Euclidean and Shape-Based Analysis of the Dynamic Mitral Annulus in Children using a Novel Open-Source Framework.

BACKGROUND: The dynamic shape of the normal adult mitral annulus has been shown to be important to mitral valve function. However, annular dynamics of the healthy mitral valve in children have yet to be explored. The aim of this study was to model and quantify the shape and major modes of variation of pediatric mitral valve annuli in four phases of the cardiac cycle using transthoracic echocardiography. METHODS: The mitral valve annuli of 100 children and young adults with normal findings on three-dimensional echocardiography were modeled in four different cardiac phases using the SlicerHeart extension for 3D Slicer. Annular metrics were quantified using SlicerHeart, and optimal normalization to body surface area was explored. Mean annular shapes and the principal components of variation were computed using custom code implemented in a new SlicerHeart module (Annulus Shape Analyzer). Shape was regressed over metrics of age and body surface area, and mean shapes for five age-stratified groups were generated. RESULTS: The ratio of annular height to commissural width of the mitral valve ("saddle shape") changed significantly throughout age for systolic phases (P < .001) but within a narrow range (median range, 0.20-0.25). Annular metrics changed statistically significantly between the diastolic and systolic phases of the cardiac cycle. Visually, the annular shape was maintained with respect to age and body surface area. Principal-component analysis revealed that the pediatric mitral annulus varies primarily in size (mode 1), ratio of annular height to commissural width (mode 2), and sphericity (mode 3). CONCLUSIONS: The saddle-shaped mitral annulus is maintained throughout childhood but varies significantly throughout the cardiac cycle. The major modes of variation in the pediatric mitral annulus are due to size, ratio of annular height to commissural width, and sphericity. The generation of age- and size-specific mitral annular shapes may inform the development of appropriately scaled absorbable or expandable mitral annuloplasty rings for children.

Hierarchical Geodesic Polynomial Model for Multilevel Analysis of Longitudinal Shape.

Longitudinal analysis is a core aspect of many medical applications for understanding the relationship between an anatomical subject's function and its trajectory of shape change over time. Whereas mixed-effects (or hierarchical) modeling is the statistical method of choice for analysis of longitudinal data, we here propose its extension as hierarchical geodesic polynomial model (HGPM) for multilevel analyses of longitudinal shape data. 3D shapes are transformed to a non-Euclidean shape space for regression analysis using geodesics on a high dimensional Riemannian manifold. At the subject-wise level, each individual trajectory of shape change is represented by a univariate geodesic polynomial model on timestamps. At the population level, multivariate polynomial expansion is applied to uni/multivariate geodesic polynomial models for both anchor points and tangent vectors. As such, the trajectory of an individual subject's shape changes over time can be modeled accurately with a reduced number of parameters, and population-level effects from multiple covariates on trajectories can be well captured. The implemented HGPM is validated on synthetic examples of points on a unit 3D sphere. Further tests on clinical 4D right ventricular data show that HGPM is capable of capturing observable effects on shapes attributed to changes in covariates, which are consistent with qualitative clinical evaluations. HGPM demonstrates its effectiveness in modeling shape changes at both subject-wise and population levels, which is promising for future studies of the relationship between shape changes over time and the level of dysfunction severity on anatomical objects associated with disease.

Modeling of the Tricuspid Valve and Right Ventricle in Hypoplastic Left Heart Syndrome With a Fontan Circulation.

