Three-dimensional Shape Analysis Research Articles

Three-Dimensional Morphometric Analysis of the Volar Cortical Shape of the Lunate Facet of the Distal Radius.

In cases of distal radius fractures, the fixation of the volar lunate facet fragment is crucial for preventing volar subluxation of the carpal bones. This study aims to clarify the sex differences in the volar morphology of the lunate facet of the distal radius and its relationship with the transverse diameter of the distal radius. Sixty-four CT scans of healthy wrists (30 males and 34 females) were evaluated. Three-dimensional (3D) images of the distal radius were reconstructed from the CT data. We defined reference point 1 as the starting point of the inclination toward the distal volar edge, reference point 2 as the volar edge of the joint on the bone axis, and reference point 3 as the volar edge of the distal radius lunate facet. From the 3D coordinates of reference points 1 to 3, the bone axis distance, volar-dorsal distance, radial-ulnar distance, 3D straight-line distance, and inclination angle were measured. The transverse diameter of the radius was measured, and its correlations with the parameters were evaluated. It was found that in males, compared to females, the transverse diameter of the radius is larger and the protrusion of the volar lunate facet is greater. This suggests that the inclination of the volar surface is steeper in males and that the volar locking plate may not fit properly with the volar cortical bone of the lunate facet, necessitating additional fixation.

Three-dimensional geometric morphometric shape analysis of chest wall kinematics in different breathing conditions.

Breathing motion is based on the differential activity of the thoracic, diaphragmatic and abdominal muscles. Muscle contributions differ between rest and exercise conditions and depend on posture and other factors. Traditionally, these changes are investigated on volumetric data using optoelectronic plethysmography (OEP). OEP offers insight into size variations of different chest wall (CW) compartments but does not provide three-dimensional visualization methods of CW breathing kinematics. Here we explore the use of three-dimensional geometric morphometrics to analyse size and shape changes caused by spontaneous breathing motion during quiet (QB), and recovery breathing (REC, immediately after heavy exercise) in two different postures (SIT, sitting on cycle ergometer; STA, standing position). Our findings show that size and shape differ significantly between inspiration and expiration and that differences are greater in REC than in QB. However, this is achieved by stronger expiration in SIT but by greater expiratory and inspiratory movements in STA. Shape analysis suggests that these differences may be attributed to constrained mobility of the shoulder girdle and a minor thoracic spine extension during inspiration owing to position on the ergometer. Breathing motion in STA seems biomechanically less constrained. Geometric morphometrics analyses can provide additional insights into data obtained by OEP.

Surface Erosion Equations for Degradation Analysis of Several Common Three-Dimensional Shapes of Plastic Materials

Surface Erosion Equations for Degradation Analysis of Several Common Three-Dimensional Shapes of Plastic Materials

Three-dimensional magnetic resonance imaging-based statistical shape analysis and machine learning-based prediction of patellofemoral instability.

This study performed three-dimensional (3D) magnetic resonance imaging (MRI)-based statistical shape analysis (SSA) by comparing patellofemoral instability (PFI) and normal femur models, and developed a machine learning (ML)-based prediction model. Twenty (19 patients) and 31 MRI scans (30 patients) of femurs with PFI and normal femurs, respectively, were used. Bone and cartilage segmentation of the distal femurs was performed and subsequently converted into 3D reconstructed models. The pointwise distance map showed anterior elevation of the trochlea, particularly at the central floor of the proximal trochlea, in the PFI models compared with the normal models. Principal component analysis examined shape variations in the PFI group, and several principal components exhibited shape variations in the trochlear floor and intercondylar width. Multivariate analysis showed that these shape components were significantly correlated with the PFI/non-PFI distinction after adjusting for age and sex. Our ML-based prediction model for PFI achieved a strong predictive performance with an accuracy of 0.909 ± 0.015, and an area under the curve of 0.939 ± 0.009 when using a support vector machine with a linear kernel. This study demonstrated that 3D MRI-based SSA can realistically visualize statistical results on surface models and may facilitate the understanding of complex shape features.

Modification of Woven Endo-Bridge After Intracranial Aneurysm Treatment: A Methodology for Three-Dimensional Analysis of Shape and Relative Position Changes.

