Incremental kernel ridge regression for the prediction of soft tissue deformations

A novel incremental simulation of facial changes following orthognathic surgery using FEM with realistic lip sliding effect

Accurate prediction of facial soft-tissue changes following orthognathic surgery is crucial for surgical outcome improvement. We developed a novel incremental simulation approach using finite element method (FEM) with a realistic lip sliding effect to improve the prediction accuracy in the lip region. First, a lip-detailed mesh is generated based on accurately digitized lip surface points. Second, an improved facial soft-tissue change simulation method is developed by applying a lip sliding effect along with the mucosa sliding effect. Finally, the orthognathic surgery initiated soft-tissue change is simulated incrementally to facilitate a natural transition of the facial change and improve the effectiveness of the sliding effects. Our method was quantitatively validated using 35 retrospective clinical data sets by comparing it to the traditional FEM simulation method and the FEM simulation method with mucosa sliding effect only. The surface deviation error of our method showed significant improvement in the upper and lower lips over the other two prior methods. In addition, the evaluation results using our lip-shape analysis, which reflects clinician's qualitative evaluation, also proved significant improvement of the lip prediction accuracy of our method for the lower lip and both upper and lower lips as a whole compared to the other two methods. In conclusion, the prediction accuracy in the clinically critical region, i.e., the lips, significantly improved after applying incremental simulation with realistic lip sliding effect compared with the FEM simulation methods without the lip sliding effect.

A New Approach of Predicting Facial Changes following Orthognathic Surgery using Realistic Lip Sliding Effect

Accurate prediction of facial soft-tissue changes following orthognathic surgery is crucial for improving surgical outcome. However, the accuracy of current prediction methods still requires further improvement in clinically critical regions, especially the lips. We develop a novel incremental simulation approach using finite element method (FEM) with realistic lip sliding effect to improve the prediction accuracy in the area around the lips. First, lip-detailed patient-specific FE mesh is generated based on accurately digitized lip surface landmarks. Second, an improved facial soft-tissue change simulation method is developed by applying a lip sliding effect in addition to the mucosa sliding effect. The soft-tissue change is then simulated incrementally to facilitate a natural transition of the facial change and improve the effectiveness of the sliding effects. A preliminary evaluation of prediction accuracy was conducted using retrospective clinical data. The results showed that there was a significant prediction accuracy improvement in the lip region when the realistic lip sliding effect was applied along with the mucosa sliding effect.

An eFTD-VP framework for efficiently generating patient-specific anatomically detailed facial soft tissue FE mesh for craniomaxillofacial surgery simulation

Accurate surgical planning and prediction of craniomaxillofacial surgery outcome requires simulation of soft tissue changes following osteotomy. This can only be achieved by using an anatomically detailed facial soft tissue model. The current state-of-the-art of model generation is not appropriate to clinical applications due to the time-intensive nature of manual segmentation and volumetric mesh generation. The conventional patient-specific finite element (FE) mesh generation methods are to deform a template FE mesh to match the shape of a patient based on registration. However, these methods commonly produce element distortion. Additionally, the mesh density for patients depends on that of the template model. It could not be adjusted to conduct mesh density sensitivity analysis. In this study, we propose a new framework of patient-specific facial soft tissue FE mesh generation. The goal of the developed method is to efficiently generate a high-quality patient-specific hexahedral FE mesh with adjustable mesh density while preserving the accuracy in anatomical structure correspondence. Our FE mesh is generated by eFace template deformation followed by volumetric parametrization. First, the patient-specific anatomically detailed facial soft tissue model (including skin, mucosa, and muscles) is generated by deforming an eFace template model. The adaptation of the eFace template model is achieved by using a hybrid landmark-based morphing and dense surface fitting approach followed by a thin-plate spline interpolation. Then, high-quality hexahedral mesh is constructed by using volumetric parameterization. The user can control the resolution of hexahedron mesh to best reflect clinicians' need. Our approach was validated using 30 patient models and 4 visible human datasets. The generated patient-specific FE mesh showed high surface matching accuracy, element quality, and internal structure matching accuracy. They can be directly and effectively used for clinical simulation of facial soft tissue change.

A clinically validated prediction method for facial soft-tissue changes following double-jaw surgery

PURPOSE

It is clinically important to accurately predict facial soft-tissue changes prior to orthognathic surgery. However, the current simulation methods are problematic, especially in anatomic regions of clinical significance, e.g., the nose, lips, and chin. We developed a new 3-stage finite element method (FEM) approach that incorporates realistic tissue sliding to improve such prediction.

METHODS

In Stage One, soft-tissue change was simulated, using FEM with patient-specific mesh models generated from our previously developed eFace template. Postoperative bone movement was applied on the patient mesh model with standard FEM boundary conditions. In Stage Two, the simulation was improved by implementing sliding effects between gum tissue and teeth using a nodal force constraint scheme. In Stage Three, the result of the tissue sliding effect was further enhanced by reassigning the soft-tissue-bone mapping and boundary conditions using nodal spatial constraint. Finally, our methods have been quantitatively and qualitatively validated using 40 retrospectively evaluated patient cases by comparing it to the traditional FEM method and the FEM with sliding effect, using a nodal force constraint method.

RESULTS

The results showed that our method was better than the other two methods. Using our method, the quantitative distance errors between predicted and actual patient surfaces for the entire face and any subregions thereof were below 1.5 mm. The overall soft-tissue change prediction was accurate to within 1.1 ± 0.3 mm, with the accuracy around the upper and lower lip regions of 1.2 ± 0.7 mm and 1.5 ± 0.7 mm, respectively. The results of qualitative evaluation completed by clinical experts showed an improvement of 46% in acceptance rate compared to the traditional FEM simulation. More than 80% of the result of our approach was considered acceptable in comparison with 55% and 50% following the other two methods.