BACKGROUND: In hypoplastic left heart syndrome, tricuspid regurgitation (TR) is associated with circulatory failure and death. We hypothesized that the tricuspid valve (TV) structure of patients with hypoplastic left heart syndrome with a Fontan circulation and moderate or greater TR differs from those with mild or less TR, and that right ventricle volume is associated with TV structure and dysfunction. METHODS: TV of 100 patients with hypoplastic left heart syndrome and a Fontan circulation were modeled using transthoracic 3-dimensional echocardiograms and custom software in SlicerHeart. Associations of TV structure to TR grade and right ventricle function and volume were investigated. Shape parameterization and analysis was used to calculate the mean shape of the TV leaflets, their principal modes of variation, and to characterize associations of TV leaflet shape to TR. RESULTS: In univariate modeling, patients with moderate or greater TR had larger TV annular diameters and area, greater annular distance between the anteroseptal commissure and anteroposterior commissure, greater leaflet billow volume, and more laterally directed anterior papillary muscle angles compared to valves with mild or less TR (all P<0.001). In multivariate modeling greater total billow volume, lower anterior papillary muscle angle, and greater distance between the anteroposterior commissure and anteroseptal commissure were associated with moderate or greater TR (P<0.001, C statistic=0.85). Larger right ventricle volumes were associated with moderate or greater TR (P<0.001). TV shape analysis revealed structural features associated with TR, but also highly heterogeneous TV leaflet structure. CONCLUSIONS: Moderate or greater TR in patients with hypoplastic left heart syndrome with a Fontan circulation is associated with greater leaflet billow volume, a more laterally directed anterior papillary muscle angle, and greater annular distance between the anteroseptal commissure and anteroposterior commissure. However, there is significant heterogeneity of structure in the TV leaflets in regurgitant valves. Given this variability, an image-informed patient-specific approach to surgical planning may be needed to achieve optimal outcomes in this vulnerable and challenging population.

Modeling Longitudinal Optical Coherence Tomography Images for Monitoring and Analysis of Glaucoma Progression.

Glaucoma causes progressive visual field deterioration and is the leading cause of blindness worldwide. Glaucomatous damage is irreversible and greatly impacts quality of life. Therefore, it is critically important to detect glaucoma early and closely monitor progression to preserve functional vision. Glaucoma is routinely monitored in the clinical setting using optical coherence tomography (OCT) for derived measures such as the thickness of important visual structures. There is not a consensus of what measures represent the most relevant biomarkers of glaucoma progression. Further, despite the increasing availability of longitudinal OCT data, a quantitative model of 3D structural change over time associated with glaucoma does not exist. In this paper we present an algorithm that will perform hierarchical geodesic modeling at the imaging level, considering 3D OCT images as observations of structural change over time. Hierarchical modeling includes subject-wise trajectories as geodesics in the space of diffeomorphisms and population level (glaucoma vs control) trajectories are also geodesics which explain subject-wise trajectories as deviations from the mean. Our preliminary experiments demonstrate a greater magnitude of structural change associated with glaucoma compared to normal aging. Our algorithm has the potential application in patient-specific monitoring and analysis of glaucoma progression as well as a statistical model of population trends and population variability.

SlicerSALT: From Medical Images to Quantitative Insights of Anatomy.

Three-dimensional (3D) shape lies at the core of understanding the physical objects that surround us. In the biomedical field, shape analysis has been shown to be powerful in quantifying how anatomy changes with time and disease. The Shape AnaLysis Toolbox (SALT) was created as a vehicle for disseminating advanced shape methodology as an open source, free, and comprehensive software tool. We present new developments in our shape analysis software package, including easy-to-interpret statistical methods to better leverage the quantitative information contained in SALT's shape representations. We also show SlicerPipelines, a module to improve the usability of SALT by facilitating the analysis of large-scale data sets, automating workflows for non-expert users, and allowing the distribution of reproducible workflows.

Geodesic Logistic Analysis of Lumbar Spine Intervertebral Disc Shapes in Supine and Standing Positions.

Non-specific lower back pain (LBP) is a world-wide public health problem that affects people of all ages. Despite the high prevalence of non-specific LBP and the associated economic burdens, the pathoanatomical mechanisms for the development and course of the condition remain unclear. While intervertebral disc degeneration (IDD) is associated with LBP, there is overlapping occurrence of IDD in symptomatic and asymptomatic individuals, suggesting that degeneration alone cannot identify LBP populations. Previous work has been done trying to relate linear measurements of compression obtained from Magnetic Resonance Imaging (MRI) to pain unsuccessfully. To bridge this gap, we propose to use advanced non-Euclidean statistical shape analysis methods to develop biomarkers that can help identify symptomatic and asymptomatic adults who might be susceptible to standing-induced LBP. We scanned 4 male and 7 female participants who exhibited lower back pain after prolonged standing using an Open Upright MRI. Supine and standing MRIs were obtained for each participant. Patients reported their pain intensity every fifteen minutes within a period of 2 h. Using our proposed geodesic logistic regression, we related the structure of their lower spine to pain and computed a regression model that can delineate lower spine structures using reported pain intensities. These results indicate the feasibility of identifying individuals who may suffer from lower back pain solely based on their spinal anatomy. Our proposed spinal shape analysis methodology have the potential to provide powerful information to the clinicians so they can make better treatment decisions.