During follow-up of patients treated with WEB devices, shape changes have been observed. The quantitative three-dimensional measurement of the WEB shape modification (WSM) would offer useful information to be studied in association with the anatomical results and try to better understand mechanisms implicated in this modification phenomenon. We present a methodology to quantify the morphology and position of the WEB device in relation to the vascular anatomy. Three-dimensional rotational angiography (3DRA) images of seven aneurysms patients treated with WEBs were used, which also accompanied by a post-treatment 3DRA image and a follow-up 3DRA image. The device was manually segmented, obtaining the 3D models after treatment and at the follow-up. Volume, surface area, height, maximum diameter and WSM ratio of both surfaces were calculated. Position changes were evaluated measuring WEB axis and relative position between post-treatment and follow-up. Changes in WEB volume and surface area were observed with a mean modification of and , respectively. The positional variables also showed differences, mean change of device axis direction was and mean change of distance was . Inter-observer and intra-observer variability analyses did not show differences (ANOVA ). This methodology allows quantifying the morphological and position changes suffered by the WEB device after treatment, offering new information to be studied in relation to the occurrence of WEB shape modification.

Automatic method for quantitatively analyzing the body condition of livestock from 3D shape

Body condition has always been an important indicator reflecting the health status of livestock, and new automated and contactless methods for assessing it have also been continuously proposed. In recent years, with the continuous expansion of research on quantitative analysis of three-dimensional shapes in the field of agriculture, amount of studies has shown that quantitative analysis of shapes can promote the development of smart agriculture. This article proposed a method for quantitatively analyzing the local three-dimensional shape of livestock to evaluate their body conditions. This is a universal method that can be applied to various species. It uses the method of point-to-point correspondence in the three-dimensional shape to finely calculate the difference between shapes, and then maps the difference value to the range of the body condition score. The article analyzed the shape of 198 dairy cows, 100 beef cattle, and 201 pigs using body condition scores as test parameters. The accuracy of body condition evaluation within the range of error of 0.5 for dairy cows, 1 for beef cattle, and 0.5 for pigs are 100%, 87.61%, and 92.09%, respectively. Compared to previous methods for assessing body condition, the method proposed in this paper is more accurate and versatile. The dataset used in this study, along with the code implementation have been made publicly available in https://gitee.com/kznd/lshape-analyser/tree/master/MATLAB.

Three-dimensional analysis of hydrogel-imbedded aortic valve interstitial cell shape and its relation to contractile behavior.

Cell-shape is a conglomerate of mechanical, chemical, and biological mechanisms that reflects the cell biophysical state. In a specific application, we consider aortic valve interstitial cells (AVICs), which maintain the structure and function of aortic heart valve leaflets. Actomyosin stress fibers help determine AVIC shape and facilitate processes such as adhesion, contraction, and mechanosensing. However, detailed 3D assessment of stress fiber architecture and function is currently impractical. Herein, we assessed AVIC shape and contractile behaviors using hydrogel-based 3D traction force microscopy to intuit the orientation and behavior of AVIC stress fibers. We utilized spherical harmonics (SPHARM) to quantify AVIC geometries through three days of incubation, which demonstrated a shift from a spherical shape to forming substantial protrusions. Furthermore, we assessed changes in post-three day AVIC shape and contractile function within two testing regimes: (1) normal contractile level to relaxation (cytochalasin D), and (2) normal contractile level to hyper-contraction (endothelin-1). In both scenarios, AVICs underwent isovolumic shape changes and produced complex displacement fields within the hydrogel. AVICs were more elongated when relaxed and more spherical in hyper-contraction. Locally, AVIC protrusions contracted along their long axis and expanded in their circumferential direction, indicating predominately axially aligned stress fibers. Furthermore, the magnitude of protrusion displacements was correlated with protrusion length and approached a consistent displacement plateau at a similar critical length across all AVICs. This implied that stress fiber behavior is conserved, despite great variations in AVIC shapes. We anticipate our findings will bolster future investigations into AVIC stress fiber architecture and function. STATEMENT OF SIGNIFICANCE: Within the aortic valve there exists a population of aortic valve interstitial cells, which orchestrate the turnover, secretion, and remodeling of its extracellular matrix, maintaining tissue integrity and ultimately sustaining the proper mechanical function. Alterations in these processes are thought to underlie diseases of the aortic valve, which affect hundreds of thousands domestically and world-wide. Yet, to date, there are no non-surgical treatments for aortic heart valve disease, in part due to our limited understanding of the underlying disease processes. In the present study, we built upon our previous study to include a full 3D analysis of aortic valve interstitial cell shapes at differing contractile levels. The resulting detailed shape and deformation analysis provided insight into the underlying stress-fiber structures and mechanical behaviors.

