Hybrid Graph Transformer for Tissue Microstructure Estimation with Undersampled Diffusion MRI Data

Advanced contemporary diffusion models for tissue microstructure often require diffusion MRI (DMRI) data with sufficiently dense sampling in the diffusion wavevector space for reliable model fitting, which might not always be feasible in practice. A potential remedy to this problem is by using deep learning techniques to predict high-quality diffusion microstructural indices from sparsely sampled data. However, existing methods are either agnostic to the data geometry in the diffusion wavevector space ( q -space) or limited to leveraging information from only local neighborhoods in the physical coordinate space ( x -space). Here, we propose a hybrid graph transformer (HGT) to explicitly consider the q -space geometric structure with a graph neural network (GNN) and make full use of spatial information with a novel residual dense transformer (RDT). The RDT consists of multiple densely connected transformer layers and a residual connection to facilitate model training. Extensive experiments on the data from the Human Connectome Project (HCP) demonstrate that our method significantly improves the quality of microstructural estimations over existing state-of-the-art methods.

Harmonization of Multi-site Cortical Data Across the Human Lifespan

Neuroimaging data harmonization has become a prerequisite in integrative data analytics for standardizing a wide variety of data collected from multiple studies and enabling interdisciplinary research. The lack of standardized image acquisition and computational procedures introduces non-biological variability and inconsistency in multi-site data, complicating downstream statistical analyses. Here, we propose a novel statistical technique to retrospectively harmonize multi-site cortical data collected longitudinally and cross-sectionally between birth and 100 years. We demonstrate that our method can effectively eliminate non-biological disparities from cortical thickness and myelination measurements, while preserving biological variation across the entire lifespan. Our harmonization method will foster large-scale population studies by providing comparable data required for investigating developmental and aging processes.

Weakly Supervised MR-TRUS Image Synthesis for Brachytherapy of Prostate Cancer

Prostate magnetic resonance imaging (MRI) offers accurate details of structures and tumors for prostate cancer brachytherapy. However, it is unsuitable for routine treatment since MR images differ significantly from trans-rectal ultrasound (TRUS) images conventionally used for radioactive seed implants in brachytherapy. TRUS imaging is fast, convenient, and widely available in the operation room but is known for its low soft-tissue contrast and tumor visualization capability in the prostate area. Conventionally, practitioners usually rely on prostate segmentation to fuse the two imaging modalities with non-rigid registration. However, prostate delineation is often not available on diagnostic MR images. Besides, the high non-linear intensity relationship between two imaging modalities poses a challenge to non-rigid registration. Hence, we propose a method to generate a TRUS-styled image from a prostate MR image to replace the role of the TRUS image in radiation therapy dose pre-planning. We propose a structural constraint to handle non-linear projections of anatomical structures between MR and TRUS images. We further include an adversarial mechanism to enforce the model to preserve anatomical features in an MR image (such as prostate boundary and dominant intraprostatic lesion (DIL)) while synthesizing the TRUS-styled counterpart image. The proposed method is compared with other state-of-art methods with real TRUS images as the reference. The results demonstrate that the TRUS images synthesized by our method can be used for brachytherapy treatment planning for prostate cancer.

From descriptive connectome to mechanistic connectome: Generative modeling in functional magnetic resonance imaging analysis

As a newly emerging field, connectomics has greatly advanced our understanding of the wiring diagram and organizational features of the human brain. Generative modeling-based connectome analysis, in particular, plays a vital role in deciphering the neural mechanisms of cognitive functions in health and dysfunction in diseases. Here we review the foundation and development of major generative modeling approaches for functional magnetic resonance imaging (fMRI) and survey their applications to cognitive or clinical neuroscience problems. We argue that conventional structural and functional connectivity (FC) analysis alone is not sufficient to reveal the complex circuit interactions underlying observed neuroimaging data and should be supplemented with generative modeling-based effective connectivity and simulation, a fruitful practice that we term "mechanistic connectome." The transformation from descriptive connectome to mechanistic connectome will open up promising avenues to gain mechanistic insights into the delicate operating principles of the human brain and their potential impairments in diseases, which facilitates the development of effective personalized treatments to curb neurological and psychiatric disorders.

