Introduction

Have you ever experienced unnerving pain on your back? maybe from a sport, standing for long hours or poor posture? It likely came from your spine. The spine is composed of 33 vertebrae bones. We’ll stick to the lumbar section for now.

The lumbar spine consists of the five vertebrae in your lower back (L1-L5). It provides support for the weight of your body, surrounds and protects your spinal cord, and allows for a wide range of body motions. Conditions such as lower back pain, arthritis, degenerative bone and disk disease, and stenosis can affect this area of the spine.

Among the treatment options available is a surgery to restore the sagittal alignment. Evidence suggests a relationship between the natural aging process and a forward sagittal posture.

Spine surgeons use many measurements to determine alignment parameters. Furthermore, alignment goals should vary based on the patient’s age to account for the naturally aging spine.

Below is a pictorial aid of some parameters used by spine surgeons along with a case study x-ray:

More recently, a relationship between the L1 Pelvic Angle (L1PA) and the Pelvic Incidence (PI) has been identified.

Pelvic incidence

Pelvic incidence (PI), is defined as the angle between the line perpendicular to the sacral endplate at its midpoint and a line connecting this point to the midpoint of the hip axis. PI increases gradually during childhood as a result of bipedal walking. After bone maturity, PI remains constant over ones lifetime.

Lumbar pelvic angles

The L1 vertebra is the smallest and most superior of the lumbar vertebrae. As the first vertebra in the lumbar region, the L1 vertebra bears the weight of the upper body and acts as a transition between the thoracic and lumbar vertebrae.

The lumbar pelvic angle L1PA changes over time. For instance, a young healthy individual might have a low L1PA of 10 degrees due to their upright posture. As they age, they may slouch forward causing this angle to increase. This might coincide with a degenerated disk that leads to back pain.

The goal of one study at OrthoCarolina Research Institute (OCRI) is to describe the relationship of L1PA to PI in an aging asymptomatic cohort to further characterize the compensatory mechanisms in these individuals. This was in an effort to identify the utility in using these measures as alignment targets in spinal deformity surgeries.

Data from 100+ participants above the age of 60 was collected using surgimap. The OCRI research team was then tasked with the analysis.

Statistical analysis

The study question of whether or not there is an equation that explains this relationship can best be answered after evaluating the results of the regression analysis done using the measurements of the 100+ participants. This was an adequate sample size at least in the context of surgical studies. A regression analysis of the outcome L1PA as explained by ones PI was performed.

There are two main take home results from a regression analysis:

The fitted regression line: an equation of a straight line in the form of y = mx + c fitted using the observed data. m is the slope and c is a constant y-intercept. Remember this math?
R-squared (coefficient of determination): a statistical measure that represents how much of the posited relationship can be explained by the regression model.

Results

The resulting model was L1PA = 0.4PI - 11 with an R-squared = 0.5.

We can also view this equation as L1PA + 11 = 0.4PI.

The R-squared value of 0.5 actually reveals a poorly fitting model. Only 50% of one’s L1PA can be explained by their PI. The rest of the variation was found to be due to the individual differences between the subjects. This is a case where a one size fits all equation is inadequate.

Case study

In the case study x-ray, the PI = 69 and L1PA = 23.

Let’s try to interpret what a model actually implies:

If this is an individual needing surgery, the surgeon CANNOT confidently use an equation that assumes L1PA + 11 should give you 0.4(69) therefore, mapping an alignment to restore the PI to 16.6 degrees from the current 23 degrees (16.6 = 27.6 - 11).

Due to the high variation between the individuals measured in our study, a correction based on this equation might be an over kill resulting in postoperative complications.

If people aged 60+ were more homogeneous in their bone structure and the way they aged, we would expect a higher R-squared hence a more reliable model.

Conclusion

There is a weak relationship between L1PA and the Pelvic Incidence due to the heterogeneous nature of the study participants.

This study reiterates the need for the surgeon to carefully consider individual patient characteristics in planning and executing deformity surgery.

Appropriate statistical analysis plays an integral part in surgical research. The quality of results depends on appropriate study design, data collection, and analysis to help the surgeons draw meaningful conclusions from data.

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Kennedy Gachigi: Research Scientist