SKELETAL POINT REPRESENTATIONS WITH GEOMETRIC DEEP LEARNING.

Skeletonization has been a popular shape analysis technique that models both the interior and exterior of an object. Existing template-based calculations of skeletal models from anatomical structures are a time-consuming manual process. Recently, learning-based methods have been used to extract skeletons from 3D shapes. In this work, we propose novel additional geometric terms for calculating skeletal structures of objects. The results are similar to traditional fitted s-reps but but are produced much more quickly. Evaluation on real clinical data shows that the learned model predicts accurate skeletal representations and shows the impact of proposed geometric losses along with using s-reps as weak supervision.

Visualization and Quantification of the Unrepaired Complete Atrioventricular Canal Valve Using Open-Source Software.

BACKGROUND: Repair of complete atrioventricular canal (CAVC) is often complicated by residual left atrioventricular valve regurgitation. The structure of the mitral and tricuspid valves in biventricular hearts has previously been shown to be associated with valve dysfunction. However, the three-dimensional (3D) structure of the entire unrepaired CAVC valve has not been quantified. Understanding the 3D structure of the CAVC may inform optimized repair. METHODS: Novel open-source work flows were created in SlicerHeart for the modeling and quantification of CAVC valves on the basis of 3D echocardiographic images. These methods were applied to model the annulus, leaflets, and papillary muscle (PM) structure of 35 patients (29 with trisomy 21) with CAVC using transthoracic 3D echocardiography. The mean leaflet and annular shapes were calculated and visualized using shape analysis. Metrics of the complete native CAVC valve structure were compared with those of normal mitral valves using the Mann-Whitney U test. Associations between CAVC structure and atrioventricular valve regurgitation were analyzed. RESULTS: CAVC leaflet metrics varied throughout systole. Compared with normal mitral valves, the left CAVC PMs were more acutely angled in relation to the annular plane (P < .001). In addition, the anterolateral PM was laterally and inferiorly rotated in CAVC, while the posteromedial PM was more superiorly and laterally rotated, relative to normal mitral valves (P < .001). Lower native CAVC atrioventricular valve annular height and annular height-to-valve width ratio before repair were both associated with moderate or greater left atrioventricular valve regurgitation after repair (P < .01). CONCLUSIONS: It is feasible to model and quantify 3D CAVC structure using 3D echocardiographic images. The results demonstrate significant variation in CAVC structure across the cohort and differences in annular, leaflet, and PM structure compared with the mitral valve. These tools may be used in future studies to catalyze future research intended to identify structural associations of valve dysfunction and to optimize repair in this vulnerable and complex population.

Statistical shape analysis of the tricuspid valve in hypoplastic left heart sydrome.

Hypoplastic left heart syndrome (HLHS) is a congenital heart disease characterized by incomplete development of the left heart. Children with HLHS undergo a series of operations which result in the tricuspid valve (TV) becoming the only functional atrioventricular valve. Some of those patients develop tricuspid regurgitation which is associated with heart failure and death and necessitates further surgical intervention. Repair of the regurgitant TV, and understanding the connections between structure and function of this valve remains extremely challenging. Adult cardiac populations have used 3D echocardiography (3DE) combined with computational modeling to better understand cardiac conditions affecting the TV. However, these structure-function analyses rely on simplistic point-based techniques that do not capture the leaflet surface in detail, nor do they allow robust comparison of shapes across groups. We propose using statistical shape modeling and analysis of the TV using Spherical Harmonic Representation Point Distribution Models (SPHARM-PDM) in order to generate a reproducible representation, which in turn enables high dimensional low sample size statistical analysis techniques such as principal component analysis and distance weighted discrimination. Our initial results suggest that visualization of the differences in regurgitant vs. non-regurgitant valves can precisely locate populational structural differences as well as how an individual regurgitant valve differs from the mean shape of functional valves. We believe that these results will support the creation of modern image-based modeling tools, and ultimately increase the understanding of the relationship between valve structure and function needed to inform and improve surgical planning in HLHS.

Skeletons, Object Shape, Statistics.