Recurrent Tissue-Aware Network for Deformable Registration of Infant Brain MR Images

Deformable registration is fundamental to longitudinal and population-based image analyses. However, it is challenging to precisely align longitudinal infant brain MR images of the same subject, as well as cross-sectional infant brain MR images of different subjects, due to fast brain development during infancy. In this paper, we propose a recurrently usable deep neural network for the registration of infant brain MR images. There are three main highlights of our proposed method. (i) We use brain tissue segmentation maps for registration, instead of intensity images, to tackle the issue of rapid contrast changes of brain tissues during the first year of life. (ii) A single registration network is trained in a one-shot manner, and then recurrently applied in inference for multiple times, such that the complex deformation field can be recovered incrementally. (iii) We also propose both the adaptive smoothing layer and the tissue-aware anti-folding constraint into the registration network to ensure the physiological plausibility of estimated deformations without degrading the registration accuracy. Experimental results, in comparison to the state-of-the-art registration methods, indicate that our proposed method achieves the highest registration accuracy while still preserving the smoothness of the deformation field. The implementation of our proposed registration network is available online https://github.com/Barnonewdm/ACTA-Reg-Net.

A cascaded nested network for 3T brain MR image segmentation guided by 7T labeling

Accurate segmentation of the brain into gray matter, white matter, and cerebrospinal fluid using magnetic resonance (MR) imaging is critical for visualization and quantification of brain anatomy. Compared to 3T MR images, 7T MR images exhibit higher tissue contrast that is contributive to accurate tissue delineation for training segmentation models. In this paper, we propose a cascaded nested network (CaNes-Net) for segmentation of 3T brain MR images, trained by tissue labels delineated from the corresponding 7T images. We first train a nested network (Nes-Net) for a rough segmentation. The second Nes-Net uses tissue-specific geodesic distance maps as contextual information to refine the segmentation. This process is iterated to build CaNes-Net with a cascade of Nes-Net modules to gradually refine the segmentation. To alleviate the misalignment between 3T and corresponding 7T MR images, we incorporate a correlation coefficient map to allow well-aligned voxels to play a more important role in supervising the training process. We compared CaNes-Net with SPM and FSL tools, as well as four deep learning models on 18 adult subjects and the ADNI dataset. Our results indicate that CaNes-Net reduces segmentation errors caused by the misalignment and improves segmentation accuracy substantially over the competing methods.

Alterations of dynamic redundancy of functional brain subnetworks in Alzheimer's disease and major depression disorders

The human brain is not only efficiently but also "redundantly" connected. The redundancy design could help the brain maintain resilience to disease attacks. This paper explores subnetwork-level redundancy dynamics and the potential of such metrics in disease studies. As such, we looked into specific functional subnetworks, including those associated with high-level functions. We investigated how the subnetwork redundancy dynamics change along with Alzheimer's disease (AD) progression and with major depressive disorder (MDD), two major disorders that could share similar subnetwork alterations. We found an increased dynamic redundancy of the subcortical-cerebellum subnetwork and its connections to other high-order subnetworks in the mild cognitive impairment (MCI) and AD compared to the normal control (NC). With gained spatial specificity, we found such a redundancy index was sensitive to disease symptoms and could act as a protective mechanism to prevent the collapse of the brain network and functions. The dynamic redundancy of the medial frontal subnetwork and its connections to the frontoparietal subnetwork was also found decreased in MDD compared to NC. The spatial specificity of the redundancy dynamics changes may provide essential knowledge for a better understanding of shared neural substrates in AD and MDD.

Fast and Accurate Craniomaxillofacial Landmark Detection via 3D Faster R-CNN

Automatic craniomaxillofacial (CMF) landmark localization from cone-beam computed tomography (CBCT) images is challenging, considering that 1) the number of landmarks in the images may change due to varying deformities and traumatic defects, and 2) the CBCT images used in clinical practice are typically large. In this paper, we propose a two-stage, coarse-to-fine deep learning method to tackle these challenges with both speed and accuracy in mind. Specifically, we first use a 3D faster R-CNN to roughly locate landmarks in down-sampled CBCT images that have varying numbers of landmarks. By converting the landmark point detection problem to a generic object detection problem, our 3D faster R-CNN is formulated to detect virtual, fixed-size objects in small boxes with centers indicating the approximate locations of the landmarks. Based on the rough landmark locations, we then crop 3D patches from the high-resolution images and send them to a multi-scale UNet for the regression of heatmaps, from which the refined landmark locations are finally derived. We evaluated the proposed approach by detecting up to 18 landmarks on a real clinical dataset of CMF CBCT images with various conditions. Experiments show that our approach achieves state-of-the-art accuracy of 0.89 ± 0.64mm in an average time of 26.2 seconds per volume.

