Shape analysis of the human brain: a brief survey

Assessing craniofacial growth and form without landmarks: A new automatic approach based on spectral methods

We present a novel method for the morphometric analysis of series of 3D shapes, and demonstrate its relevance for the detection and quantification of two craniofacial anomalies: trigonocephaly and metopic ridges, using CT-scans of young children. Our approach is fully automatic, and does not rely on manual landmark placement and annotations. Our approach furthermore allows to differentiate shape classes, enabling successful differential diagnosis between trigonocephaly and metopic ridges, two related conditions characterized by triangular foreheads. These results were obtained using recent developments in automatic nonrigid 3D shape correspondence methods and specifically spectral approaches based on the functional map framework. Our method can capture local changes in geometric structure, in contrast to methods based, for instance, on global shape descriptors. As such, our approach allows to perform automatic shape classification and provides visual feedback on shape regions associated with different classes of deformations. The flexibility and generality of our approach paves the way for the application of spectral methods in quantitative medicine.

Using Optimal Transport to Improve Spherical Harmonic Quantification of Complex Biological Shapes

The knowledge of the anatomical shape of both gross and microscopic structures is the key to understanding the effects of disease processes on cellular structure. Geometric morphometric methods, such as Procrustes superimposition, and Spherical Harmonics (SPHARM), have been used to capture the biological shape variation and group differences in morphology. Previous SPHARM-MAT techniques use the CALD algorithm to parameterize the mesh surface. It starts from initial mapping and performs local and global smoothing methods alternately to control the area and length distortions simultaneously. However, this parameterization may not be sufficient in complex morphological cases. To bridge this gap, we propose SPHARM-OT, an enhanced SPHARM surface modeling method using optimal transport (OT) for spherical parameterization. First, the genus 0 3D objects are conformally mapped onto a sphere. Then the optimal transport theory via spherical power diagram is introduced to minimize the area distortion. This new algorithm can effectively reduce the area distortion and lead to a better reconstruction result. We demonstrate the effectiveness of the method by applying it to the human sphenoidal paranasal sinuses.

Statistical morphological analysis reveals characteristic paraspinal muscle asymmetry in unilateral lumbar disc herniation

Growing evidence suggests an association of lumbar paraspinal muscle morphology with low back pain (LBP) and lumbar pathologies. Unilateral spinal disorders provide unique models to study this association, with implications for diagnosis, prognosis, and management. Statistical shape analysis is a technique that can identify signature shape variations related to phenotypes but has never been employed in studying paraspinal muscle morphology. We present the first investigation using this technique to reveal disease-related paraspinal muscle asymmetry, using MRIs of patients with a single posterolateral disc herniation at the L5-S1 spinal level and unilateral leg pain. Statistical shape analysis was conducted to reveal disease- and phenotype-related morphological variations in the multifidus and erector spinae muscles at the level of herniation and the one below. With the analysis, shape variations associated with disc herniation were identified in the multifidus on the painful side at the level below the pathology while no pathology-related asymmetry in cross-sectional area (CSA) and fatty infiltration was found in either muscle. The results demonstrate higher sensitivity and spatial specificity for the technique than typical CSA and fatty infiltration measures. Statistical shape analysis holds promise in studying paraspinal muscle morphology to improve our understanding of LBP and various lumbar pathologies.

Ventricle shape analysis using modified WKS for atrophy detection

Brain ventricle is one of the biomarkers for detecting neurological disorders. Studying the shape of the ventricles will aid in the diagnosis process of atrophy and other CSF-related neurological disorders, as ventricles are filled with CSF. This paper introduces a spectral analysis algorithm based on wave kernel signature. This shape signature was used for studying the shape of segmented ventricles from the brain images. Based on the shape signature, the study groups were classified as normal subjects and atrophy subjects. The proposed algorithm is simple, effective, automated, and less time consuming. The proposed method performed better than the other methods heat kernel signature, scale invariant heat kernel signature, wave kernel signature, and spectral graph wavelet signature, which were used for validation purpose, by producing 94-95% classification accuracy by classifying normal and atrophy subjects correctly for CT, MR, and OASIS datasets.

