Dual-zone material assignment method for correcting partial volume effects in image-based bone models

In image-based finite element analysis of bone, partial volume effects (PVEs) arise from image blur at tissue boundaries and as a byproduct of geometric reconstruction and meshing during model creation. In this study, we developed and validated a material assignment approach to mitigate partial volume effects. Our validation data consisted of physical torsion testing of intact tibiae from N = 20 Swiss alpine sheep. We created finite element models from micro-CT scans of these tibiae using three popular element types (10-node tetrahedral, 8-node hexahedral, and 20-node hexahedral). Without partial volume management, the models over-predicted the torsional rigidity compared to physical biomechanical tests. To address this problem, we implemented a dual-zone material model to treat elements that overlap low-density surface voxels as soft tissue rather than bone. After in situ inverse optimization, the dual-zone material model produced strong correlations and high absolute agreement between the virtual and physical tests. This suggests that with appropriate partial volume management, virtual mechanical testing can be a reliable surrogate for physical biomechanical testing. For maximum flexibility in partial volume management regardless of element type, we recommend the use of the following dual-zone material model for ovine tibiae: soft-tissue cutoff density of 665 mgHA/cm3 with a soft tissue modulus of 50 MPa (below cutoff) and a density-modulus conversion slope of 10,225 MPa-cm3/mgHA for bone (above cutoff).

Harmonization of in-plane resolution in CT using multiple reconstructions from single acquisitions

PURPOSE

To providea methodology that removes the spatial variability of in-plane resolution using different CT reconstructions. The methodology does not require any training, sinogram, or specific reconstruction method.

METHODS

The methodology is formulated as a reconstruction problem. The desired sharp image is modeled as an unobservable variable to be estimated from an arbitrary number of observations with spatially variant resolution. The methodology comprises three steps: (1) density harmonization, which removes the density variability across reconstructions; (2) point spread function (PSF) estimation, which estimates a spatially variant PSF with arbitrary shape; (3) deconvolution, which is formulated as a regularized least squares problem. The assessment was performed with CT scans of phantoms acquired with three different Siemens scanners (Definition AS, Definition AS+, Drive). Four low-dose acquisitions reconstructed with backprojection and iterative methods were used for the resolution harmonization. A sharp, high-dose (HD) reconstruction was used as a validation reference. The different factors affecting the in-plane resolution (radial, angular, and longitudinal) were studied with regression analysis of the edge decay (between 10% and 90% of the edge spread function (ESF) amplitude).

RESULTS

Results showed that the in-plane resolution improves remarkably and the spatial variability is substantially reduced without compromising the noise characteristics. The modulated transfer function (MTF) also confirmed a pronounced increase in resolution. The resolution improvement was also tested by measuring the wall thickness of tubes simulating airways. In all scanners, the resolution harmonization obtained better performance than the HD, sharp reconstruction used as a reference (up to 50 percentage points). The methodology was also evaluated in clinical scans achieving a noise reduction and a clear improvement in thin-layered structures. The estimated ESF and MTF confirmed the resolution improvement.

CONCLUSION

We propose a versatile methodology to reduce the spatial variability of in-plane resolution in CT scans by leveraging different reconstructions available in clinical studies. The methodology does not require any sinogram, training, or specific reconstruction, and it is not limited to a fixed number of input images. Therefore, it can be easily adopted in multicenter studies and clinical practice. The results obtained with our resolution harmonization methodology evidence its suitability to reduce the spatially variant in-plane resolution in clinical CT scans without compromising the reconstruction's noise characteristics. We believe that the resolution increase achieved by our methodology may contribute in more accurate and reliable measurements of small structures such as vasculature, airways, and wall thickness.

Theory, method, and test tools for determination of 3D MTF characteristics in cone-beam CT

PURPOSE

The modulation transfer function (MTF) is widely used as an objective metric of spatial resolution of medical imaging systems. Despite advances in capability for three-dimensional (3D) isotropic spatial resolution in computed tomography (CT) and cone-beam CT (CBCT), MTF evaluation for such systems is typically reported only in the axial plane, and practical methodology for assessment of fully 3D spatial resolution characteristics is lacking. This work reviews fundamental theoretical relationships of two-dimensional (2D) and 3D spread functions and reports practical methods and test tools for analysis of 3D MTF in CBCT.

METHODS

Fundamental aspects of 2D and 3D MTF measurement are reviewed within a common notational framework, and three MTF test tools with analysis code are reported and made available online (https://istar.jhu.edu/downloads/): (a) a multi-wire tool for measurement of the axial plane MTF [denoted as M T F ( f r ; φ = 0 ∘ ) , where φ is the measurement angle out of the axial plane] as a function of position in the axial plane; (b) a wedge tool for measurement of the MTF in any direction in the 3D Fourier domain [e.g.,  φ  = 45°, denoted as M T F ( f r ; φ = 45 ∘ ) ]; and (c) a sphere tool for measurement of the MTF in any or all directions in the 3D Fourier domain. Experiments were performed on a mobile C-arm with CBCT capability, showing that M T F ( f r ; φ = 45 ∘ ) yields an informative one-dimensional (1D) representation of the overall 3D spatial resolution characteristics, capturing important characteristics of the 3D MTF that might be missed in conventional analysis. The effects of anisotropic filters and detector readout mode were investigated, and the extent to which a system can be said to provide "isotropic" resolution was evaluated by quantitative comparison of MTF at various φ .

