All measurements have been conducted in the context of the multicentric ‘DIAGNOSTIK-BILANZ’-study, including 10 centres for recruitment and CT-measurements, organized by the Molecular Imaging North Competence Centre, a department of Radiology and Neuroradiology, University Medical Centre Schleswig–Holstein (UKSH), Kiel University, Kiel, Germany. Volunteers included were patients on long-term bisphosphonate treatment (at least the last 4 years). Spinal CT-measurements were performed with two different protocols of QCT, a high-resolution protocol for enhanced depiction of the trabecular vertebral structure (HR-QCT) and a low dose QCT-protocol to enable density measurements on larger part of the spine compared to standard QCT, which usually is applied to the lumbar spine only.

All patient measurements (data not included in this publication) were performed on the vertebrae simultaneously with a calibration phantom (Bone Density Calibration Phantom, BDC-Phantom) being placed below the spine. In Kiel, a similar setup using the BDC-Phantom together with a phantom simulating human vertebra (European Spine Phantom, ESP) (both phantoms: QRM GmbH, Moehrendorf, Germany) were used for weekly measurements over a total period of 14 months (27.07.2016–12.09.2017). After the first 12 weeks of measuring, a 9 months’ lasting recess was implemented in the testing process followed by a second measurement period of 12 weeks. We implemented a recess between two measurement periods in order to imitate a typical clinical set-up in which the patient re-visits his/her physician for additional scanning. During every individual measurement the ESP was placed on the BDC-Phantom to simulate a patient’s scan (Fig. S1, Appendix). This paper is based on measurements obtained on the ESP.

The ESP consists of three artificial vertebrae with nominal trabecular hydroxyapatite densities of 50 (in L1), 100 (in L2) and 200 (in L3) mg HA/cm3 and nominal cortical densities of 800 mg/cm3 for each vertebra surrounded by tissue mimicking material (Fig. S1). Cortical thickness increases from L1 to L3 [14]. Measured BMD values for ESP for trabecular compartments as stated in an acceptance-test-protocol by QRM GmbH are 50.5 mg HA/cm3 (L1), 101.2 mg HA/cm3 (L2), L3 200.6 mg HA/cm3 (L3) [15]. The BDC-Phantom comprises three parallel rods with hydroxyapatite densities of 100.0, 0.0 and 200.0 mg/cm3 [16]. Exact values for the phantom used in Kiel were 99.5 mg/cm3, 0 mg/cm3 and 203.0 mg HA /cm3.

All measurements were performed with the SOMATOM Sensation 64 (Siemens AG, Erlangen, Germany), a 64-multislice CT scanner, using two different scanning protocols: a high-resolution protocol and a low dose protocol (Table S1, Appendix). The HR was run with the B70s kernel, increment 0.3 mm and slickness 0.6 mm. Low dose images can be acquired and reconstructed with different reconstructions kernels, increments and slice thickness. Since these protocols can also affect accuracy and precision, we studied three different bone-kernels (B40s, B60s, and B80s) with a range of different combinations of increments and slice thickness values (Table S1, Appendix). While ‘hard’ kernels (e.g., B80s) produce a sharp image with comparatively high noise value, ‘soft’ kernels (B40s) create images with a lower spatial resolution but less noise [7, 17]. The HR protocol was set up to enable an additional measurement of trabecular and cortical structure parameters in patients. Although structural assessment of bone is not relevant in this study due to the lack of interior structures in the ESP, sharper images with higher resolution can be achieved combined with less noise due to the higher radiation dose. For the low dose protocol, nine different reconstructions were used to cover a wider range of possible applications of the method (Table 1). The low dose protocol was implemented in the patient study to enable a scanning of a larger part of the spine with still acceptable radiation dose. For the high-resolution protocol, a tube current of 120 kV, a tube current time product of 355 mAs and a field of view (FoV) of 80 mm was chosen. For the low dose protocol, a tube current of 80 kV, a tube current time product of 120 mAs and a FoV of 200 mm was used.