Phenotypic variability in the shield morphology of wild- vs. lab-reared eumalacostracan larvae

Morphological identification of planktic crustacean larvae is required in many scientific contexts, such as ecology or taxonomy. Due to a still low availability of genetic sequences for many ingroups of Eumalacostraca, this task is still more feasible by morphological methods. Our understanding of eumalacostracan larval morphology is challenged by phenotypic variability. We investigated four eumalacostracan ingroups: Galatheidae, Hippoidea, Raninidae and Stomatopoda. Representatives of all four groups develop through spine-bearing planktic larval stages. Incorporating dorsal and lateral shield outlines into three-dimensional shape analysis of the shields, we compare specimens from the wild with laboratory-reared specimens. Using graphical and statistical analysis methods, we find that at least the lateral morphology of the shields of Hippoidea and Raninidae seems to be too strongly dependent on phylogeny to show phenotypic variability with our current sample size, but Hippoidea do show phenotypic variability in their dorsal shield morphology. In Galatheidae and Stomatopoda, a clear difference in shield morphology can be found between wild-caught and laboratory-reared specimens. This difference likely represents phenotypic variability. The exact environmental signals causing this phenotypic variability are still unknown, but some candidates are discussed.

Quantifying the Severity of Metopic Craniosynostosis Using Unsupervised Machine Learning.

Quantifying the severity of head shape deformity and establishing a threshold for operative intervention remains challenging in patients with metopic craniosynostosis (MCS). This study combines three-dimensional skull shape analysis with an unsupervised machine-learning algorithm to generate a quantitative shape severity score (cranial morphology deviation) and provide an operative threshold score. Head computed tomography scans from subjects with MCS and normal controls (5 to 15 months of age) were used for objective three-dimensional shape analysis using ShapeWorks software and in a survey for craniofacial surgeons to rate head-shape deformity and report whether they would offer surgical correction based on head shape alone. An unsupervised machine-learning algorithm was developed to quantify the degree of shape abnormality of MCS skulls compared to controls. One hundred twenty-four computed tomography scans were used to develop the model; 50 (24% MCS, 76% controls) were rated by 36 craniofacial surgeons, with an average of 20.8 ratings per skull. The interrater reliability was high (intraclass correlation coefficient, 0.988). The algorithm performed accurately and correlates closely with the surgeons assigned severity ratings (Spearman correlation coefficient, r = 0.817). The median cranial morphology deviation for affected skulls was 155.0 (interquartile range, 136.4 to 194.6; maximum, 231.3). Skulls with ratings of 150.2 or higher were very likely to be offered surgery by the experts in this study. This study describes a novel metric to quantify the head shape deformity associated with MCS and contextualizes the results using clinical assessments of head shapes by craniofacial experts. This metric may be useful in supporting clinical decision making around operative intervention and in describing outcomes and comparing patient population across centers.

Learning the Hidden Signature of Fetal Arch Anatomy: a Three-Dimensional Shape Analysis in Suspected Coarctation of the Aorta

Neonatal coarctation of the aorta (CoA) is a common congenital heart defect. Its antenatal diagnosis remains challenging, and its pathophysiology is poorly understood. We present a novel statistical shape modeling (SSM) pipeline to study the role and predictive value of arch shape in CoA in utero. Cardiac magnetic resonance imaging (CMR) data of 112 fetuses with suspected CoA was acquired and motion-corrected to three-dimensional volumes. Centerlines from fetal arches were extracted and used to build a statistical shape model capturing relevant anatomical variations. A linear discriminant analysis was used to find the optimal axis between CoA and false positive cases. The CoA shape risk score classified cases with an area under the curve of 0.907. We demonstrate the feasibility of applying a SSM pipeline to three-dimensional fetal CMR data while providing novel insights into the anatomical determinants of CoA and the relevance of in utero arch anatomy for antenatal diagnosis of CoA.Graphical abstract

Laminin-111 mutant studies reveal a hierarchy within laminin-111 genes in their requirement for basal epithelial tissue folding

