<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>3D Imaging | Mahyar's world 🌏</title><link>https://mahyar-osn.github.io/tag/3d-imaging/</link><atom:link href="https://mahyar-osn.github.io/tag/3d-imaging/index.xml" rel="self" type="application/rss+xml"/><description>3D Imaging</description><generator>Wowchemy (https://wowchemy.com)</generator><language>en-us</language><lastBuildDate>Fri, 10 Nov 2023 00:00:00 +0000</lastBuildDate><image><url>https://mahyar-osn.github.io/media/icon_hu35e4e9c9135f02752aab27d124db531b_75212_512x512_fill_lanczos_center_3.png</url><title>3D Imaging</title><link>https://mahyar-osn.github.io/tag/3d-imaging/</link></image><item><title>3D Reconstruction of Human Olfactory Projection</title><link>https://mahyar-osn.github.io/projects/olfactory/</link><pubDate>Fri, 10 Nov 2023 00:00:00 +0000</pubDate><guid>https://mahyar-osn.github.io/projects/olfactory/</guid><description>&lt;p>&lt;strong>Authors&lt;/strong>: Victoria F Low, Chinchien Lin, Shan Su, Mahyar Osanlouy, Mona Khan, Soroush Safaei, Gonzalo Maso Talou, Maurice A Curtis, Peter Mombaerts&lt;br>
&lt;strong>Publication&lt;/strong>: &lt;em>Communications Biology&lt;/em> (November 2024)&lt;br>
&lt;strong>Code&lt;/strong>: &lt;a href="https://zenodo.org/records/7865523" target="_blank" rel="noopener">Zenodo Repository&lt;/a>&lt;br>
&lt;strong>Interactive 3D Model&lt;/strong>: &lt;a href="https://mip.datavisualiser.cloud.edu.au/neuroglancer/A1147/it13" target="_blank" rel="noopener">Neuroglancer Platform&lt;/a>&lt;/p>
&lt;hr>
&lt;h2 id="overview">Overview&lt;/h2>
&lt;p>This study presents a computational pipeline to reconstruct the 3D microanatomy of the human olfactory system, from the
nasal cavity to the olfactory bulb—using fluorescence histology, deep learning, and high-performance computing (HPC).
The workflow addresses challenges in processing terabyte-scale datasets and provides new insights into olfactory sensory
neuron (OSN) distribution and axon trajectories.&lt;/p>
&lt;hr>
&lt;h2 id="key-computational-contributions">Key Computational Contributions&lt;/h2>
&lt;ol>
&lt;li>&lt;strong>First end-to-end pipeline&lt;/strong> for large-scale 3D reconstruction of human olfactory tissues (~7.45 cm³ specimen, 1234
sections).&lt;/li>
&lt;li>&lt;strong>CNN-based segmentation&lt;/strong> achieving Dice scores &amp;gt;0.85 for critical structures (OSNs, glomeruli, vasculature).&lt;/li>
&lt;li>&lt;strong>HPC-optimized registration&lt;/strong> reducing banana-effect artifacts via multi-resolution deformable alignment.&lt;/li>
&lt;li>&lt;strong>Public 3D dataset&lt;/strong> enabling interactive exploration of olfactory projection via Neuroglancer.&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h2 id="methodology">Methodology&lt;/h2>
&lt;h3 id="computational-pipeline">Computational Pipeline&lt;/h3>
&lt;img src="2025-04-13_22-28.png" alt="Receptive fields" width="400">
&lt;p>&lt;em>From fluorescence histology to 3D visualization – click to expand&lt;/em>&lt;/p>
&lt;ol>
&lt;li>
&lt;p>&lt;strong>Fluorescence Histology&lt;/strong>&lt;/p>
&lt;ul>
&lt;li>Quadruple staining: Hoechst (nuclei), UEA1 (OSNs), OMP (mature OSNs), VGLUT2 (axon terminals).&lt;/li>
&lt;li>Whole-slide scanning: 1.097 µm/pixel resolution, ~2.9 TB raw data.&lt;/li>
&lt;/ul>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>CNN Segmentation&lt;/strong>&lt;/p>
&lt;ul>