Objects and object complexes in 3D, as well as those in 2D, have many possible representations. Among them skeletal representations have special advantages and some limitations. For the special form of skeletal representation called "s-reps," these advantages include strong suitability for representing slabular object populations and statistical applications on these populations. Accomplishing these statistical applications is best if one recognizes that s-reps live on a curved shape space. Here we will lay out the definition of s-reps, their advantages and limitations, their mathematical properties, methods for fitting s-reps to single- and multi-object boundaries, methods for measuring the statistics of these object and multi-object representations, and examples of such applications involving statistics. While the basic theory, ideas, and programs for the methods are described in this paper and while many applications with evaluations have been produced, there remain many interesting open opportunities for research on comparisons to other shape representations, new areas of application and further methodological developments, many of which are explicitly discussed here.

Skeletal model-based analysis of the tricuspid valve in hypoplastic left heart syndrome.

Hypoplastic left heart syndrome (HLHS) is a congenital heart disease characterized by incomplete development of the left heart. Children with HLHS undergo a series of operations which result in the tricuspid valve (TV) becoming the only functional atrioventricular valve. Many HLHS patients develop tricuspid regurgitation and right ventricle enlargement which is associated with heart failure and death without surgical intervention on the valve. Understanding the connections between the geometry of the TV and its function remains extremely challenging and hinders TV repair planning. Traditional analysis methods rely on simple anatomical measures which do not capture information about valve geometry in detail. Recently, surface-based shape representations such as SPHARM-PDM have been shown to be useful for tasks such as discriminating between valves with normal or poor function. In this work we propose to use skeletal representations (s-reps), a more feature-rich geometric representation, for modeling the leaflets of the tricuspid valve. We propose an extension to previous s-rep fitting approaches to incorporate application-specific anatomical landmarks and population information to improve correspondence. We use several traditional statistical shape analysis techniques to evaluate the efficiency of this representation: using principal component analysis (PCA) we observe that it takes fewer modes of variation compared to boundary-based approaches to represent 90% of the population variation, while distance-weighted discrimination (DWD) shows that s-reps provide for more significant classification between valves with less regurgitation and those with more. These results show the power of using s-reps for modeling the relationship between structure and function of the tricuspid valve.

Virtual Simulation for Interactive Visualization of 3D Fracture Fixation Biomechanics.

INTRODUCTION: In the surgical fixation of fractures, proper biomechanical stability is key in preventing clinical complications including poor fracture healing, residual deformity, loss of fixation, or implant failure. Stability is largely influenced by treatment decisions made by the surgeon. The interplay of surgeon-controlled variables and their effect on the three-dimensional (3D) biomechanics of a fracture fixation construct are often not intuitive, and current training methods do not facilitate a deep understanding of these interactions. METHODS: A simulation software interface, FracSim, was developed. FracSim is built on a large precomputed library of finite element simulations. The software allows a surgeon to make adjustments to a virtual fracture fixation construct/weight-bearing plan and immediately visualize how these changes affect 3D biomechanics, including implant stress and fracture gap strain, important for clinical success. Twenty-one orthopaedic residents completed an instructor-led educational session with FracSim focused on bridge plating. Subjects completed pretests and posttests of knowledge of biomechanical concepts and a questionnaire. RESULTS: Subjects scored a mean of 5.6/10 on the pretest of biomechanical knowledge. Senior residents scored better than junior residents (P = 0.04). After the educational session with FracSim, residents improved their test scores to a mean of 8.0/10, with a significant improvement (P < 0.001). Questionnaire scores indicated that subjects believed that FracSim had realistic implants, constructs, and motions and that training with FracSim was purposeful, desirable, efficient, fun, and useful for enhancing the understanding of fracture fixation biomechanics. DISCUSSION: This new type of simulation software enables interactive visualization of 3D fracture fixation biomechanics. Limitations of this study include lack of a control group undergoing traditional education and lack of a delayed posttest to assess retention. FracSim may provide an effective and engaging way to promote a deeper understanding of biomechanical concepts in the orthopaedic learner.

Toward automatic atlas-based surgical planning for septoplasty.