The process of morphogenesis carefully crafts cells into complex organ structures which allows them to perform their unique functions. During brain development, the neuroepithelial tissue must go through apical and basal folding which is mediated through the instruction of both intrinsic and extrinsic factors. While much is known about apical folding, the mechanisms that regulate basal folding are less understood. Using the highly conserved zebrafish midbrain-hindbrain boundary (MHB) as an epithelial tissue model, we have identified the basement membrane protein laminin-111 as a key extrinsic factor in basal tissue folding. Laminin-111 is a highly conserved, heterotrimeric protein that lines the basal surface of the neuroepithelium. Laminin-111 is comprised of one alpha, one beta, and one gamma chain encoded by the genes lama1, lamb1, and lamc1, respectively. Human mutations in individual laminin-111 genes result in disparate disease phenotypes; therefore, we hypothesized that each laminin gene would have a distinctive role in tissue morphogenesis. Using zebrafish mutants for laminin-111 genes, we found that each laminin chain has a unique impact on basal folding. We found that lamc1 is the most critical gene for MHB morphogenesis, followed by lama1, and finally lamb1a. This hierarchy was discovered via three-dimensional single cell shape analysis, localization of myosin regulatory light chain (MRLC), and with analysis of MHB tissue folding later in development. These findings are essential for development of novel techniques in tissue engineering and to elucidate differences in human diseases due to specific chain mutations.

Icing on Full-Scale Swept Wings in Flight and Icing Wind Tunnel

Inflight ice accretion on aircraft wings has been critically important for development and certification of transport category aircraft. With recent efforts toward certification by analysis, it is becoming increasingly important to characterize ice accretions in icing wind tunnels, the primary source of validation data for higher-fidelity three-dimensional ice shape analysis codes to be used in aircraft certification, in comparison with those in natural icing environments. In this study, a series of natural icing flight tests and icing wind tunnel tests were conducted on a transport category aircraft. The results were compared at similar test conditions on protected and unprotected surfaces of swept wings and empennage. For unprotected surfaces, both tests resulted in scallop ice, with natural icing flight test resulting in significantly smaller ice accretions. For protected surfaces, runback ice was formed on the lower wing surface in both tests, with natural icing flight test resulting in significantly less and sparser runback ice. Differences in scallop ice structures, limitations of icing wind tunnels, and scaling methods are considered the potential contributing factors to the differences. The results indicate a need for further studies on case-to-case comparison of ice accretions in the two test methods focusing on full-scale aircraft conditions.

Feasibility of a longitudinal statistical atlas model to study aortic growth in congenital heart disease

Studying anatomical shape progression over time is of utmost importance to refine our understanding of clinically relevant processes. These include vascular remodeling, such as aortic dilation, which is particularly important in some congenital heart defects (CHD). A novel methodological framework for three-dimensional shape analysis has been applied for the first time in a CHD scenario, i.e., bicuspid aortic valve (BAV) disease, the most common CHD. Three-dimensional aortic shapes (n = 94) reconstructed from cardiovascular magnetic resonance imaging (MRI) data as surface meshes represented the input for a longitudinal atlas model, using multiple scans over time (n = 2–4 per patient). This model relies on diffeomorphism transformations in the absence of point-to-point correspondence, and on the right combination of initialization, estimation and registration parameters. We computed the shape trajectory of an average disease progression in our cohort, as well as time-dependent parameters, geometric variations and the average shape of the population. Results cover a spatiotemporal spectrum of visual and numerical information that can be further used to run clinical associations. This proof-of-concept study demonstrates the feasibility of applying advanced statistical shape models to track disease progression and stratify patients with CHD.

Ovariectomized rat model and shape variation in the bony labyrinth.

Postmenopausal osteoporosis is a serious concern in aging individuals, but has not been explored for its potential to alter the shape of the inner ear by way of increased remodeling in the otic capsule. The otic capsule, or bony labyrinth, is thought to experience uniquely limited remodeling after development due to high levels of osteoprotegerin. On this basis, despite the widespread remodeling that accompanies osteoporosis, we hypothesize that both the shape and volume of the semicircular canals will resist such changes. To test this hypothesis, we conducted three-dimensional geometric morphometric shape analysis on microcomputed tomographic data collected on the semicircular canals of an ovariectomized (OVX) rat model. A Procrustes ANOVA found no statistically significant differences in shape between surgery and sham groups, and morphological disparity testing likewise found no differences in shape variation. Univariate testing found no differences in semicircular volume between OVX and control groups. The range of variation in the OVX group, however, is greater than in the sham group but this difference does not reach statistical significance, perhaps because of a combination of small effect size and low sample size. This finding suggests that labyrinthine shape remains a tool for assessing phylogeny and function in the fossil record, but that it is possible that osteoporosis may be contributing to intraspecific shape variation in the bony labyrinth. This effect warrants further exploration at a microstructural level with continued focus on variables related to remodeling.