Altered Connectedness of the Brain Chronnectome During the Progression to Alzheimer's Disease

Graph theory has been extensively used to investigate brain network topology and its changes in disease cohorts. However, many graph theoretic analysis-based brain network studies focused on the shortest paths or, more generally, cost-efficiency. In this work, we use two new concepts, connectedness and 2-connectedness, to measure different global properties compared to the previously widely adopted ones. We apply them to unravel interesting characteristics in the brain, such as redundancy design and further conduct a time-varying brain functional network analysis for characterizing the progression of Alzheimer's disease (AD). Specifically, we define different connectedness and 2-connectedness states and evaluate their dynamics in AD and its preclinical stage, mild cognitive impairment (MCI), compared to the normal controls (NC). Results indicate that, compared to MCI and NC, brain networks of AD tend to be more frequently connected at a sparse level. For MCI, we found that their brains are more likely to be 2-connected in the minimal connected state as well indicating increasing redundancy in brain connectivity. Such a redundant design could ensure maintained connectedness of the MCI's brain network in the case that pathological damages break down any link or silenced any node, making it possible to preserve cognitive abilities. Our study suggests that the redundancy in the brain functional chronnectome could be altered in the preclinical stage of AD. The findings can be successfully replicated in a retest study and with an independent MCI dataset. Characterizing redundancy design in the brain chronnectome using connectedness and 2-connectedness analysis provides a unique viewpoint for understanding disease affected brain networks.

Magnetic Resonance Fingerprinting of the Pediatric Brain

Magnetic resonance fingerprinting (MRF) is increasingly being used to evaluate brain development and differentiate normal and pathologic tissues in children. MRF can provide reliable and accurate intrinsic tissue properties, such as T1 and T2 relaxation times. MRF is a powerful tool in evaluating brain disease in pediatric population. MRF is a new quantitative MR imaging technique for rapid and simultaneous quantification of multiple tissue properties.

Synthetic digital reconstructed radiographs for MR-only robotic stereotactic radiation therapy: A proof of concept

PURPOSE

To create synthetic CTs and digital reconstructed radiographs (DRRs) from MR images that allow for fiducial visualization and accurate dose calculation for MR-only radiosurgery.

METHODS

We developed a machine learning model to create synthetic CTs from pelvic MRs for prostate treatments. This model has been previously proven to generate synthetic CTs with accuracy on par or better than alternate methods, such as atlas-based registration. Our dataset consisted of 11 paired CT and conventional MR (T2) images used for previous CyberKnife (Accuray, Inc) radiotherapy treatments. The MR images were pre-processed to mimic the appearance of fiducial-enhancing images. Two models were trained for each parameter case, using a sub-set of the available image pairs, with the remaining images set aside for testing and validation of the model to identify the optimal patch size and number of image pairs used for training. Four models were then trained using the identified parameters and used to generate synthetic CTs, which in turn were used to generate DRRs at angles 45° and 315°, as would be used for a CyberKnife treatment. The synthetic CTs and DRRs were compared visually and using the mean squared error and peak signal-to-noise ratio against the ground-truth images to evaluate their similarity.

RESULTS

The synthetic CTs, as well as the DRRs generated from them, gave similar visualization of the fiducial markers in the prostate as the true counterparts. There was no significant difference found for the fiducial localization for the CTs and DRRs. Across the 8 DRRs analyzed, the mean MSE between the normalized true and synthetic DRRs was 0.66 ± 0.42% and the mean PSNR for this region was 22.9 ± 3.7 dB. For the full CTs, the mean MAE was 72.9 ± 88.1 HU and the mean PSNR was 31.2 ± 2.2 dB.

CONCLUSIONS

Our machine learning-based method provides a proof of concept of a way to generate synthetic CTs and DRRs for accurate dose calculation and fiducial localization for use in radiation treatment of the prostate.