&lt;li>Architecture: Modified 2D U-Net with 4 input channels (Hoechst + 3 markers).&lt;/li>
&lt;li>Training: Bootstrap approach with iterative ground truth expansion (20-45 sections/structure).&lt;/li>
&lt;li>Key layers:
&lt;pre tabindex="0">&lt;code># Simplified U-Net structure
encoder = [Conv2D(8→16→32), MaxPooling2D]
bottleneck = Conv2D(64) + Upsampling2D
decoder = [Conv2D(32→16→8), Concatenate(skip connections)]
&lt;/code>&lt;/pre>&lt;/li>
&lt;/ul>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>HPC Registration&lt;/strong>&lt;/p>
&lt;ul>
&lt;li>&lt;strong>Intra-block&lt;/strong>: Parallel registration of 247 blocks (5 sections each) using SimpleElastix.&lt;/li>
&lt;li>&lt;strong>Inter-block&lt;/strong>: Banana-effect correction via affine + B-spline transformations between blocks.&lt;/li>
&lt;li>Metrics: Mutual information for intensity alignment, DSC for structural consistency.&lt;/li>
&lt;/ul>
&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h2 id="results">Results&lt;/h2>
&lt;h3 id="segmentation-performance">Segmentation Performance&lt;/h3>
&lt;table>
&lt;thead>
&lt;tr>
&lt;th>Structure&lt;/th>
&lt;th>Dice Score&lt;/th>
&lt;th>Binary Cross-Entropy&lt;/th>
&lt;/tr>
&lt;/thead>
&lt;tbody>
&lt;tr>
&lt;td>Vasculature&lt;/td>
&lt;td>0.808&lt;/td>
&lt;td>0.0148&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>OSNs&lt;/td>
&lt;td>0.760&lt;/td>
&lt;td>0.0173&lt;/td>
&lt;/tr>
&lt;tr>
&lt;td>Glomeruli&lt;/td>
&lt;td>0.779&lt;/td>
&lt;td>0.0017&lt;/td>
&lt;/tr>
&lt;/tbody>
&lt;/table>
&lt;p>&lt;em>OSN segmentation achieved single-cell resolution in sparse regions but grouped cells in dense zones.&lt;/em>&lt;/p>
&lt;h3 id="registration-efficiency">Registration Efficiency&lt;/h3>
&lt;ul>
&lt;li>1082 CPU hours on 96 Intel Xeon Gold 6136 cores&lt;/li>
&lt;li>16% error reduction vs. sequential registration&lt;/li>
&lt;li>Tolerance: ±80 µm axial drift corrected&lt;/li>
&lt;/ul>
&lt;h3 id="key-findings">Key Findings&lt;/h3>
&lt;ol>
&lt;li>&lt;strong>OSN Count&lt;/strong>: ~2.7 million OSNs calculated via morphometric extrapolation (90% CI: 2.4–2.9M).&lt;/li>
&lt;li>&lt;strong>Fila Olfactoria&lt;/strong>: 34 foramina identified in cribriform plate (17/side).&lt;/li>
&lt;li>&lt;strong>Non-uniform Distribution&lt;/strong>: Olfactory epithelium showed serrated borders and posterior-anterior density gradient.&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h2 id="implications">Implications&lt;/h2>
&lt;h3 id="technical-advancements">Technical Advancements&lt;/h3>
&lt;ul>
&lt;li>&lt;strong>Scalable ML&lt;/strong>: Method enables processing of whole-brain datasets (~100x mouse brain volume).&lt;/li>
&lt;li>&lt;strong>Clinical Potential&lt;/strong>: Pipeline adaptable for Parkinson’s/Alzheimer’s studies via α-synuclein/tau staining.&lt;/li>
&lt;li>&lt;strong>Open Science&lt;/strong>: First public 3D olfactory dataset with ~5.8 GB/channel resolution.&lt;/li>
&lt;/ul>
&lt;h3 id="biological-insights">Biological Insights&lt;/h3>
&lt;ul>
&lt;li>Challenges mouse-to-human extrapolation: ~10x fewer OSNs/glomerulus vs. mice.&lt;/li>
&lt;li>Provides baseline for studying SARS-CoV-2 olfactory dysfunction.&lt;/li>
&lt;/ul>
&lt;hr>
&lt;h2 id="computational-tools-used">Computational Tools Used&lt;/h2>
&lt;ul>
&lt;li>&lt;strong>Segmentation&lt;/strong>: TensorFlow U-Net, Fiji for ground truth&lt;/li>
&lt;li>&lt;strong>Registration&lt;/strong>: SimpleElastix, ITK&lt;/li>