A new framework for analysis of three-dimensional shape and architecture of human skeletal muscles from in vivo imaging data.

A new framework is presented for comprehensive analysis of the three-dimensional shape and architecture of human skeletal muscles from magnetic resonance and diffusion tensor imaging data. The framework comprises three key features: 1) identification of points on the surface of and inside a muscle that have a correspondence to points on and inside another muscle, 2) reconstruction of average muscle shape and average muscle fiber orientations, and 3) utilization of data on between-muscle variation to visualize and make statistical inferences about changes or differences in muscle shape and architecture. The general use of the framework is demonstrated by its application to three case studies. Analysis of data obtained before and after 8 wk of strength training revealed there was little regional variation in hypertrophy of the vastus medialis and vastus lateralis and no systematic change in pennation angle. Analysis of passive muscle lengthening revealed heterogeneous changes in shape of the medial gastrocnemius and confirmed the ability of the methods to detect subtle changes in muscle fiber orientation. Analysis of the medial gastrocnemius of children with unilateral cerebral palsy showed that muscles in the more-affected limb were shorter, thinner, and less wide than muscles in the less-affected limb and had slightly more pennate muscle fibers in the central and proximal part of the muscle. Among other applications, the framework can be used to explore the mechanics of muscle contraction, investigate adaptations of muscle architecture, build anatomically realistic computational models of skeletal muscles, and compare muscle shape and architecture between species.NEW & NOTEWORTHY Muscle architecture is conventionally measured using simple scalar metrics such as muscle volume and average fascicle lengths. Here, a new framework is proposed for analysis of complex changes in three-dimensional architecture of whole human muscles from magnetic resonance and diffusion tensor imaging data. The general use of the framework is demonstrated through visualization, quantification, and statistical analysis of the effect of strength training, passive lengthening and cerebral palsy on three-dimensional muscle shape and architecture.

Evaluation of Scapula and Humerus Bone Change after Repair of Small- to Medium-Sized Rotator Cuff Tears: Comparison between Healing and Retear Groups Using Three-Dimensional Computed Tomography.

Rotator cuff tendon retears after rotator cuff repair cause glenohumeral joint instability, which results in changes in the glenoid and humerus head. However, limited data are available on the bone change after repair of small- to medium-sized rotator cuff tears. The aim of this study was to evaluate the difference of glenoid and humerus bone changes between healing and retear groups after repair of small- to medium-sized rotator cuff tears. Among patients who had arthroscopic repair due to small- to medium-sized rotator cuff tears from January 2009 to January 2017, 49 patients who underwent both preoperative and postoperative (at least 3 years after surgery) shoulder computed tomography were enrolled. Using three-dimensional reconstruction program (3D Slicer) and shape analysis program (SlicerSALT), we compared the occurrence and degree of glenoid bone change, glenoid inclination change, retroversion change, and glenoid center, as well as the degree of humerus head change, between the healing and retear groups. The occurrence of glenoid bone change was significantly more common in the retear group than in the healing group (p = 0.026). The degree of bone change in the 11-1 o'clock axial plane and 10-8 o'clock, 11-7 o'clock, and 12-6 o'clock coronal plane and the degree of glenoid inclination change were significantly larger in the retear group than the healing group (p = 0.026, p = 0.026, p = 0.026, p = 0.026, and p = 0.014, respectively), but the average value of glenoid bone change in the retear group was within the range of 0.14 to 1.01 mm for each plane. The mean humeral head change was 5.69 ± 3.67 mm increase in the retear group and 1.27 ± 2.02 mm increase in the healing group. Compared with the healing group, the retear group showed statistically significantly increased humeral head change (p < 0.001). There was difference in glenoid and humerus bone change between the healing and retear groups at midterm follow-up after repair of small- to medium-sized tears. However, considering the measurement bias, the difference between the two groups was within the measurement error range.