CONCLUSION

The FEM simulation method with improved sliding effect showed significant accuracy improvement in the whole face and the clinically significant regions (i.e., nose and lips) in comparison with the other published FEM methods, with or without sliding effect using a nodal force constraint. The qualitative validation also proved the clinical feasibility of the developed approach.

Design, development and clinical validation of computer-aided surgical simulation system for streamlined orthognathic surgical planning

PURPOSE

There are many proven problems associated with traditional surgical planning methods for orthognathic surgery. To address these problems, we developed a computer-aided surgical simulation (CASS) system, the AnatomicAligner, to plan orthognathic surgery following our streamlined clinical protocol.

METHODS

The system includes six modules: image segmentation and three-dimensional (3D) reconstruction, registration and reorientation of models to neutral head posture, 3D cephalometric analysis, virtual osteotomy, surgical simulation, and surgical splint generation. The accuracy of the system was validated in a stepwise fashion: first to evaluate the accuracy of AnatomicAligner using 30 sets of patient data, then to evaluate the fitting of splints generated by AnatomicAligner using 10 sets of patient data. The industrial gold standard system, Mimics, was used as the reference.

RESULT

When comparing the results of segmentation, virtual osteotomy and transformation achieved with AnatomicAligner to the ones achieved with Mimics, the absolute deviation between the two systems was clinically insignificant. The average surface deviation between the two models after 3D model reconstruction in AnatomicAligner and Mimics was 0.3 mm with a standard deviation (SD) of 0.03 mm. All the average surface deviations between the two models after virtual osteotomy and transformations were smaller than 0.01 mm with a SD of 0.01 mm. In addition, the fitting of splints generated by AnatomicAligner was at least as good as the ones generated by Mimics.

CONCLUSION

We successfully developed a CASS system, the AnatomicAligner, for planning orthognathic surgery following the streamlined planning protocol. The system has been proven accurate. AnatomicAligner will soon be available freely to the boarder clinical and research communities.

Out-of-Sample Extensions for Non-Parametric Kernel Methods

Choosing suitable kernels plays an important role in the performance of kernel methods. Recently, a number of studies were devoted to developing nonparametric kernels. Without assuming any parametric form of the target kernel, nonparametric kernel learning offers a flexible scheme to utilize the information of the data, which may potentially characterize the data similarity better. The kernel methods using nonparametric kernels are referred to as nonparametric kernel methods. However, many nonparametric kernel methods are restricted to transductive learning, where the prediction function is defined only over the data points given beforehand. They have no straightforward extension for the out-of-sample data points, and thus cannot be applied to inductive learning. In this paper, we show how to make the nonparametric kernel methods applicable to inductive learning. The key problem of out-of-sample extension is how to extend the nonparametric kernel matrix to the corresponding kernel function. A regression approach in the hyper reproducing kernel Hilbert space is proposed to solve this problem. Empirical results indicate that the out-of-sample performance is comparable to the in-sample performance in most cases. Experiments on face recognition demonstrate the superiority of our nonparametric kernel method over the state-of-the-art parametric kernel methods.

Prediction of soft tissue deformations after CMF surgery with incremental kernel ridge regression

Facial soft tissue deformation following osteotomy is associated with the corresponding biomechanical characteristics of bone and soft tissues. However, none of the methods devised to predict soft tissue deformation after osteotomy incorporates population-based statistical data. The aim of this study is to establish a statistical model to describe the relationship between biomechanical characteristics and soft tissue deformation after osteotomy. We proposed an incremental kernel ridge regression (IKRR) model to accomplish this goal. The input of the model is the biomechanical information computed by the Finite Element Method (FEM). The output is the soft tissue deformation generated from the paired pre-operative and post-operative 3D images. The model is adjusted incrementally with each new patient's biomechanical information. Therefore, the IKRR model enables us to predict potential soft tissue deformations for new patient by using both biomechanical and statistical information. The integration of these two types of data is critically important for accurate simulations of soft-tissue changes after surgery. The proposed method was evaluated by leave-one-out cross-validation using data from 11 patients. The average prediction error of our model (0.9103mm) was lower than some state-of-the-art algorithms. This model is promising as a reliable way to prevent the risk of facial distortion after craniomaxillofacial surgery.

An eFace-Template Method for Efficiently Generating Patient-Specific Anatomically-Detailed Facial Soft Tissue FE Models for Craniomaxillofacial Surgery Simulation

Accurate surgical planning and prediction of craniomaxillofacial surgery outcome requires simulation of soft-tissue changes following osteotomy. This can only be accomplished on an anatomically-detailed facial soft tissue model. However, current anatomically-detailed facial soft tissue model generation is not appropriate for clinical applications due to the time intensive nature of manual segmentation and volumetric mesh generation. This paper presents a novel semi-automatic approach, named eFace-template method, for efficiently and accurately generating a patient-specific facial soft tissue model. Our novel approach is based on the volumetric deformation of an anatomically-detailed template to be fitted to the shape of each individual patient. The adaptation of the template is achieved by using a hybrid landmark-based morphing and dense surface fitting approach followed by a thin-plate spline interpolation. This methodology was validated using 4 visible human datasets (regarded as gold standards) and 30 patient models. The results indicated that our approach can accurately preserve the internal anatomical correspondence (i.e., muscles) for finite element modeling. Additionally, our hybrid approach was able to achieve an optimal balance among the patient shape fitting accuracy, anatomical correspondence and mesh quality. Furthermore, the statistical analysis showed that our hybrid approach was superior to two previously published methods: mesh-matching and landmark-based transformation. Ultimately, our eFace-template method can be directly and effectively used clinically to simulate the facial soft tissue changes in the clinical application.