Dilated perivascular space is related to reduced free-water in surrounding white matter among healthy adults and elderlies but not in patients with severe cerebral small vessel disease

Perivascular space facilitates cerebral interstitial water clearance. However, it is unclear how dilated perivascular space (dPVS) affects the interstitial water of surrounding white matter. We aimed to determine the presence and extent of changes in normal-appearing white matter water components around dPVS in different populations. Twenty healthy elderly subjects and 15 elderly subjects with severe cerebral small vessel disease (CSVD, with lacunar infarction 6 months before the scan) were included in our study. And other 28 healthy adult subjects were enrolled under a different scanning parameter to see if the results are comparable. The normal-appearing white matter around dPVS was categorized into 10 layers (1 mm thickness each) based on their distance to dPVS. We evaluated the mean isotropic-diffusing water volume fraction in each layer. We discovered a significantly reduced free-water content in the layers closely adjacent to the dPVS in the healthy elderlies. however, this reduction around dPVS was weaker in the CSVD subjects. We also discovered an elevated free-water content within dPVS. DPVS played different roles in healthy subjects or CSVD subjects. The reduced water content around dPVS in healthy subjects suggests these MR-visible PVSs are not always related to the stagnation of fluid.

Real-Time Mapping of Tissue Properties for Magnetic Resonance Fingerprinting

Magnetic resonance fingerprinting (MRF) is a relatively new multi-parametric quantitative imaging method that involves a two-step process: (i) reconstructing a series of time frames from highly-undersampled non-Cartesian spiral k-space data and (ii) pattern matching using the time frames to infer tissue properties (e.g., T 1 and T 2 relaxation times). In this paper, we introduce a novel end-to-end deep learning framework to seamlessly map the tissue properties directly from spiral k-space MRF data, thereby avoiding time-consuming processing such as the non-uniform fast Fourier transform (NUFFT) and the dictionary-based fingerprint matching. Our method directly consumes the non-Cartesian k -space data, performs adaptive density compensation, and predicts multiple tissue property maps in one forward pass. Experiments on both 2D and 3D MRF data demonstrate that quantification accuracy comparable to state-of-the-art methods can be accomplished within 0.5 s, which is 1,100 to 7,700 times faster than the original MRF framework. The proposed method is thus promising for facilitating the adoption of MRF in clinical settings.

Highly Reproducible Whole Brain Parcellation in Individuals via Voxel Annotation with Fiber Clusters

A central goal in systems neuroscience is to parcellate the brain into discrete units that are neurobiologically coherent. Here, we propose a strategy for consistent whole-brain parcellation of white matter (WM) and gray matter (GM) in individuals. We parcellate the brain into coherent parcels using non-negative matrix factorization based on voxel annotation using fiber clusters. Tractography is performed using an algorithm that mitigates gyral bias, allowing full gyral and sulcal coverage for reliable parcellation of the cortical ribbon. Experimental results indicate that parcellation using our approach is highly reproducible with 100% test-retest parcel identification rate and is highly consistent with significantly lower inter-subject variability than FreeSurfer parcellation. This implies that reproducible parcellation can be obtained for subject-specific investigation of brain structure and function.

Vox2Surf: Implicit Surface Reconstruction from Volumetric Data

Surface reconstruction from volumetric T1-weighted and T2-weighted images is a time-consuming multi-step process that often involves careful parameter fine-tuning, hindering a more wide-spread utilization of surface-based analysis particularly in large-scale studies. In this work, we propose a fast surface reconstruction method that is based on directly learning a continuous-valued signed distance function (SDF) as implicit surface representation. This continuous representation implicitly encodes the boundary of the surface as the zero isosurface. Given the predicted SDF, the target 3D surface is reconstructed by applying the marching cubes algorithm. Our implicit reconstruction method concurrently predicts the surfaces of the brain parenchyma, the white matter and pial surfaces, the subcortical structures, and the ventricles. Evaluation based on data from the Human Connectome Project indicates that surface reconstruction of a total of 22 cortical and subcortical structures can be completed in less than 20 min.

DLLNet: An Attention-Based Deep Learning Method for Dental Landmark Localization on High-Resolution 3D Digital Dental Models

Dental landmark localization is a fundamental step to analyzing dental models in the planning of orthodontic or orthognathic surgery. However, current clinical practices require clinicians to manually digitize more than 60 landmarks on 3D dental models. Automatic methods to detect landmarks can release clinicians from the tedious labor of manual annotation and improve localization accuracy. Most existing landmark detection methods fail to capture local geometric contexts, causing large errors and misdetections. We propose an end-to-end learning framework to automatically localize 68 landmarks on high-resolution dental surfaces. Our network hierarchically extracts multi-scale local contextual features along two paths: a landmark localization path and a landmark area-of-interest segmentation path. Higher-level features are learned by combining local-to-global features from the two paths by feature fusion to predict the landmark heatmap and the landmark area segmentation map. An attention mechanism is then applied to the two maps to refine the landmark position. We evaluated our framework on a real-patient dataset consisting of 77 high-resolution dental surfaces. Our approach achieves an average localization error of 0.42 mm, significantly outperforming related start-of-the-art methods.

