Question

I am starting to learn spinal anatomy and I want to determine the Instantaneous axes of rotation (IAR) of individual vertebrae. I have referred many research papers but haven't come across any useful material.

Let's say I have the center points of superior and inferior plates of L5. Similarly I have the center point of superior plate of S1.
Is there any way to mathematically determine the IAR for L5 for lumbar flexion(say) ?.

Answer 1

Yes, you can mathematically determine the Instantaneous Axis of Rotation (IAR) for lumbar flexion of L5 using the center points of the superior and inferior plates of L5 and the center point of the superior plate of S1. One common method is to use the concept of screw axis theory, which involves the application of spatial geometry to define the rotation axis in three-dimensional space.

Step-by-step explanation:

Determining the Instantaneous Axis of Rotation (IAR) for lumbar flexion involves applying principles of screw axis theory. Let's denote the center point of the superior plate of L5 as
`\(_L5S\)`, the center point of the inferior plate of L5 as
`\(_L5I\)`, and the center point of the superior plate of S1 as
`\(_S1S\)`. The IAR can be calculated by finding the common perpendicular between the line connecting
`\(_L5S\)` and
`\(_L5I\)` and the line connecting
`\(_L5S\)` and
`\(_S1S\)`. This common perpendicular represents the axis of rotation for lumbar flexion.

To mathematically express this, you can use vector algebra. Let
`\(\vec{V}_(L5S-L5I)\)` be the vector from
`\(_L5S\) to \(_L5I\)` and
`\(\vec{V}_(L5S-S1S)\)` be the vector from
`\(_L5S\)` to
`\(_S1S\)`. The cross product of these vectors
`(\(\vec{V}_(L5S-L5I) * \vec{V}_(L5S-S1S)\))`gives a vector along the axis of rotation. Normalize this vector to obtain the unit vector representing the Instantaneous Axis of Rotation.

In conclusion, utilizing spatial geometry and vector algebra, you can determine the Instantaneous Axis of Rotation for lumbar flexion based on the given center points of L5 and S1.