Nonlinear interaction between APOE ε4 allele load and age in the hippocampal surface of cognitively intact individuals

The ε4 allele of the gene Apolipoprotein E is the major genetic risk factor for Alzheimer's Disease. APOE ε4 has been associated with changes in brain structure in cognitively impaired and unimpaired subjects, including atrophy of the hippocampus, which is one of the brain structures that is early affected by AD. In this work we analyzed the impact of APOE ε4 gene dose and its association with age, on hippocampal shape assessed with multivariate surface analysis, in a ε4-enriched cohort of n = 479 cognitively healthy individuals. Furthermore, we sought to replicate our findings on an independent dataset of n = 969 individuals covering the entire AD spectrum. We segmented the hippocampus of the subjects with a multi-atlas-based approach, obtaining high-dimensional meshes that can be analyzed in a multivariate way. We analyzed the effects of different factors including APOE, sex, and age (in both cohorts) as well as clinical diagnosis on the local 3D hippocampal surface changes. We found specific regions on the hippocampal surface where the effect is modulated by significant APOE ε4 linear and quadratic interactions with age. We compared between APOE and diagnosis effects from both cohorts, finding similarities between APOE ε4 and AD effects on specific regions, and suggesting that age may modulate the effect of APOE ε4 and AD in a similar way.

Pair-wise vs group-wise registration in statistical shape model construction: representation of physiological and pathological variability of bony surface morphology

Statistical shape models (SSM) of bony surfaces have been widely proposed in orthopedics, especially for anatomical bone modeling, joint kinematic analysis, staging of morphological abnormality, and pre- and intra-operative shape reconstruction. In the SSM computation, reference shape selection, shape registration and point correspondence computation are fundamental aspects determining the quality (generality, specificity and compactness) of the SSM. Such procedures can be made critical by the presence of large morphological dissimilarities within the surfaces, not only because of anthropometrical variability but also mainly due to pathological abnormalities. In this work, we proposed a SW pipeline for SSM construction based on pair-wise (PW) shape registration, which requires the a-priori selection of the reference shape, and on a custom iterative point correspondence algorithm. We addressed large morphological deformations in five different bony surface sets, namely proximal femur, distal femur, patella, proximal fibula and proximal tibia, extracted from a retrospective patient dataset. The technique was compared to a method from the literature, based on group-wise (GW) shape registration. As a main finding, the proposed technique provided generalization and specificity median errors, for all the five bony regions, lower than 2 mm. The comparative analysis provided basically similar results. Particularly, for the distal femur that was the shape affected by the largest pathological deformations, the differences in generalization, specificity and compactness were lower than 0.5 mm, 0.5 mm, and 1%, respectively. We can argue the proposed pipeline, along with the robust correspondence algorithm, is able to compute high-quality SSM of bony shapes, even affected by large morphological variability.

Quantitative MRI Brain Studies in Mild Cognitive Impairment and Alzheimer's Disease: A Methodological Review

Classifying and predicting Alzheimer's disease (AD) in individuals with memory disorders through clinical and psychometric assessment is challenging, especially in mild cognitive impairment (MCI) subjects. Quantitative structural magnetic resonance imaging acquisition methods in combination with computer-aided diagnosis are currently being used for the assessment of AD. These acquisitions methods include voxel-based morphometry, volumetric measurements in specific regions of interest (ROIs), cortical thickness measurements, shape analysis, and texture analysis. This review evaluates the aforementioned methods in the classification of cases into one of the following three groups: normal controls, MCI, and AD subjects. Furthermore, the performance of the methods is assessed on the prediction of conversion from MCI to AD. In parallel, it is also assessed which ROIs are preferred in both classification and prognosis through the different states of the disease. Structural changes in the early stages of the disease are more pronounced in the medial temporal lobe, especially in the entorhinal cortex, whereas with disease progression, both entorhinal cortex and hippocampus offer similar discriminative power. However, for the conversion from MCI subjects to AD, entorhinal cortex provides better predictive accuracies rather than other structures, such as the hippocampus.

Test-retest reliability of brain morphology estimates

Metrics of brain morphology are increasingly being used to examine inter-individual differences, making it important to evaluate the reliability of these structural measures. Here we used two open-access datasets to assess the intersession reliability of three cortical measures (thickness, gyrification, and fractal dimensionality) and two subcortical measures (volume and fractal dimensionality). Reliability was generally good, particularly with the gyrification and fractal dimensionality measures. One dataset used a sequence previously optimized for brain morphology analyses and had particularly high reliability. Examining the reliability of morphological measures is critical before the measures can be validly used to investigate inter-individual differences.

Shape analysis based on depth-ordering

In this paper we propose a new method for shape analysis based on the ordering of shapes using band-depth. We use this band-depth to non-parametrically define a global depth for a shape with respect to a reference population, typically consisting of normal control subjects. This allows us to globally quantify differences with respect to "normality". Using the depth-ordering of shapes also allows the detection of localized shape differences by using α-central values of shapes. We propose permutation tests to statistically assess global and local shape differences. We further determine the directionality of shape differences (local inflation versus deflation). The method is evaluated on a synthetically generated striatum dataset, and applied to detect shape differences in the hippocampus between subjects with first-episode schizophrenia and normal controls.