&lt;li>&lt;strong>Visualization&lt;/strong>: ParaView, Neuroglancer&lt;/li>
&lt;li>&lt;strong>HPC&lt;/strong>: New Zealand eScience Infrastructure (NeSI)&lt;/li>
&lt;/ul>
&lt;p>
&lt;figure >
&lt;div class="d-flex justify-content-center">
&lt;div class="w-100" >&lt;img alt="Neuroglancer screenshot placeholder" srcset="
/projects/olfactory/2025-04-13_22-30_hu0a3d9e68d0bcba58dbfed67f020b6e7c_1016129_378c0bcc687f8925b56e8df10b0a25fa.webp 400w,
/projects/olfactory/2025-04-13_22-30_hu0a3d9e68d0bcba58dbfed67f020b6e7c_1016129_c29f28f27c7b3ae1fc51e30bdf455294.webp 760w,
/projects/olfactory/2025-04-13_22-30_hu0a3d9e68d0bcba58dbfed67f020b6e7c_1016129_1200x1200_fit_q75_h2_lanczos_3.webp 1200w"
src="https://mahyar-osn.github.io/projects/olfactory/2025-04-13_22-30_hu0a3d9e68d0bcba58dbfed67f020b6e7c_1016129_378c0bcc687f8925b56e8df10b0a25fa.webp"
width="760"
height="564"
loading="lazy" data-zoomable />&lt;/div>
&lt;/div>&lt;/figure>
&lt;em>Interactive 3D exploration&lt;/em>&lt;/p>
&lt;hr></description></item><item><title>Spatiotemporal patterns in the embryonic heart</title><link>https://mahyar-osn.github.io/projects/embryo/</link><pubDate>Mon, 25 Sep 2023 00:00:00 +0000</pubDate><guid>https://mahyar-osn.github.io/projects/embryo/</guid><description>&lt;p>&lt;strong>Authors&lt;/strong>: Nazanin Ebrahimi, Mahyar Osanlouy, Chris Bradley, Fabiana Kubke, Dane Gerneke, Peter Hunter &lt;br>
&lt;strong>Publication&lt;/strong>: &lt;em>iScience.&lt;/em> (July 2022)&lt;br>
&lt;strong>Dataset&lt;/strong>: &lt;a href="https://doi.org/10.17632/jwj6m5yxct.1" target="_blank" rel="noopener">Mendeley Data&lt;/a>&lt;/p>
&lt;h2 id="overview">Overview&lt;/h2>
&lt;p>This study presents an innovative hybrid experimental-computational pipeline to investigate the &lt;strong>spatiotemporal growth patterns&lt;/strong> underlying cardiac C-looping in embryonic chick hearts. C-looping is a critical phase in heart development where the straight heart tube transforms into a C-shaped structure, setting the stage for proper chamber formation. Abnormalities during this process are linked to congenital heart defects. The work combines &lt;strong>multi-scale imaging&lt;/strong>, &lt;strong>deep learning-based cell segmentation&lt;/strong>, and &lt;strong>biomechanical modeling&lt;/strong> to bridge cellular dynamics with tissue-level deformations, offering new insights into the mechanisms driving heart morphogenesis.&lt;/p>
&lt;hr>
&lt;h2 id="key-contributions">Key Contributions&lt;/h2>
&lt;ol>
&lt;li>&lt;strong>First 3D multi-scale dataset&lt;/strong> of C-looping hearts, integrating cell-to-organism level data from confocal microscopy and micro-CT.&lt;/li>
&lt;li>&lt;strong>Fully automated 3D myocardial cell segmentation&lt;/strong> using a custom convolutional neural network (CNN), achieving a Dice coefficient of 0.91 ± 0.1.&lt;/li>
&lt;li>&lt;strong>Finite Element (FE) biomechanical models&lt;/strong> capturing spatiotemporal heart geometry changes across four developmental timepoints.&lt;/li>
&lt;li>&lt;strong>Variance-driven analysis&lt;/strong> revealing how inter-cellular space (ICS) and cellular heterogeneity contribute to tissue growth.&lt;/li>
&lt;li>&lt;strong>Open-source pipeline&lt;/strong> for integrating cellular features with tissue-level kinematics, enabling future studies on cardiac morphogenesis.&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h2 id="methodology">Methodology&lt;/h2>