Three-dimensional shape analysis of flexible pectoral fins in turn swimming motions of goby

Three-dimensional shape analysis of flexible pectoral fins in turn swimming motions of goby

Mapping Complex Brain Torque Components and Their Genetic Architecture and Phenomic Associations in 24,112 Individuals

BackgroundThe functional significance and mechanisms determining the development and individual variability of structural brain asymmetry remain unclear. Here, we systematically analyzed all relevant components of the most prominent structural asymmetry, brain torque (BT), and their relationships with potential genetic and nongenetic modifiers in a sample comprising 24,112 individuals from six cohorts. MethodsBT features, including petalia, bending, dorsoventral shift, brain tissue distribution asymmetries, and cortical surface positional asymmetries, were directly modeled using a set of automatic three-dimensional brain shape analysis approaches. Age-, sex-, and handedness-related effects on BT were assessed. The genetic architecture and phenomic associations of BT were investigated using genome- and phenome-wide association scans. ResultsOur results confirmed the population-level predominance of the typical counterclockwise torque and suggested a first attenuating, then enlarging dynamic across the life span (3–81 years) primarily for frontal, occipital, and perisylvian BT features. Sex/handedness, BT, and cognitive function of verbal-numerical reasoning were found to be interrelated statistically. We observed differential heritability of up to 56% for BT, especially in temporal language areas. Individual variations of BT were also associated with various phenotypic variables of neuroanatomy, cognition, lifestyle, sociodemographics, anthropometry, physical health, and adult and child mental health. Our genomic analyses identified a number of genetic associations at lenient significance levels, which need to be further validated using larger samples in the future. ConclusionsThis study provides a comprehensive description of BT and insights into biological and other factors that may contribute to the development and individual variations of BT.

Calcaneal shape variation in humans, nonhuman primates, and early hominins

The foot has played a prominent role in evaluating early hominin locomotion. The calcaneus, in particular, plays an important role in weight-bearing. Although the calcanei of early hominins have been previously scrutinized, a three-dimensional analysis of the entire calcaneal shape has not been conducted. Here, we investigate the relationship between external calcaneal shape and locomotion in modern Homo sapiens (n = 130), Gorilla (n = 86), Pan (n = 112), Pongo (n = 31), Papio (n = 28), and hylobatids (Hylobates, Symphalangus; n = 32). We use these results to place the calcanei attributed to Australopithecus sediba, A. africanus, A. afarensis, H. naledi, and Homo habilis/Paranthropus boisei into a locomotor context. Calcanei were scanned using either surface scanning or micro-CT and their external shape analyzed using a three-dimensional geometric morphometric sliding semilandmark analysis. Blomberg's K statistic was used to estimate phylogenetic signal in the shape data. Shape variation was summarized using a principal components analysis. Procrustes distances between all taxa as well as distances between each fossil and the average of each taxon were calculated. Blomberg's K statistic was small (K = 0.1651), indicating weak phylogenetic effects, suggesting variation is driven by factors other than phylogeny (e.g., locomotion or body size). Modern humans have a large calcaneus relative to body size and display a uniquely convex cuboid facet, facilitating a rigid midfoot for bipedalism. More arboreal great apes display relatively deeper cuboid facet pivot regions for increased midfoot mobility. Australopithecus afarensis demonstrates the most human-like calcaneus, consistent with obligate bipedalism. Homo naledi is primarily modern human-like, but with some intermediate traits, suggesting a different form of bipedalism than modern humans. Australopithecus africanus, A. sediba, and H. habilis/P. boisei calcanei all possess unique combinations of human and nonhuman ape-like morphologies, suggesting a combination of bipedal and arboreal behaviors.

Three-dimensional shape analysis of peripapillary retinal pigment epithelium-basement membrane layer based on OCT radial images

Abstract The peripapillary retinal pigment epithelium-basement membrane (ppRPE/BM) layer angle was recently proposed as a potential index for estimating intracranial pressure noninvasively. However, the ppRPE/BM layer angle, measured from the optical coherence tomography (OCT) scans, varied across the radial directions of the optic disc. This made the ppRPE/BM layer angle difficult to be utilized in its full potential. In this study, we developed a mathematical model to quantify the ppRPE/BM layer angles across radial scans in relation to the ppRPE/BM 3D morphology in terms of its 3D angle and scanning tilt angles. Results showed that the variations of the ppRPE/BM layer angle across radial scans were well explained by its 3D angle and scanning tilt angles. The ppRPE/BM layer 3D angle was reversely fitted from the measured ppRPE/BM layer angles across radial directions with application to six eyes from four patients, who underwent medically necessary lumbar puncture. The fitted curve from our mathematical model matched well with the experimental measurements (R 2 &gt; 0.9 in most cases). This further validated our mathematical model. The proposed model in this study has elucidated the variations of ppRPE/BM layer angle across 2D radial scans from the perspective of the ppRPE/BM layer 3D morphology. It is expected that the ppRPE/BM layer 3D angle developed in this study could be further exploited as a new biomarker for the optic disc.