A mechanistic approach for the calculation of intervertebral mobility in mammals based on vertebrae osteometry

In this paper, we develop and validate an osteometry-based mechanistic approach to calculation of available range of motion (aROM) in presacral intervertebral joints in sagittal bending (SB), lateral bending (LB), and axial rotation (AR). Our basic assumption was the existence of a mechanistic interrelation between the geometry of zygapophysial articular facets and aROM. Trigonometric formulae are developed for aROM calculation, of which the general principle is that the angle of rotation is given by the ratio of the arc length of motion to the radius of this arc. We tested a number of alternative formulae against available in vitro data to identify the most suitable geometric ratios and coefficients for accurate calculation. aROM values calculated with the developed formulae show significant correlation with in vitro data in SB, LB, and AR (Pearson r = 0.900) in the reference mammals (man, sheep, pig, cow). It was found that separate formulae for different zygapophysial facet types (radial (Rf), tangential (Tf), radial with a lock (RfL)) give significantly greater accuracy in aROM calculation than the formulae for the presacral spine as a whole and greater accuracy than the separate formulae for different spine regions (cervical, thoracic, lumbar). The advantage of the facet-specific formulae over the region-specific ones shows that the facet type is a more reliable indicator of the spine mobility than the presence or absence of ribs. The greatest gain in calculation accuracy with the facet-specific formulae is characteristic in AR aROM. The most important theoretical outcome is that the evolutionary differentiation of the zygapophysial facets in mammals, that is the emergence of Tf joints in the rib cage area of the spine, was more likely associated with the development of AR rather than with SB mobility and, hence, with cornering rather than with forward galloping. The AR aROM can be calculated with the formulae common for man, sheep, pig, and cow. However, the SB aROM of the human spine is best calculated with different coefficient values in the formulae than those for studied artiodactyls. The most suitable coefficient values indicate that the zygapophysial articular facets tend to slide past each other to a greater extent in the human thoracolumbar spine rather than in artiodactyls. Due to this, artiodactyls retain relatively greater facet overlap in extremely flexed and extremely extended spine positions, which may be more crucial for their quadrupedal gallop than for human bipedal locomotion. The SB, LB, and AR aROMs are quite separate in respect of the formulae structure in the cervical region (radial facet type). However, throughout the thoracolumbar spine (tangential and radial with lock facets), the formulae for LB and AR are basically similar differing in coefficient values only. This means that, in the thoracolumbar spine, the greater the LB aROM, the greater the AR aROM, and vice versa. The approach developed promises a wide osteological screening of extant and extinct mammals to study the sex, age, geographical variations, and disorders.