CBCT Segmentation and Additive Manufacturing for the Management of Root Canals with Ledges: A Case Report and Technique

Cone-beam computed tomography (CBCT) assessment of a ledge could be useful to a clinician; however, using this information effectively during a treatment procedure can be challenging. Advanced additive manufacturing technologies combined with semi-automated segmentation of root canals can help simulate the ledge and help in management of these iatrogenic complications. A patient presented after unsuccessful root canal treatment with a ledge on the left mandibular first molar. A CBCT was taken, and the images imported into a segmentation software (Mimics, Materialise). The canal was isolated, and segmentation performed along with the other structures of the tooth. A 3-dimensional digital model of the internal structures of the canal were used to design a mock-up which was additively manufactured. This was used as a preclinical guide to simulate the procedure, precurve the file, and manage the canal. This novel technique using virtual modeling from CBCT data post ledge formation allowed for successful and quick management of a tooth with ledges.

A gamma ray sourceless efficiency calibration method based on the Boolean operation of the ray deposition process

The general sourceless efficiency calibration has two major methods, Monte Carlo simulation and numerical calculation. Monte Carlo simulation as an important method to address the efficiency calibration in complex measurement systems, despite it being highly accurate, but inefficient and time-consuming. And although the numerical calculation is computationally efficient, its accuracy is highly influenced by the multiple Compton scattering of rays in sensitive body, and it is difficult to deal with complex measurement systems. To solve the above problems, this paper proposes a discrete numerical calculation combined with the graphical Boolean operations method for sourceless efficiency calibration. The method starts with a Monte Carlo simulation to obtain the rays deposition process in an infinite sensitive body and record deposition locations as a matrix; then, for different measurement systems, discrete numerical calculations are used to rapidly obtain the transmission process of rays to the sensitive body of the detector; finally, the two are combined to obtain the detection efficiency of the rays by using graphical Boolean operations. For the given two test models, the error between the measured and calculated results of ²⁴¹Am, ¹³⁷Cs, ⁶⁰Co at 60 positions is within -3.61∼9.71%, and the error between the measured and calculated results of the soil source is within -1.27 to 4.26%, indicating that the method has high reliability in sourceless efficiency calibration. And in comparison with Monte Carlo simulations, it is found that the method has a good agreement with Monte Carlo simulation in efficiency calibration and the computational speed has been greatly improved.

Immersed boundary-conformal isogeometric method for linear elliptic problems

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage the geometric flexibility of the immersed boundary method with the advantages of a conformal discretization, such as intuitive control of mesh resolution around the boundary, higher accuracy per degree of freedom, automatic satisfaction of interface kinematic conditions, and the ability to strongly impose Dirichlet boundary conditions. In the proposed method, starting with a boundary representation of a geometric model, we extrude it to obtain a corresponding conformal layer. Next, a given background B-spline mesh is cut with the conformal layer, leading to two disconnected regions: an exterior region and an interior region. Depending on the problem of interest, one of the two regions is selected to be coupled with the conformal layer through Nitsche's method. Such a construction involves Boolean operations such as difference and union, which therefore require proper stabilization to deal with arbitrarily cut elements. In this regard, we follow our precedent work called the minimal stabilization method (Antolin et al in SIAM J Sci Comput 43(1):A330-A354, 2021). In the end, we solve several 2D benchmark problems to demonstrate improved accuracy and expected convergence with IBCM. Two applications that involve complex geometries are also studied to show the potential of IBCM, including a spanner model and a fiber-reinforced composite model. Moreover, we demonstrate the effectiveness of IBCM in an application that exhibits boundary-layer phenomena.

3D Boolean operations in virtual surgical planning

PURPOSE

Boolean operations in computer-aided design or computer graphics are a set of operations (e.g. intersection, union, subtraction) between two objects (e.g. a patient model and an implant model) that are important in performing accurate and reproducible virtual surgical planning. This requires accurate and robust techniques that can handle various types of data, such as a surface extracted from volumetric data, synthetic models, and 3D scan data.

METHODS

This article compares the performance of the proposed method (Boolean operations by a robust, exact, and simple method between two colliding shells (BORES)) and an existing method based on the Visualization Toolkit (VTK).

RESULTS

In all tests presented in this article, BORES could handle complex configurations as well as report impossible configurations of the input. In contrast, the VTK implementations were unstable, do not deal with singular edges and coplanar collisions, and have created several defects.

CONCLUSIONS

The proposed method of Boolean operations, BORES, is efficient and appropriate for virtual surgical planning. Moreover, it is simple and easy to implement. In future work, we will extend the proposed method to handle non-colliding components.