Phantomless calibration of CT scans for hip fracture risk prediction in silico: Comparison with phantom-based calibration

Abstract

Finite element models built from quantitative computed tomography images rely on element-wise mapping of material properties starting from Hounsfield Units (HU), which can be converted into mineral densities upon calibration. While calibration is preferably carried out by scanning a phantom with known-density components, conducting phantom-based calibration may not always be possible. In such cases, a phantomless procedure, where the scanned subject's tissues are used as a phantom, is an interesting alternative. The aim of this study was to compare a phantom-based and a phantomless calibration method on 41 postmenopausal women. The proposed phantomless calibration utilized air, adipose, and muscle tissues, with reference equivalent mineral density values of -797, -95, and 38 mg/cm3, extracted from a previously performed phantom-based calibration. A 9-slice volume of interest (VOI) centred between the femoral head and knee rotation centres was chosen. Reference HU values for air, adipose, and muscle tissues were extracted by identifying HU distribution peaks within the VOI, and patient-specific calibration was performed using linear regression. Comparison of FE models calibrated with the two methods showed average relative differences of 1.99% for Young's modulus1.30% for tensile and 1.34% for compressive principal strains. Excellent correlations (R2 > 0.99) were identified for superficial maximum tensile and minimum compressive strains. Maximum normalised root mean square relative error (RMSRE) values settled at 4.02% for Young's modulus, 2.99% for tensile, and 3.22% for compressive principal strains, respectively. The good agreement found between the two methods supports the adoption of the proposed methodology when phantomless calibration is needed.

Fig 1. Definition of VOIcut from CT scan slices.

(a) RP definition based on the Femur Head Centre and Knee Centre. (b) VOI definition based on RP and OP by removing the portion extending 5cm posteriorly from the RP. (c) VOIcut selection. The visualization of the CT scan was obtained from the data collected during the study, which is available at [42].

Fig 2. Example of fitted distribution of the HU in the VOIcut, with the extracted peaks of air, adipose and muscle tissues.

The "pdf value" on the y-axis represents the probability density function value.

Fig 3. Graphical overview of the study.

Upper panel: the calibration phantom was employed to calibrate the CT scans for Group 1 subjects so that reference density values for air, adipose, and muscle tissues could be computed. These reference density values were later employed to calibrate through a phantomless calibration procedure the CT images of Group 2 subjects. Phantom scans were also available to calibrate Group 2 subjects, so that the outcomes of the phantomless and phantom-based calibration methodologies could be compared. Lower panel: phantom-based calibrations of Group 2 subjects were also employed to compute reference values for air, adipose, and muscle tissues to assess potential effects of different CT acquisition parameters on the reference density values. In the figure, ρ_HA stands for the density of the phantom, f stands for the distribution of the HU in the VOIcut (pdf value), HU_phantom and HU_subject stand for HU values extracted from the CT scan of the phantom and subject, respectively.

Fig 4. Distribution of element-wise relative differences in Young’s modulus between both calibration methods.

Violin plots showing the distributions of element-wise relative differences in Young’s modulus values between phantom-based and phantomless calibration for Group 2 subjects. The solid black line represents the mean value, while the blue solid line represents the median. Outliers, identified using the inter-quartile range method, have been excluded.

Fig 5. Spatial distribution of relative differences between Young’s modulus values coming from phantom-based and phantomless calibrations.

Frontal plane is the mean frontal section from the anterior view of the femur.

Fig 6. Distribution of point-to-point relative differences in superficial principal strains coming from both calibration methods.

Violin plots showing the distributions of the point-to-point relative differences computed on superficial tensile (a) and compressive (b) principal strain values between phantom-based and phantomless calibrations, considering all 28 simulated femur impact poses for each the 17 subjects in Group 2. The solid black line represents the mean, the blue solid line represents the median. Outliers, identified using the inter-quartile range, have been excluded.

Fig 7. Linear regressions plots between phantom-based and phantomless calibrations-derived highest tensile and lowest compressive strains.

The highest superficial tensile (a) and the lowest superficial compressive (b) principal strains for each of the 28 simulated impact poses for each of 17 subjects contained in Group 2 (R² > 0.99).