PURPOSE: Surgery for nasal airway obstruction (NAO) has a high failure rate, with up to 50% of patients reporting persistent symptoms postoperatively. Virtual surgery planning has the potential to improve surgical outcomes, but current manual methods are too labor-intensive to be adopted on a large scale. This manuscript introduces an automatic atlas-based approach for performing virtual septoplasties. METHODS: A cohort of 47 healthy subjects and 26 NAO patients was investigated. An atlas of healthy nasal geometry was constructed. The automatic virtual septoplasty method consists of a multi-stage registration approach to fit the atlas to a target NAO patient, automatically segment the patient's septum and airway, and deform the patient image to have a non-deviated septum. RESULTS: Our automatic virtual septoplasty method straightened the septum successfully in 18 out of 26 NAO patients (69% of cases). In these cases, the ratio of the higher to the lower airspace cross-sectional areas in the left and right nasal cavities improved from 1.47 ± 0.45 to 1.16 ± 0.33 in the region surrounding the septal deviation, showing that the nasal airway became more symmetric after virtual septoplasty. CONCLUSION: This automated virtual septoplasty technique has the potential to greatly reduce the effort required to perform computational fluid dynamics (CFD) analysis of nasal airflow for NAO surgical planning. Future studies are needed to investigate if virtual surgery planning using this method is predictive of subjective symptoms in NAO patients after septoplasty.

Wavelet Guided 3D Deep Model to improve Dental Microfracture Detection.

Epidemiological studies indicate that microfractures (cracks) are the third most common cause of tooth loss in industrialized countries. An undetected crack will continue to progress, often with significant pain, until the tooth is lost. Previous attempts to utilize cone beam computed tomography (CBCT) for detecting cracks in teeth had very limited success. We propose a model that detects cracked teeth in high resolution (hr) CBCT scans by combining signal enhancement with a deep CNNbased crack detection model. We perform experiments on a dataset of 45 ex-vivo human teeth with 31 cracked and 14 controls. We demonstrate that a model that combines classical wavelet-based features with a deep 3D CNN model can improve fractured tooth detection accuracy in both micro-Computed Tomography (ground truth) and hr-CBCT scans. The CNN model is trained to predict a probability map showing the most likely fractured regions. Based on this fracture probability map we detect the presence of fracture and are able to differentiate a fractured tooth from a control tooth. We compare these results to a 2D CNN-based approach and we show that our approach provides superior detection results. We also show that the proposed solution is able to outperform oral and maxillofacial radiologists in detecting fractures from the hr-CBCT scans. Early detection of cracks will lead to the design of more appropriate treatments and longer tooth retention.

Fitting unbranching skeletal structures to objects.

Representing an object by a skeletal structure can be powerful for statistical shape analysis if there is good correspondence of the representations within a population. Many anatomic objects have a genus-zero boundary and can be represented by a smooth unbranching skeletal structure that can be discretely approximated. We describe how to compute such a discrete skeletal structure ("d-s-rep") for an individual 3D shape with the desired correspondence across cases. The method involves fitting a d-s-rep to an input representation of an object's boundary. A good fit is taken to be one whose skeletally implied boundary well approximates the target surface in terms of low order geometric boundary properties: (1) positions, (2) tangent fields, (3) various curvatures. Our method involves a two-stage framework that first, roughly yet consistently fits a skeletal structure to each object and second, refines the skeletal structure such that the shape of the implied boundary well approximates that of the object. The first stage uses a stratified diffeomorphism to produce topologically non-self-overlapping, smooth and unbranching skeletal structures for each object of a population. The second stage uses loss terms that measure geometric disagreement between the skeletally implied boundary and the target boundary and avoid self-overlaps in the boundary. By minimizing the total loss, we end up with a good d-s-rep for each individual shape. We demonstrate such d-s-reps for various human brain structures. The framework is accessible and extensible by clinical users, researchers and developers as an extension of SlicerSALT, which is based on 3D Slicer.

Dental microfracture detection using wavelet features and machine learning.

