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Updated: Apr 19, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
Published on: April 11, 2018
A standardized representation of spinal quality of motion
Shannon A Zirbel1, Dean K Stolworthy1, Larry L Howell1
1Mechanical Engineering Department, Brigham Young University, Provo, UT, USA.
Abstract:
The experimentally determined torque-rotation curve of the lumbar spine is mathematically described with a proposed dual-inflection point Boltzmann equation. The result is a method for describing functional spinal unit motion data. The benefit of the model is that each of the coefficients has a specific meaning in relation to the torque-rotation curve: the points A and B identify the respective minimum and maximum rotations of the functional spinal unit, m1 and m2 indicate the inflection points of the curve where the stiffness changes markedly, and α1 and α2 are associated with the rates of change of the curve at m1 and m2, respectively. The dual-inflection point Boltzmann captures the full quality of motion of the spinal segment and can also be used to derive relevant parameters such as range of motion, midrange stiffness, and hysteresis.
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