Study population
This study is a retrospective longitudinal multicentric study conducted at Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico of Milan, Italy; IRCCS Istituto Ortopedico Galeazzi in Milan, Italy; and IRCCS Policlinico San Donato, San Donato Milanese, Italy.
Female patients were selected among those who attended our densitometric service for routine evaluation of bone density and vertebral fractures. Among them, we enrolled 174 women that fulfilled the inclusion/exclusion criteria. The inclusion criteria were the presence of a dorso-lumbar spine x-ray and both femoral and spine DXA scans performed at the same time of the x-ray. The exclusion criteria were the presence of bone metabolic disorders (except for primary osteoporosis), and any history of traumatic and/or pathological fractures. We also excluded those patients undergoing pharmacological treatments known to interfere with bone metabolism (e.g., glucocorticoid therapy), except for osteoporosis treatments. Data had been collected within the time frame from September 2010 to August 2018.
All patients underwent a baseline lumbar spine and femoral DXA scans to quantify femur and lumbar spine bone mineral content (BMC), BMD and BSI, together with a spine x-ray to calculate the Spine Deformity Index (SDI) in order to quantify the severity of vertebral fractures [17]. A fracture was considered as a one-unit increase of SDI. Demographic, anthropometric and clinical data were collected. All patients had imaging follow-up consisting of plain x-rays and a DXA study after a period that lasted from 1 to 9 years (mean 3.34, SD 1.91, median 2.72). For each patient, we evaluated two sets of exams (lumbar and femoral DXA, dorso-lumbar x-ray), one at baseline and one at follow-up.
Patients gave their written informed consent to the management of their sensitive data for scientific research. Local Ethical Committees’ approval was obtained: Comitato Etico Milano Area 2. Protocol N 2.0 BQ. 265_2017, 13 June 2017 for IRCCS Fondazione Ca’ Granda Ospedale Maggiore Policlinico, Milan, Italy; Comitato Etico San Raffaele; Studio clinico 2.0 BQ, version 4.0, 8 August 2019, for IRCCS Istituto Ortopedico Galeazzi, Milan; and IRCCS Policlinico San Donato, San Donato Milanese (MI). Figure 1 summarises the study flowchart.
DXA data acquisition
Bone density was assessed by DXA, using a Hologic Discovery A for Fondazione IRCCS Ca’ Granda Ospedale Maggiore Policlinico and IRCCS Policlinico San Donato, and a Hologic QDR-Discovery W for IRCCS Istituto Ortopedico Galeazzi.
Experienced and dedicated technicians performed all the exams according to the International Society for Clinical Densitometry guidelines [18]. All patients underwent an L1–L4 spine scan and hip scan. Those vertebrae affected by fragility fractures were manually excluded from the DXA analysis, in order to avoid fictitious BMD values. Both BMD and BSI were automatically obtained from the same region of interest of the lumbar spine and hip scans.
BSI computation was obtained by an automated software with the use of a constant strain FEA triangular mesh. The pressure applied to the vertebra and hip is specific for each patient and is based on the relationship between forces and the patient’s weight and height, as postulated by Han et al.’s study [19]. The definition of the model’s mechanical properties was done in a stiffness matrix by assigning an elastic modulus depending on the regional BMD values, in accordance with the Morgan's equation [20]. BSI calculation is obtained using a triangular mesh designed on the bone, segmented by the DXA software. In the case of the lumbar spine, the loading force applied to each vertebra is calculated following simulation data provided by Han et al.’s study in standing conditions [19] and uniformly distributed onto the upper facet of each vertebra, whereas the lower side is used as a constraint. In the case of hip scans, loading and constraints follow the indications provided by Terzini et al. [21], with the head and distal femur constrained, and force applied on the greater trochanteric area following a sideway fall condition.