Active Cortex Tractography

Most existing diffusion tractography algorithms are affected by gyral bias, causing the termination of streamlines at gyral crowns instead of sulcal banks. In this paper, we propose a tractography technique, called active cortex tractography (ACT), to overcome gyral bias by enabling fiber streamlines to curve naturally into the cortex. We show that the cortex can play an active role in cortical tractography by providing anatomical information to overcome orientation ambiguities as the streamlines enter the superficial white matter in gyral blades and approach the cortex. This is achieved by devising a direction scouting mechanism that takes into account the white matter surface normal vectors. The scouting mechanism allows probing of directions further in space to prepare the streamlines to turn at appropriate angles. The surface normal vectors guide the streamlines to turn into the cortex, perpendicular to the white-gray matter interface. Evaluation using synthetic, macaque and human data with different streamline seeding schemes demonstrates that ACT improves cortical tractography.

SkullEngine: A Multi-Stage CNN Framework for Collaborative CBCT Image Segmentation and Landmark Detection

Accurate bone segmentation and landmark detection are two essential preparation tasks in computer-aided surgical planning for patients with craniomaxillofacial (CMF) deformities. Surgeons typically have to complete the two tasks manually, spending ~12 hours for each set of CBCT or ~5 hours for CT. To tackle these problems, we propose a multi-stage coarse-to-fine CNN-based framework, called SkullEngine, for high-resolution segmentation and large-scale landmark detection through a collaborative, integrated, and scalable JSD model and three segmentation and landmark detection refinement models. We evaluated our framework on a clinical dataset consisting of 170 CBCT/CT images for the task of segmenting 2 bones (midface and mandible) and detecting 175 clinically common landmarks on bones, teeth, and soft tissues. Experimental results show that SkullEngine significantly improves segmentation quality, especially in regions where the bone is thin. In addition, SkullEngine also efficiently and accurately detect all of the 175 landmarks. Both tasks were completed simultaneously within 3 minutes regardless of CBCT or CT with high segmentation quality. Currently, SkullEngine has been integrated into a clinical workflow to further evaluate its clinical efficiency.

Surface-Guided Image Fusion for Preserving Cortical Details in Human Brain Templates

Human brain templates are a basis for comparison of brain features across individuals. They should ideally capture an atomical details at both coarse and fine scales to facilitate comparison at varying granularity. Brain template construction typically involves spatial normalization and image fusion. While significant efforts have been dedicated to improving brain templates with sophisticated spatial normalization algorithms, image fusion is typically carried out using intensity-based averaging, causing blurring of anatomical structures. Here, we present an image fusion method that exploits cortical surfaces as guidance to help preserve details in brain templates. Our method encodes cortical boundary information given by a cortical surface mesh in a signed distance function (SDF) map. We use the SDF map to help determine localized contributions of the individual images, especially at cortical boundaries, in image fusion. Experimental results demonstrate that our method significantly improves the preservation of fine gyral and sulcal details, resulting in detailed brain templates with good surface-volume agreement.

Skull Segmentation from CBCT Images via Voxel-Based Rendering

Skull segmentation from three-dimensional (3D) cone-beam computed tomography (CBCT) images is critical for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Convolutional neural network (CNN)-based methods are currently dominating volumetric image segmentation, but these methods suffer from the limited GPU memory and the large image size (e.g., 512 × 512 × 448). Typical ad-hoc strategies, such as down-sampling or patch cropping, will degrade segmentation accuracy due to insufficient capturing of local fine details or global contextual information. Other methods such as Global-Local Networks (GLNet) are focusing on the improvement of neural networks, aiming to combine the local details and the global contextual information in a GPU memory-efficient manner. However, all these methods are operating on regular grids, which are computationally inefficient for volumetric image segmentation. In this work, we propose a novel VoxelRend-based network (VR-U-Net) by combining a memory-efficient variant of 3D U-Net with a voxel-based rendering (VoxelRend) module that refines local details via voxel-based predictions on non-regular grids. Establishing on relatively coarse feature maps, the VoxelRend module achieves significant improvement of segmentation accuracy with a fraction of GPU memory consumption. We evaluate our proposed VR-U-Net in the skull segmentation task on a high-resolution CBCT dataset collected from local hospitals. Experimental results show that the proposed VR-U-Net yields high-quality segmentation results in a memory-efficient manner, highlighting the practical value of our method.

