Prediction equations for human thoracic and lumbar vertebral morphometry

Abstract

Statistical correlations between anatomical dimensions of human vertebral structures have indicated a potential for the prediction of vertebral morphometry, which could be applied to the creation of simplified geometrical models of the spine excluding the need for preliminary processing of medical images. The aim of this study was to perform linear and nonlinear regressions with published anatomical data to generate prediction equations for 20 vertebral parameters of the human thoracic and lumbar spine as a function of only one given parameter that was measured by X-ray. Each parameter was considered individually as a potential predictor variable in terms of its correlation with all of the other parameters, together with the readiness with which lateral X-rays could be obtained. Based on this, the parameter vertebral body height posterior was chosen and the statistical analyses described here are related to this parameter. Our linear, exponential and logarithmic regressions provided significant predictions of anterior vertebral structures. However, third-order polynomial prediction equations allowed an improvement on these predictions (P-values < 0.001), e.g. endplates and spinal canal (R(2), 0.970-0.995) as well as pedicle heights and the spinous process (R(2), 0.811-0.882), in addition to a reasonable prediction of the posterior vertebral structures, which have shown a low or no correlation in previous studies, e.g. pedicle inclination and transverse process (R(2), 0.514-0.693) (anova). Comparisons of the theoretical predictions with two other sets of experimental data indicated that the predictions generally agree well with the experimental data. A time-efficient approach for obtaining anatomical data for the description of human thoracic and lumbar geometry was provided by this method, which requires the measurement of only one parameter per vertebra (vertebral body height posterior) from a lateral X-ray and the set of developed prediction equations. Vertebral models based on this type of parameterized geometry could be used in biomechanical studies that require geometry variation, such as in spinal deformations, including scoliosis.

Fig. 1

Schematic representation of the vertebral anatomical parameters that were considered for linear and nonlinear regression analyses.

Fig. 2

Description of the statistical procedure performed for two vertebral parameters. (A) Correlation of experimental data of the thoracic and lumbar spine (in this case, VBHP vs. EPWS) and set of prediction equations generated from linear, logarithmic, exponential and polynomial regression analyses (y is the value of EPWS and x is the value of VBHP on each vertebral level). (B) Values of EPWS predicted using linear and polynomial equations are superimposed on experimental data to allow the selection of the best equation. Dotted curve indicates SD of the experimental data. Residual plots evaluation shows that the polynomial equation is significantly better.

Fig. 3

Linear and polynomial predictions of parameters related to endplates and vertebral body (EPWS, EPWI, EPDS, EPDI, EPIS and EPII) (A-F) superimposed on experimental data of Panjabi et al. (1991, *. Dotted curve indicates SD of the experimental data.

Fig. 4

Linear and polynomial predictions of parameters related to pedicles (PWL, PWR, PHL, PHR, PTIL, PTIR, PSIL and PSIR) (A-H) superimposed on experimental data of Panjabi et al. (1991, *. Dotted curve indicates SD of the experimental data.

Fig. 5

Linear and polynomial predictions of other vertebral posterior structures (SCW, SCD, SPL and TPW) (A-D) superimposed on experimental data of Panjabi et al. (1991, *. Dotted curve indicates SD of the experimental data.

Fig. 6

Geometric models of the human thoracic (T1–12) and lumbar (L1–4) vertebrae constructed with parameters related to endplates and vertebral bodies (EPWS, EPWI, EPDS, EPDI, EPIS, EPII, VBW and VBD). The first model corresponds to the data of Panjabi et al. (1991, and was created using eight parameters per vertebral level (a total of 128 parameters). The other models were generated using only the values of the VBHP of each vertebral level and predicted parameters from linear, exponential, logarithmic and polynomial equations.

Fig. 7

Comparison of some predicted vertebral parameters (EPWS, PHL, PSIL and SCW) with corresponding experimental data from Berry et al. (1987) (left column, A–D) and Scoles et al. (1988) (right column, E–H) in selected vertebral levels. The means and 95% confidence intervals (dotted lines) of the experimental and predicted values are shown.