomatic population (709 asymptomatic volunteers were assessed). The simulation modules allows to measure effect of pelvic tilt decompensation on C7 balance and simulate PSO as well as Smith-Petersen osteotomies depending on the level and the amount of correction.
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