&lt;h3 id="experimental-workflow">Experimental Workflow&lt;/h3>
&lt;ol>
&lt;li>
&lt;p>&lt;strong>Multi-modal imaging&lt;/strong>:&lt;/p>
&lt;ul>
&lt;li>&lt;strong>Confocal microscopy&lt;/strong>: Whole-mount staining (WGA, NCAM-1, DAPI) provided 3D cell-resolution images of myocardial cells.&lt;/li>
&lt;li>&lt;strong>Micro-CT scanning&lt;/strong>: Sub-micron resolution imaging contextualized heart geometry within the entire embryo.&lt;/li>
&lt;li>&lt;strong>Optical clearing&lt;/strong>: Enabled high-resolution imaging while preserving 3D architecture.&lt;/li>
&lt;/ul>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Temporal staging&lt;/strong>: Embryos were ordered developmentally using anatomical landmarks and dorsal detachment metrics.&lt;/p>
&lt;/li>
&lt;/ol>
&lt;img src="workflow.jpg" alt="drc-worfklow" width="800">
&lt;h3 id="computational-workflow">Computational Workflow&lt;/h3>
&lt;ol>
&lt;li>
&lt;p>&lt;strong>3D Deep Learning for Cell Segmentation&lt;/strong>:&lt;/p>
&lt;ul>
&lt;li>A &lt;strong>3D U-Net architecture&lt;/strong> was trained to segment individual myocardial cells from confocal stacks.&lt;/li>
&lt;li>Achieved 91% Dice similarity compared to manual segmentation, reducing processing time from &lt;strong>8 hours to seconds&lt;/strong> per 100 cells.&lt;/li>
&lt;li>Addressed memory constraints via a traceable slicing-merging algorithm for large-scale image processing.&lt;/li>
&lt;/ul>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Finite Element Modeling&lt;/strong>:&lt;/p>
&lt;ul>
&lt;li>Anatomically accurate FE meshes were fitted to heart geometries using OpenCMISS.&lt;/li>
&lt;li>RMS fitting error &amp;lt; 3 μm enabled precise representation of tissue deformation.&lt;/li>
&lt;/ul>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Spatiotemporal Analysis&lt;/strong>:&lt;/p>
&lt;ul>
&lt;li>Cellular features (volume, anisotropy, orientation) were mapped onto FE meshes.&lt;/li>
&lt;li>&lt;strong>General Linear Model (GLM)&lt;/strong> linked tissue growth to cellular dynamics (cell number, ICS volume, anisotropy).&lt;/li>
&lt;/ul>
&lt;/li>
&lt;/ol>
&lt;img src="segmentation.png" alt="drc-worfklow" width="800">
&lt;hr>
&lt;h2 id="results">Results&lt;/h2>
&lt;ol>
&lt;li>
&lt;p>&lt;strong>Differential Growth Patterns&lt;/strong>:&lt;/p>
&lt;ul>
&lt;li>Ventral regions showed ~2x higher tissue growth than dorsal regions, driven by increased cell proliferation and ICS expansion.&lt;/li>
&lt;li>Outer curvature cells exhibited circumferential alignment, while inner curvature cells remained isotropic.&lt;/li>
&lt;/ul>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Role of Inter-Cellular Space (ICS)&lt;/strong>:&lt;/p>
&lt;ul>
&lt;li>ICS accounted for 30–45% of tissue volume changes, highlighting its role in accommodating growth.&lt;/li>
&lt;li>Ventral ICS volume increased by 62% during bending phases.&lt;/li>
&lt;/ul>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Variance as a Developmental Signal&lt;/strong>:&lt;/p>
&lt;ul>
&lt;li>&lt;strong>Ring-shaped variance patterns&lt;/strong> in cell volume/anisotropy emerged around the outer curvature, suggesting mechanical feedback loops.&lt;/li>
&lt;li>High-variance regions correlated with zones of rapid tissue remodeling.&lt;/li>
&lt;/ul>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Tissue-Cell Dynamics&lt;/strong>:&lt;/p>
&lt;ul>