Image processing was conducted with the software package StructuralInsight to calculate BMD from CT attenuation values. This imaging processing software was developed by our section and combines all important quantitative CT data processing steps including quality assurance, calibration, threshold segmentation and analysis [18]. Intermediate application of a mask, created especially for these artificial vertebrae, helped to find a well-defined region prior to thresholding (Fig. S2, Appendix).

The ESP was scanned on top of the BDC, permitting analysis with simultaneous calibration. In the first analysis the densities of the artificial vertebrae of the ESP were calibrated using the densities of the compartments of the BDC, which was scanned at the same time (simultaneous calibration). To simulate an asynchronous (global) calibration uncalibrated data were calibrated by using one mean calibration curve only, calculated from the average CT-values of the BDC from all measurements (one curve for HR protocol and one for all low dose protocols). Analogous to the asynchronous (global) calibration for the asynchronous (monthly) calibration (only applied onto datasets with kernel B40s, 1.0 mm slice thickness) the first synchronous calibration curve of each month was used for calibrating all following datasets of this particular month. Secondly all datasets were processed using threshold segmentation. As depicted in figure S2 (appendix) narrower segmentation masks were placed in transverse planes in the middle of the vertebrae due to the problem that in low resolution scans with thick layers (e.g., 3.0 mm) inferior and superior endplates of adjacent vertebral bodies could not be differentiated thus leading to segmentation errors. By using a narrower segmentation mask threshold segmentation for thick layers remained possible. As a result, only vertical parts of the cortex of each ESP vertebra were analysed.

The statistical analyses were carried out using Microsoft Excel (Microsoft Inc. 2013) and JMP 5.0.1 (SAS Institute Inc. 2001). Due to technical defaults 5 out of 240 total measurement scans were preliminarily excluded (all with kernel B80s, 4 with 0.6 slice thickness, 1 with 1.0 mm slice thickness) while 3  measurements with B70s kernel were partially incomplete, showing only L2. For further analysis 235 scans with 2882 out of 3024 data points were included (Table S1, Appendix). Precision errors were expressed by the calculation of the coefficients of variation. Coefficients of variation were calculated separately for each method and each body as well as a mean for vertebrae L1–L3 from the standard deviation of all BMD values during the measurement phase. We distinguished between midterm-precision (defined as the standard deviation calculated over one measurement period, 12 weeks) from long-term precision (which was defined as the standard deviation calculated over the total measurement period, 1.5 years), aiming for the lowest possible value. Accuracy is defined by the deviations of measured BMD from nominal values (mean of vertebrae L1–L3). For the asynchronous calibration methods deviations of mean BMD from standard ESP values were calculated for each ESP vertebral body and a mean over L1–L3 (Fig. 1a, b). To examine potential drifts in BMD a linear regression analysis was performed over time and annual rates of change (separately for the single vertebrae L1, L2, and L3 and averaged over three vertebrae L1–L3) were calculated for each method. 362 out of 382 data points were included for linear regression analysis with reconstruction kernels B70s, 0.6 mm and B40s, 1.0 mm slice thickness and monthly calibration with B40s, 1.0 mm slice thickness (Fig. 2a–h).

a, b Bars depict accuracy errors (deviation of mean BMD from standard ESP values) and error bars depict mean mid-term precision errors (for vertebrae L1–L3) for trabecular bone (*) (a) and cortical bone (b) with asynchronous (global) calibration for all reconstruction kernels and monthly calibration for B40s, 1.0 mm slice thickness, (*for trabecular compartments nominal BMD values according to the QRM acceptance-test were used)

a–d Trabecular BMD-values over time for simultaneous (top) and global (bottom) calibrations with reconstruction kernels B70s, 0.6 mm and B40s, 1.0 mm slice thickness and monthly calibration with B40s, 1.0 mm slice thickness. e–h Cortical BMD-values over time for simultaneous and global calibrations with reconstruction kernels B70s, 0.6 mm and B40s, 1.0 mm slice thickness and monthly calibration with B40s, 1.0 mm slice thickness

In the following section we present results of the BMD values averaged over all three vertebrae for the high-resolution protocol, kernel B70s, and the kernels B40s, B60s, B80s to investigate the impact of a sharp kernel with high resolution and a weak kernel with low radiation dose on the measurements.