Among the osteoporotic outpatients followed by the Bone Metabolic Unit at Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico of Milan, Italy, 143 consecutive patients fulfilling the inclusion/exclusion criteria were enrolled in this study. Inclusion criterion was the presence of a fragility fracture within 1 year before. Exclusion criteria were bone diseases or pharmacological treatments known to interfere with bone metabolism, traumatic and pathological fractures. Treatment for osteoporosis was not an exclusion criterion. All patients underwent yearly spine x-ray examination and DXA bone densitometry every 2 years after baseline. All patients signed a written informed consent and local Ethical Committee approval was obtained (Comitato Etico Milano Area 2. Protocol N 2.0 BQ. 265_2017, 13th June 2017).
The spine x-ray evaluation was performed for the assessment of the spine deformity index (SDI) [10]. We considered the worsening of the SDI by one unit as the expression of a refracture.
Lumbar spine DXA bone densitometry (Hologic Discovery A system, Hologic Inc., Marlborough, MA, USA; software version 13.3.0.1) was performed in order to obtain bone quantity and quality indexes: lumbar spine BMD (g/cm2), TBS and BSI.
For calculating BSI we should consider that an object that is constrained in the direction of the force will show a deformation. The extent of the deformation depends upon many factors like the magnitude and direction of the force as well as the material properties and the geometry of the object.
In this context, the calculation of BSI is obtained dividing each vertebra of the DXA lumbar scan into small triangular elements, with the load applied to upper surface and the constraints to the lower one. The solution of this system provides the deformation status of the vertebra with the related strain and stresses. In a previous study, the in vitro BSI least significant change appeared to be about three times that of BMD in all scan modalities and fat thicknesses interpositions [11].
The load applied to the vertebra is calculated specifically for each patient according to Han equations [12] and depends on patient’s weight and height, whereas the mechanical properties are defined in a stiffness matrix assigning elastic modulus depending on local BMD [7]. The BSI represents the level of the strain inside the vertebra, with the assumption that a higher strain level (i.e., a high BSI) indicates a greater risk condition. Figure 1 (upper left and right) shows an example of bone strain distribution within a lumbar DXA scan and the related BSI calculation. The image resulting from BSI algorithms shows the lumbar vertebrae of the patients divided in small triangular elements. The size of each element is regulated automatically by the Delaunay triangulation algorithm applied to the contour of the object, whereas the colour is proportional to the level of the strain calculated. The colour map follows a ramp from blue (low strain) to green (intermediate strain), yellow, and red (high strain) indicating an increase of the risk factor proportionated to the increase of the strain. In this way, it is simple to detect areas with high strain peaks that probably are more prone to fracture. The colour (strain level) of each triangle depends, in addition to the local features (e.g., local BMD), on the BMD distribution around the element, the geometry of the object and the load applied on it.
BSI allows to consider all these features opportunely weighted, providing a way to analyse the data. Figure 1 bottom shows an example of bone strain distribution within a fractured lumbar spine vertebra.
Statistical analysis
Mean, standard deviation (SD), median, and range have been calculated for quantitative variables; absolute and per cent frequencies have been calculated for qualitative variables. The two subgroups (refractured and not refractured) have been compared by means of the Student t test or Chi-square test in the case of quantitative or qualitative variables, respectively. A p value lower than 0.05 (two tailed) has been considered as statistically significant. The cumulative probability of not having a refracture has been estimated by the Kaplan-Meier product-limit method. The ability of the bone variables to predict refractures has been assessed by means of Cox proportionality hazard regression (SAS 9.2 version) and its proportionality assumption has been formally assessed by means of the proportionality test.
We note that with a sample size of 143 patients and 61 events, leading to an approximately conservative event rate of 0.30, a satisfactory power value (> 0.80) is obtained to demonstrate a hazard ratio at least of 1.35.