Ultimately, the BSI values relate to the average strain inside the specific lumbar vertebra and hip region, obtained with linear elastic analysis and with the assumption that a higher strain level (high BSI) indicates a greater risk condition. Figure 2 shows an example of a DXA scan with the corresponding BSI analysis.
X-ray data acquisition
Patients underwent an anteroposterior and lateral x-ray of the spine in order to investigate the presence of vertebral fractures (VFs) at the beginning and at the end of the follow-up. The vast majority of spine x-ray examinations were performed in the supine position, and all scans were performed in two projections (frontal and lateral). A radiologist with more than 10 years of experience in osteoporosis imaging assessed all the plain films to evaluate the presence/absence of VFs. We preferred to directly evaluate the images and not the radiological reports as it has been shown that many mild fractures may go unreported [22]. The SDI was calculated using Genant’s semi-quantitative approach by evaluating the vertebrae from T4 to L4; Genant’s visual semiquantitative method consists of giving each vertebra a degree of deformity (mild, moderate and severe) based on the visually apparent degree of vertebral height loss. Fractures are also classified according to the type of deformity (wedge fractures, biconcave fractures, or compressive fractures) [23, 24].
Predictive analysis with supervised artificial neural networks
Advanced intelligent systems based on the novel coupling of ANNs and evolutionary algorithms have been applied in this study. Supervised ANNs [25] were applied to create a mathematical model to predict the different class outcomes (fracture occurrence versus no fracture occurrence) starting from available clinical and densitometric data. The learning mechanism of the supervised ANNs can make their output coincide with a pre-established target. The presence of learning constraints allows for the supervised ANN output to coincide with the predefined target. The standard formula of these ANNs is y = f (x,w*), where w* represents the set of parameters which best approximates the function.
Data preprocessing was performed using a re-sampling system named TWIST developed by Semeion Research Centre. The TWIST system consists of an ensemble of two previously described systems: T&T and IS [26].
To find out the connectivity traces among variables, a new mapping method was adopted, with the use of a mathematical approach based on an artificial adaptive system; this was done to define the association strength between variables within the dataset (the Auto-CM algorithm). The Auto-CM system is a three-layered architecture fourth-generation unsupervised ANNs able to compute the multi-dimensional association of the strength of each variable with all other variables in a dataset, using a mathematical approach based on recursive non-linear equations. Subsequently to the training phase, the weight matrix of the Auto-CM reflects the warped landscape of the dataset. Therefore, a filter represented by a minimum spanning tree is applied to the Auto-CM system, finally producing a map of the main connections between the variables of the dataset (connectivity map, as detailed in Buscema et al.) [16, 27].
As for previous clinical studies [12, 28,29,30], after a training phase, the Auto-CM determines the so-called weights of the vectors’ matrix, proportional to the strength of many-to-many connections across all variables, and can be easily visualised by transforming them into physical distances: variables whose connection weights are higher become relatively closer, and vice versa. We transformed the thirteen input variables into 26 input variables, scaled from 0 to 1. Consider, for example, the variable lumbar BMD: absolute natural values range from 0.521 to 1.3. In transformation 1.3, the highest value becomes 1 and 0.521 becomes 0. All other values are scaled to this new range: for example, the value 0.64 becomes 0.15, the value 0.93 becomes 0.53 and so on. In the complement transformation, we permit the system to point out the fuzzy position of the variables, also in accordance with its lower values. With this approach, the projection of the preliminary variables shows high values; on the other side, the complement transformation showed low values of the original variables. We named these two forms as “high” and “low” on the map. This preprocessing is required to compare all the possible variables and to understand the possible links between variables when the values tend to be high or low.
Statistics
Variables were expressed as mean ± standard deviation (SD) ranges. For comparisons between the groups, an independent-samples t-test was used. A two-tailed probability value of 0.05 was considered statistically significant. The linear correlation index between variables was calculated by the Pearson test. A p-value < 0.05 was considered to be statistically significant. Statistical analysis was performed with the XLSTAT package 2018.