Microfractures (cracks) are the third most common cause of tooth loss in industrialized countries. If they are not detected early, they continue to progress until the tooth is lost. Cone beam computed tomography (CBCT) has been used to detect microfractures, but has had very limited success. We propose an algorithm to detect cracked teeth that pairs high resolution (hr) CBCT scans with advanced image analysis and machine learning. First, microfractures were simulated in extracted human teeth (n=22). hr-CBCT and microCT scans of the fractured and control teeth (n=14) were obtained. Wavelet pyramid construction was used to generate a phase image of the Fourier transformed scan which were fed to a U-Net deep learning architecture that localizes the orientation and extent of the crack which yields slice-wise probability maps that indicate the presence of microfractures. We then examine the ratio of high-probability voxels to total tooth volume to determine the likelihood of cracks per tooth. In microCT and hr-CBCT scans, fractured teeth have higher numbers of such voxels compared to control teeth. The proposed analytical framework provides a novel way to quantify the structural breakdown of teeth, that was not possible before. Future work will expand our machine learning framework to 3D volumes, improve our feature extraction in hr-CBCT and clinically validate this model. Early detection of microfractures will lead to more appropriate treatment and longer tooth retention.

An open-source solution for shape modeling and analysis of objects of challenging topologies.

Shape analysis is an important and powerful tool in a wide variety of medical applications. Many shape analysis techniques require shape representations which are in correspondence. Unfortunately, popular techniques for generating shape representations do not handle objects with complex geometry or topology well, and those that do are not typically readily available for non-expert users. We describe a method for generating correspondences across a population of objects using a given template. We also describe its implementation and distribution via SlicerSALT, an open-source platform for making powerful shape analysis techniques more widely available and usable. Finally, we show results of this implementation on mouse femur data.

User-Guided Segmentation of Multi-modality Medical Imaging Datasets with ITK-SNAP.

ITK-SNAP is an interactive software tool for manual and semi-automatic segmentation of 3D medical images. This paper summarizes major new features added to ITK-SNAP over the last decade. The main focus of the paper is on new features that support semi-automatic segmentation of multi-modality imaging datasets, such as MRI scans acquired using different contrast mechanisms (e.g., T1, T2, FLAIR). The new functionality uses decision forest classifiers trained interactively by the user to transform multiple input image volumes into a foreground/background probability map; this map is then input as the data term to the active contour evolution algorithm, which yields regularized surface representations of the segmented objects of interest. The new functionality is evaluated in the context of high-grade and low-grade glioma segmentation by three expert neuroradiogists and a non-expert on a reference dataset from the MICCAI 2013 Multi-Modal Brain Tumor Segmentation Challenge (BRATS). The accuracy of semi-automatic segmentation is competitive with the top specialized brain tumor segmentation methods evaluated in the BRATS challenge, with most results obtained in ITK-SNAP being more accurate, relative to the BRATS reference manual segmentation, than the second-best performer in the BRATS challenge; and all results being more accurate than the fourth-best performer. Segmentation time is reduced over manual segmentation by 2.5 and 5 times, depending on the rater. Additional experiments in interactive placenta segmentation in 3D fetal ultrasound illustrate the generalizability of the new functionality to a different problem domain.

An Interactive, Patient-Specific Virtual Surgical Planning System for Upper Airway Obstruction Treatments.

Upper airway obstructions leading todifficulty breathing are significant problems that often require surgery to improve patient quality of life. However, these surgeries often have poor outcomes with little symptom improvement. This paper outlines the design of an interactive, patient-specific virtual surgical planning system that uses patient CT scans to generate three-dimensional representations of the airways and incorporates computational fluid dynamics (CFD) as a part of the surgical planning process. Individualized virtual surgeries can be performed by editing these models, which are then analyzed using CFD to compare pre- and post- surgery flow characteristics to assess patient symptom improvement. The prototype system shows significant promise by being intuitive, interactive, with a potential fast flow solver that provides near real-time feedback to the clinician.

Skeletal Shape Correspondence Through Entropy.

We present a novel approach for improving the shape statistics of medical image objects by generating correspondence of skeletal points. Each object's interior is modeled by an s-rep, i.e., by a sampled, folded, two-sided skeletal sheet with spoke vectors proceeding from the skeletal sheet to the boundary. The skeleton is divided into three parts: the up side, the down side, and the fold curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along that skeleton in each training sample so as to tighten the probability distribution on those spokes' geometric properties while sampling the object interior regularly. As with the surface/boundary-based correspondence method of Cates et al., entropy is used to measure both the probability distribution tightness and the sampling regularity, here of the spokes' geometric properties. Evaluation on synthetic and real world lateral ventricle and hippocampus data sets demonstrate improvement in the performance of statistics using the resulting probability distributions. This improvement is greater than that achieved by an entropy-based correspondence method on the boundary points.