Patient-Specific Phantomless Estimation of Bone Mineral Density and Its Effects on Finite Element Analysis Results: A Feasibility Study

Abstract

Objectives: This study proposes a regression model for the phantomless Hounsfield units (HU) to bone mineral density (BMD) conversion including patient physical factors and analyzes the accuracy of the estimated BMD values.

Methods: The HU values, BMDs, circumferences of the body, and cross-sectional areas of bone were measured from 39 quantitative computed tomography images of L2 vertebrae and hips. Then, the phantomless HU-to-BMD conversion was derived using a multiple linear regression model. For the statistical analysis, the correlation between the estimated BMD values and the reference BMD values was evaluated using Pearson's correlation test. Voxelwise BMD and finite element analysis (FEA) results were analyzed in terms of root-mean-square error (RMSE) and strain energy density, respectively.

Results: The HU values and circumferences were statistically significant (p < 0.05) for the lumbar spine, whereas only the HU values were statistically significant (p < 0.05) for the proximal femur. The BMD values estimated using the proposed HU-to-BMD conversion were significantly correlated with those measured using the reference phantom: Pearson's correlation coefficients of 0.998 and 0.984 for the lumbar spine and proximal femur, respectively. The RMSEs of the estimated BMD values for the lumbar spine and hip were 4.26 ± 0.60 (mg/cc) and 8.35 ± 0.57 (mg/cc), respectively. The errors of total strain energy were 1.06% and 0.91%, respectively.

Conclusions: The proposed phantomless HU-to-BMD conversion demonstrates the potential of precisely estimating BMD values from CT images without the reference phantom and being utilized as a viable tool for FEA-based quantitative assessment using routine CT images.

Figure 1

Screenshots of the semiautomatic calculation software (FatScan, N2 systems): (a) at the L2 level, the circumferences of the body and cross-sectional area of bone are segmented; and (b) at the hip level, the circumferences of the body and cross-sectional area of the bone are segmented. In this case, the circumference of the L2 level is 89.559 cm, and the cross-sectional area of L2 is 17.205 cm². The circumference of the hip level is 94.858 cm, and the cross-sectional area of the hip is 77.406 cm².

Figure 2

Pearson's correlation test of the estimated BMD values and those derived using a reference phantom: (a) Pearson's correlation coefficient of 0.998 for the L2 level, and (b) Pearson's correlation coefficient of 0.984 for the hip level (p < 0.05).

Figure 3

Distribution of elastic modulus, strain energy density, and error of strain energy density in the L2 vertebra: (a) case of using the reference BMD values with an external phantom, (b) case of using BMD values estimated by the proposed phantomeless HU-to-BMD conversion, and (c) case of using the simplified conversion of linear volume fraction approach.

Figure 4

Distribution of elastic modulus, strain energy density, and error of strain energy density in the proximal femur: (a) case of using the reference BMD values with an external phantom, (b) case of using BMD values estimated by the proposed phantomeless HU-to-BMD conversion, and (c) case of using the simplified conversion of linear volume fraction approach.

Figure 5

BMD contour plot at the axial level of the L2 vertebra: (a) the reference BMD using an external phantom, (b) BMD estimated using the proposed phantomless HU-to-BMD conversion, (c) a deviation between the reference and estimated BMD values, and (d) BMD deviation on a different scale.

Figure 6

BMD contour plot at the axial level of the hip joint: (a) the reference BMD using an external phantom, (b) BMD estimated using the proposed phantomless HU-to-BMD conversion, (c) a deviation between the reference and estimated BMD values, and (d) BMD deviation on a different scale.