Precision Measurements and Parametric Models of Vertebral Endplates

This accurate and reproducible method can be used to obtain detailed and comprehensive geometry data from vertebral endplates and to develop a parametrical model without digitizing too many landmarks. This reverse engineering system can be used to efficiently develop an accurate representation of the anatomical character of sophisticated vertebrae surfaces with good reliability and reproducibility. This protocol can contribute to the design of personalized spinal implants, surgical planning, clinical diagnoses, and the development of accurate finite element models.

The method can be used for the sophisticated morphological studies and the parametric model can apply to other imaging modalities such as computed tomography and MRI. Although a beginner may need extra time to complete the procedure, the technique requires a short learning curve overall, to master. Demonstrating the procedure will be Hang Feng, a clinician from my laboratory.

Before beginning the procedure, place a dry cervical vertebra, without pathologic deformation or broken parts, vertically onto the platform of the scanner, with the endplate facing the camera lens. Start the scanning process to obtain CloudPoint data and open the software for processing point clouds. Click Import to import the point cloud data and generate a digital graphic of the vertebra.

Click Wrap to package the imaging data into a STL format file, to transform the point cloud into Mesh, which will convert a point object into a polygon object and open an appropriate 3D reconstruction and data processing software program. Under the New sub-menu, Click File and select Part in the list of types. Click Start and Shape and Digitized Shape Editor.

Then click the Import icon, select the STL format file and click Apply and Okay. To define the endplate 3D co-ordinate system, Mark one anatomic landmark on each of the left and right endpoints of the epiphysial rim and mark landmark on anterior median point. Click the Line icon and select the two trailing edge endpoints to define a posterior frontal line.

Click the Plane icon to set the plane type to be normal to the curve and select the posterior frontal line in anterior median point to define the midsagittal plane. Click Start, Shape, and Quick Surface Reconstruction. To generate an intersecting curve, Click the Planar Section icon enter 1 in the number option and select the end plate image and midsagittal plane.

Click Curve from the Scan icon and select the intersection of the intersecting curve and posterior epiphysial rim, defining the intersection as the as the posterior median point. Click the Point icon, Points and Planes Repetition. Then, select the midsagittal diameter and enter 1 in the Instances option, to define of the midpoint of the midsagittal diameter.

Click the Axis System icon and select the midpoint of the midsagittal diameter, as the origin. The line parallel to the posterior frontal line as the x-axis, the midsagittal diameter as the y-axis and the line pointing forward and perpendicular to the X-Y plane as the z-axis The appropriateness of the coordinate system can be determined according to whether the intersection of the defined midsagittal plane line and the coronal plane is perpendicular to the endplate section. To fit the characteristic curves, and points on the endplate surface, select the midsagittal diameter and enter 3 in the Instances option to divide the midsagittal diameter equally into four parts.

Click the Planar Section icon, enter 1 in the number option, and select the endplate image and the X-Z plane to generate an intersecting curve. Click Curve from the Scan icon, and select the two intersections of the X-Z plane and epiphyseal rim. Define the line between the two intersections as the mid frontal diameter and divide the mid frontal diameter equally into four parts.

To measure the length of a quarter of the midsagittal diameter, click the Measure Between icon. To generate two fitting curves, on one side of the frontal part, click the Planar Section icon, enter 2 in the number option, and enter the measured value in the Step option, and select the endplate image and X-Z plane. Then, click Swap to generate two fitting curves on the other side.

Next, select 11 equidistant points in each curve, and obtain nine fitting curves on the endplate surface, as demonstrated. Then, click Curve from the Scan icon and select the intersection of the fitting curves and the midsagittal curve, to obtain a total of 66 points on each endplate. To measure the length of the line parameter that is the distance between two measured points, click the Measure Between icon.

To measure the concavity parameters, click Start, Shape, and Generative Shape Design, and click the Sketch icon and the X-Y plane. Click the Circle icon and origin and drag the cursor of the mouse to an appropriate distance before clicking. Then, click the Exit Workbench icon.

Click the Offset icon, select the filled plane, and enter an appropriate value in the offset option, until it is tangent to the most concave part. Zoom in and click Start, Shape and Quick Surface Reconstruction, followed by the 3D Curve icon, to find and create the most concave point. Then, click the Measure Between icon, and select the most concave point and X-Y plane, to measure the whole endplate concavity depth.

To quantify the surface area parameters, click the Measure Inertia icon, and click endplate surface, to measure the surface area. To determine the fit order of the parametric equation, open the data analysis and visualization software, and input X the corresponding data in the command window. Click Enter and input Z the corresponding data.

Then input the code as indicated. For parameter equation fitting, input cftool"and click Enter to bring up the curve fitting tool. Then, input the co-ordinates of a curve in the command window as demonstrated.

Select Polynomial and enter the fit order to gain the parametric equation of the endplate surface. To obtain the geometric data, input the X and Y co-ordinate values of any point on the endplate in the command window, and input the parameters of the equation that have been fitted, using the Polynomial tool. Then, input the equation and click Enter to obtain the result.

To obtain the 3D simulation graphics, enter the polynomial parameters into the command window, and input the code as indicated. Input the indicated code and equation. Then, enter the indicated code.

Using a highly accurate optical 3D range flatbed scanner, as demonstrated, these representative endplates were converted into more than 4500 digital points, to adequately characterize their morphology. Using the measurement protocol as demonstrated, a spatial analysis of the endplate surfaces was conducted, and representative curves were fitted and quantified on the surface to characterize each endplate morphology. The measurements included the concavity depth and concavity apex location in the midsagittal plane.

In addition to those of the whole endplate concavity and any specific sections of interest. Next, the components of the endplates, epiphyseal rim, and central endplate were separated and their lengths and areas were obtained. The parametric equation of each curve was then deduced, based on the co-ordinates of 11 points.

Defining a 3D co-ordinated system for each endplate, is critical for the success of the protocol. The uncovertebral joint can be distinguished from the endplate by defining a best-fit plane, in terms of the anterior-most and posterior-most points of the bilateral uncinate processes. This protocol provides an accurate and reproducible method for performing a morphological study of complex surfaces.