The relationship of whole human vertebral body creep to geometric, microstructural and material properties.

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J Orthop Res


INTRODUCTION: Creep, the time-dependent deformation of a structure under prolonged load, is understood to play an important role in deformity of vertebrae due to progressive accumulation of residual strain [1]. Permanent deformation resulting from creep may develop at physiological load levels and contribute to ultimate failure of the bone tissue [2,3]. To date, creep properties have not been described in isolated human vertebral bodies. We aim to establish relationships between measures of creep of whole human cadaveric vertebrae and geometric, microstructural and hard tissue properties. METHODS: Thoracic 12 vertebrae were harvested under local IRB approval from 23 donors (13M/10F, 41-97y). Specimens were scanned using microcomputed tomography (μCT), dual x-ray absorptiometry (DXA), and high resolution computed tomography (CT). Standard quantities representing geometric, microstructural and material type properties of the bone tissue were calculated from the three modalities. Within each variable type, parameters causing high multicollinearity (as determined by a variance inflation factor>5) were eliminated. The final set of parameters consisted of 3 geometric (CTderived bone volume [Vol], anterior-posterior projected area [Area.AP], and average cortical thickness [Ct.Th]), 4 microstructural (μCT bone volume fraction [BV/TV], trabecular thickness [Tb.Th], degree of anisotropy [DA], and connectivity density [Conn.Dn]), and 2 material variables (average [GV.Av] and standard deviation [GV.SD] of μCT gray value-based tissue mineral density). Bone mineral density (BMD) was also calculated from DXA in AP (BMD.AP) and LM (BMD.LM) directions and from CT in cancellous (cBMD), shell (shBMD), and integral (iBMD) volumes. Specimens were then loaded to 1000N and held for 2 hours, load was removed, and recovery was recorded for another 2 hours [1]. Creep deformation (Dcr, ptB-ptA Fig.1), creep recovery (Rcr, ptC-ptD Fig.1), residual displacement (Dres, ptD Fig.1), and residual from creep alone (Dres-cr, Dcr-Rcr) were calculated. In order to correct for the dependence of creep parameters on elastic displacement, displacements were normalized using elastic deformation (ptA Fig.1) (i.e., Dcr-norm, Rcr-norm, Dres-norm, Dres-cr-norm). A function of the form “Dcr = a(1-EXP(-(t/τcr)n))+Ct” (τcr: time constant; n: stretch exponent; C: creep rate) was fit to the creep portion of the data (pts A to B, Fig.1). Multiple regression models were constructed using a stepwise procedure to examine relationships between measures of creep and geometric, microstructural, and material parameters (JMP 10, SAS Institute). If a BMD variable was found to be significantly correlated to a creep variable, the BMD variable was introduced first and forced to stay in the model. Significance in multiple regression models was considered as p<0.05. RESULTS: Creep, recovery and creep rate were associated with BMD but residual displacement measures were not (Table 1). Normalization of creep variables by vertebral stiffness eliminated BMD variables from the models. GV.SD positively contributed to models of Dres, Dres-norm, Dres-cr, and Dres-cr-norm. Conn.Dn positively contributed to models of Dcr (Fig. 2) and Dres-cr and negatively contributed to models of C. DISCUSSION: Creep deformations generally demonstrated inverse relationships with measures of bone density and vertebral size, indicating, not surprisingly, that bones that are larger and denser deform and recover less in the creep process [4]. However, BMD variables were not significant in models of displacement normalized by stiffness, indicating that the ability of BMDs to predict creep behavior may be limited by the strength of the relationship between creep and elastic behavior. The variability of GVs (GV.SD), but not their average, was consistently present in all significant deformation models, even those normalized by stiffness. This result agrees with previously reported associations of mineral density variability with creep deformations for whole rat vertebral bodies [5]. The arrangement of de sities within the bone phase, independent from microstructural organization and average bone mass, may thus be a factor in creep of vertebral bone. A correlation between mineral density variability and creep rate, but not deformations, was noted in human vertebral cancellous cores [6] suggesting that excised tissue may not fully reflect the creep behavior of the whole vertebra. Further work is needed to understand the relative contribution of mineralization distributions in the cancellous, shell and endplate components of a vertebra to its creep and how this contribution is affected by disease. After taking into account BMD and tissue mineral heterogeneity, Conn.Dn was positively correlated with Dcr and Dres-cr, suggesting that, all things being equal, creep response improves with decreased connectivity. This finding seems counterintuitive but not entirely unfounded, as previous studies have demonstrated negative correlations between stiffness and Conn.Dn [7,8]. The negative correlation found between creep rate and Conn.Dn suggests that this effect is due to a faster response to load in vertebrae with higher connectivity and that creep displacement will eventually get higher for vertebrae with less connectivity. However, the duration for this to be observed may be longer than a day-night cycle, i.e., too long to be beneficial [2]. When the dependence of creep on elastic displacement is separated by normalization, Conn.Dn was no longer present in the models, suggesting that the association of Conn.Dn with Dcr and Dres is not independent from its association with stiffness. The presented models help in understanding the relationships between the time dependent deformation of vertebral bone and geometric, microstructural and material properties; however, a portion of the variability is not explained by the current set of parameters. Although image-based predictors of vertebral creep are potentially useful, further work is needed to identify additional tissue properties that can fully describe the creep behavior of a human vertebra. (Figure Presented).



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