RESULTS

All three test tools provided consistent measurement of M T F ( f r ; φ = 0 ∘ ) , and the wedge and sphere tools demonstrated how measurement of the MTF in directions outside the axial plane ( φ > 0 ∘ ) can reveal spatial resolution characteristics to which conventional axial MTF measurement is blind. The wedge tool was shown to reduce statistical measurement error compared to the sphere tool due to improved sampling, and the sphere tool was shown to provide a basis for measurement of the MTF in any or all directions (outside the null cone) from a single scan. The C-arm system exhibited non-isotropic spatial resolution with conventional non-isotropic 1D apodization filters (i.e., frequency cutoff filters) - which is common in CBCT - and implementation of isotropic 2D apodization yielded quantifiably isotropic MTF. Asymmetric pixel binning modes were similarly shown to impart non-isotropic effects on the 3D MTF, and the overall 3D MTF characteristics were evident in each case with a single, 1D measurement of the 1D M T F ( f r ; φ = 45 ∘ ).

CONCLUSION

Three test tools and corresponding MTF analysis methods were presented within a consistent framework for analysis of 3D spatial resolution characteristics in a manner amenable to routine, practical measurements. Experiments on a CBCT C-arm validated many intuitive aspects of 3D spatial resolution and quantified the extent to which a CBCT system may be considered to have isotropic resolution. Measurement of M T F ( f r ; φ = 45 ∘ ) provided a practical 1D measure of the underlying 3D MTF characteristics and is extensible to other CT or CBCT systems offering high, isotropic spatial resolution.

Can CT image deblurring improve finite element predictions at the proximal femur?

The aim of this study was to determine if a CT image deblurring algorithm can improve CT-based FE modelling accuracy at the proximal femur. Experimental data (CT scans of fourteen proximal fresh-frozen cadaveric femurs, non-destructive surface strain measurements in stance and sideways fall loading configurations on all femurs, and failure loads obtained in stance for seven specimens, in sideways fall for the other seven) were taken from a recent study (Schileo et al., 2014). An estimate of the 3D Point Spread Function for each CT scan was used within a deconvolution solver to perform the deblurring. The most proximal regions of three specimens were scanned using an HRpQCT scanner and compared to the original and deblurred CT images to quantify errors in bone contour estimates and determine correlation of intensity values within the bone contours. Subject-specific FE models of the proximal femur were generated. The accuracy of deblurred FE predictions against experimental measurements was compared to the published (non-deblurred) FE results. When compared to HRpQCT, CT deblurring led to lower mean surface distances (0.31 vs. 0.49mm) and higher CT intensity correlations with respect to the original CT. All indicators of strain prediction accuracy were significantly improved in deblurred FE models, more markedly at the femoral neck (peak error reduced by 38%). Failure load prediction, based on a simple elastic limit model, was also improved in deblurred FE models, although differently for stance and sideways fall loading conditions. In stance, correlation was unchanged, but specimen-wise errors were reduced (mean error 10% vs. 15%). In sideways fall, correlation notably increased (R(2)=0.95 vs. 0.81), despite a general overestimation of failure load. In summary, the proposed CT deblurring technique yielded moderate but significant improvements in FE predictions, and may thus be considered a first step toward the improvement of CT-based FE models of the human femur.

Independent measurement of femoral cortical thickness and cortical bone density using clinical CT

The local structure of the proximal femoral cortex is of interest since both fracture risk, and the effects of various interventions aimed at reducing that risk, are associated with cortical properties focused in particular regions rather than dispersed over the whole bone. Much of the femoral cortex is less than 3mm thick, appearing so blurred in clinical CT that its actual density is not apparent in the data, and neither thresholding nor full-width half-maximum techniques are capable of determining its width. Our previous work on cortical bone mapping showed how to produce more accurate estimates of cortical thickness by assuming a fixed value of the cortical density for each hip. However, although cortical density varies much less over the proximal femur than thickness, what little variation there is leads to errors in thickness measurement. In this paper, we develop the cortical bone mapping technique by exploiting local estimates of imaging blur to correct the global density estimate, thus providing a local density estimate as well as more accurate estimates of thickness. We also consider measurement of cortical mass surface density and the density of trabecular bone immediately adjacent to the cortex. Performance is assessed with ex vivo clinical QCT scans of proximal femurs, with true values derived from high resolution HRpQCT scans of the same bones. We demonstrate superior estimation of thickness than is possible with alternative techniques (accuracy 0.12 ± 0.39 mm for cortices in the range 1-3mm), and that local cortical density estimation is feasible for densities >800 mg/cm(3).

To what extent can linear finite element models of human femora predict failure under stance and fall loading configurations?

Proximal femur strength estimates from computed tomography (CT)-based finite element (FE) models are finding clinical application. Published models reached a high in-vitro accuracy, yet many of them rely on nonlinear methodologies or internal best-fitting of parameters. The aim of the present study is to verify to what extent a linear FE modelling procedure, fully based on independently determined parameters, can predict the failure characteristics of the proximal femur in stance and sideways fall loading configurations. Fourteen fresh-frozen cadaver femora were CT-scanned. Seven femora were tested to failure in stance loading conditions, and seven in fall. Fracture was monitored with high-speed videos. Linear FE models were built from CT images according to a procedure already validated in the prediction of strains. An asymmetric maximum principal strain criterion (0.73% tensile, 1.04% compressive limit) was used to define a node-based risk factor (RF). FE-predicted failure load, mode (tensile/compressive) and location were determined from the first node reaching RF=1. FE-predicted and measured failure loads were highly correlated (R(2)=0.89, SEE=814N). In all specimens, FE models correctly identified the failure mode (tensile in stance, compressive in fall) and the femoral region where fracture started (supero-lateral neck aspect). The location of failure onset was accurately predicted in eight specimens. In summary, a simple FE model, adaptable in the future to multiple loads (e.g. including muscles), was highly correlated with experimental failure in two loading conditions on specimens ranging from normal to osteoporotic. Thus, it can be suitable for use in clinical studies.