A Self-Supervised Deep Framework for Reference Bony Shape Estimation in Orthognathic Surgical Planning

Virtual orthognathic surgical planning involves simulating surgical corrections of jaw deformities on 3D facial bony shape models. Due to the lack of necessary guidance, the planning procedure is highly experience-dependent and the planning results are often suboptimal. A reference facial bony shape model representing normal anatomies can provide an objective guidance to improve planning accuracy. Therefore, we propose a self-supervised deep framework to automatically estimate reference facial bony shape models. Our framework is an end-to-end trainable network, consisting of a simulator and a corrector. In the training stage, the simulator maps jaw deformities of a patient bone to a normal bone to generate a simulated deformed bone. The corrector then restores the simulated deformed bone back to normal. In the inference stage, the trained corrector is applied to generate a patient-specific normal-looking reference bone from a real deformed bone. The proposed framework was evaluated using a clinical dataset and compared with a state-of-the-art method that is based on a supervised point-cloud network. Experimental results show that the estimated shape models given by our approach are clinically acceptable and significantly more accurate than that of the competing method.

Deep Simulation of Facial Appearance Changes Following Craniomaxillofacial Bony Movements in Orthognathic Surgical Planning

Facial appearance changes with the movements of bony segments in orthognathic surgery of patients with craniomaxillofacial (CMF) deformities. Conventional bio-mechanical methods, such as finite element modeling (FEM), for simulating such changes, are labor intensive and computationally expensive, preventing them from being used in clinical settings. To overcome these limitations, we propose a deep learning framework to predict post-operative facial changes. Specifically, FC-Net, a facial appearance change simulation network, is developed to predict the point displacement vectors associated with a facial point cloud. FC-Net learns the point displacements of a pre-operative facial point cloud from the bony movement vectors between pre-operative and simulated post-operative bony models. FC-Net is a weakly-supervised point displacement network trained using paired data with strict point-to-point correspondence. To preserve the topology of the facial model during point transform, we employ a local-point-transform loss to constrain the local movements of points. Experimental results on real patient data reveal that the proposed framework can predict post-operative facial appearance changes remarkably faster than a state-of-the-art FEM method with comparable prediction accuracy.

Noise Mapping and Removal in Complex-Valued Multi-Channel MRI via Optimal Shrinkage of Singular Values

In magnetic resonance imaging (MRI), noise is a limiting factor for higher spatial resolution and a major cause of prolonged scan time, owing to the need for repeated scans. Improving the signal-to-noise ratio is therefore key to faster and higher-resolution MRI. Here we propose a method for mapping and reducing noise in MRI by leveraging the inherent redundancy in complex-valued multi-channel MRI data. Our method leverages a provably optimal strategy for shrinking the singular values of a data matrix, allowing it to outperform state-of-the-art methods such as Marchenko-Pastur PCA in noise reduction. Our method reduces the noise floor in brain diffusion MRI by 5-fold and remarkably improves the contrast of spiral lung ¹⁹F MRI. Our framework is fast and does not require training and hyper-parameter tuning, therefore providing a convenient means for improving SNR in MRI.

Estimating Reference Bony Shape Models for Orthognathic Surgical Planning Using 3D Point-Cloud Deep Learning

Orthognathic surgical outcomes rely heavily on the quality of surgical planning. Automatic estimation of a reference facial bone shape significantly reduces experience-dependent variability and improves planning accuracy and efficiency. We propose an end-to-end deep learning framework to estimate patient-specific reference bony shape models for patients with orthognathic deformities. Specifically, we apply a point-cloud network to learn a vertex-wise deformation field from a patient's deformed bony shape, represented as a point cloud. The estimated deformation field is then used to correct the deformed bony shape to output a patient-specific reference bony surface model. To train our network effectively, we introduce a simulation strategy to synthesize deformed bones from any given normal bone, producing a relatively large and diverse dataset of shapes for training. Our method was evaluated using both synthetic and real patient data. Experimental results show that our framework estimates realistic reference bony shape models for patients with varying deformities. The performance of our method is consistently better than an existing method and several deep point-cloud networks. Our end-to-end estimation framework based on geometric deep learning shows great potential for improving clinical workflows.