An open-access plug-in program for 3D modelling distinct material properties of cortical and trabecular bone

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We demonstrate the development and use of a pre-processing plug-in program with a 3D modelling image processing software suite (Synopsys Simpleware, ScanIP) to assist with identifying, isolating, and defining cortical and trabecular bone material properties from patient specific computed tomography scans. The workflow starts by calibrating grayscale values of each constituent element with a phantom – a standardized object with defined densities. Using an established power law equation, we convert the apparent density value per voxel to a Young’s Modulus. The resulting “calibrated” scan can be used for modeling and in-silico experimentation with Finite Element Analysis.

Background

The methods of modeling bone, in considering the differing material properties between trabecular to cortical bone, has been discussed and debated at length for decades in the literature [1–5]. The debate chiefly concerns the structures, densities, and Young’s Moduli of trabecular and cortical bone. Trabecular bone is primarily a spongy and anisotropic material, meant for transferring loads from articular surfaces to the denser cortical bone [2]. Cortical bone, however, is more consistent in density and stiffness, being more necessary for handling higher stressors from repeated loads of tension and compression [4, 5]. This leads authors to determine a variety of equations based on power law regressions for the determination of Young’s Modulus for the more variable spectrum of trabecular bone [1, 2], while cortical bone is usually represented with a constant Young’s Modulus [4].

The ability to define these material properties accurately in mathematical models is invaluable to translating medical device design and surgical principles to clinical applications. Orthopedic medical devices restore a patient’s function by providing an environment for bone healing or joint function. Surgeons make their best predictions for the optimal implant choice based on a patient’s bone quality, comorbidities, and their previous experiences with an implant. Accurate computational models allow surgeons and medical device engineers to simulate the performance of each implant type within a patient’s bone to make informed decisions regarding implant design, selection and surgical technique [6, 7].

We wish to present a methodology in which the previously used method of determining bone mineral density using Quantitative Computed Tomography (QCT) [8] is applied to determine material properties in Finite Element Analysis (FEA). Although modeling based on CT scans itself is not novel [1, 2, 8, 9], we incorporate this methodology into our work as a streamlined workflow with existing modeling software for convenient clinical and research applications.

Our workflow preprocesses Computed Tomography (CT) scans of bones using Synopsys® Simpleware ScanIP software and its Python scripting tool, produced by our lab in coordination with the Synopsys® Simpleware engineering team. As a supplemental file in this publication, we share the Plug-In Program (PIP) as open access as a supplement of this paper. Although, ScanIP is a versatile and effective tool for modeling structure as well as material properties, conversions are made from density to Young’s Modulus all using a power law equation, which we deem to be inappropriate for calculating cortical bone due to the above-mentioned differences. Although Morgan et al. [1] describe a power law equation for density to modulus conversion, they were created with trabecular bone in mind. For cortical bone, therefore, we consider a constant modulus as determined by Reilly and Burstein [4]. In the following work, we describe how grayscale values from individual CT elements, or voxels, are transformed into Young’s Moduli in a three-step process (Fig.  ). First, the user enters a cutoff density for trabecular/cortical bone as well as corresponding grayscale and QCT density values. A way of obtaining grayscale and QCT density values are outlined in the Methods Section. Second, the QCT values of the Digital Imaging and Communications in Medicine (DICOM) format are converted to a wet apparent density. Finally, the wet apparent density values are converted to a Young’s Modulus based on the corresponding tissue. The adjusted DICOM files can then be used to create a 3D model and subsequent FEA.

Computed tomography

Computed tomography (CT) scans are composed of x-rays from various angles, which are then transformed into cross-sectional images through computer processing. Series of two-dimensional images made of pixels are used to represent three dimensional volumes, commonly known as voxels, of the scanned subject. These series are typically stored as Digital Imaging and Communications in Medicine (DICOM) files, a common means for storing and transmitting medical imaging data such as CT scans. The values of the radiodensities are measured in Hounsfield units (HU). HU quantify the linear attenuation; the number of x-rays emitted by a CT scanner that are absorbed or scattered per unit thickness of the sample. HU are based on reference values for the linear attenuation at standard temperature and pressure of water (0 HU), and air (− 1000 HU) [10].

HU=1000μ-μwaterμwater-μair

While HU are negative if the radiodensity of the sample is less than that of water, radiodensities in CT images are stored only as positive values. Observed HU are first scaled using a rescale intercept (b) and rescale slope (m) before they are stored in the DICOM.

HU=m*storedvalue+b

The DICOM metadata stores the rescale intercept and slope under tags (0028,1052) and (0028,1053) (“DICOM Tags”). The values we manipulate in our PIP are the DICOM values (adjusted HU), and not the HU. Due to how the values are transformed to CT densities, the original unit does not influence the relationships as long as internal consistency is maintained.

Types of densities that are obtained from CT

Our workflow requires conversion to a density in each voxel based on the grayscale image that most closely reflects what its real-world density might be. In considering that the density of the physical bone cannot be measured to complete accuracy, we term various densities as calculated densities to describe what we would obtain for individual voxels of data. Wet apparent density describes the wet mass divided by the bulk volume of a sample in a voxel, from which we can obtain Young’s Moduli values [8]. This is calculated through a power law regression, as described by Morgan et al. [4]. Lotz et al. [11] describes a method of obtaining wet apparent density values through a linear regression equation with quantitative CT (QCT) density. QCT values describe the bone mineral density of bone structure in each voxel of an image [8]. The benefits of QCT density allow a detailed map of bone density, to the extent that trabecular bone can be distinguished from cortical bone [8].