&lt;li>GLM analysis explained 70% of tissue growth variance, with cell number (β = 0.48, p &amp;lt; 0.001) and ICS (β = 0.32, p &amp;lt; 0.01) as key predictors.&lt;/li>
&lt;li>Cell orientation aligned with tissue deformation vectors during rotation (r &amp;gt; 0.8) but not bending phases.&lt;/li>
&lt;/ul>
&lt;/li>
&lt;/ol>
&lt;hr>
&lt;h2 id="implications">Implications&lt;/h2>
&lt;ul>
&lt;li>&lt;strong>Mechanistic Insights&lt;/strong>: Challenges the &amp;ldquo;differential growth hypothesis&amp;rdquo; by showing ICS and cellular heterogeneity are equally critical to looping.&lt;/li>
&lt;li>&lt;strong>Toolkit for Developmental Biology&lt;/strong>: The pipeline is extensible to other organs/species, enabling studies on how cellular noise shapes tissue patterning.&lt;/li>
&lt;li>&lt;strong>Clinical Relevance&lt;/strong>: Provides a framework to explore how genetic mutations disrupt growth coordination, informing congenital heart defect research.&lt;/li>
&lt;li>&lt;strong>AI/ML Impact&lt;/strong>: Demonstrates the power of deep learning in automating large-scale 3D biological image analysis.&lt;/li>
&lt;/ul>
&lt;img src="deformation.jpg" alt="drc-worfklow" width="800"></description></item><item><title>SFEAL</title><link>https://mahyar-osn.github.io/projects/sfeal/</link><pubDate>Fri, 22 Sep 2023 00:00:00 +0000</pubDate><guid>https://mahyar-osn.github.io/projects/sfeal/</guid><description>&lt;p>&lt;strong>Authors&lt;/strong>: Mahyar Osanlouy, Alys R. Clark, Haribalan Kumar, Clair King, Margaret L. Wilsher, David G. Milne, Ken Whyte, Eric A. Hoffman &amp;amp; Merryn H. Tawhai
&lt;strong>Publication&lt;/strong>: &lt;em>Nature Scientific Reports.&lt;/em> (September 2020)&lt;br>
&lt;strong>Code&lt;/strong>: &lt;a href="https://github.com/mahyar-osn/SFEAL" target="_blank" rel="noopener">Mendeley Data&lt;/a>&lt;/p>
&lt;h2 id="overview">Overview&lt;/h2>
&lt;p>This project presents a quantitative investigation into age‐related variations in lung and fissure shape among healthy adults (aged 20–90 years). By integrating advanced finite element mesh fitting techniques with statistical shape modeling and principal component analysis (PCA), the study establishes a robust framework for capturing and quantifying subtle geometric changes in lung morphology. Such a mathematical framework provides a normative baseline against which pathological alterations may be compared.&lt;/p>
&lt;h2 id="key-contributions">Key Contributions&lt;/h2>
&lt;ul>
&lt;li>
&lt;p>&lt;strong>Integration of Finite Element Modeling and PCA:&lt;/strong>&lt;br>
• Developed a high-order finite element (FE) mesh fitted to segmented lung surfaces, incorporating curvature and smoothness constraints.&lt;br>
• Applied PCA to reduce dimensionality, isolating principal modes of shape variation.&lt;/p>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Mathematical Modeling of Shape Deformations:&lt;/strong>&lt;br>
• Formulated an energy minimization problem that couples data fidelity with smoothness constraints.&lt;br>
• Expressed lung shape variations as weighted perturbations from a mean model in a high-dimensional space.&lt;/p>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Clinical Insights:&lt;/strong>&lt;br>
• Revealed strong associations between lung geometry, age, and BMI.&lt;br>
• Enabled detection of subtle fissure shifts and volumetric changes, likely reflecting underlying tissue elasticity.&lt;/p>
&lt;/li>
&lt;/ul>
&lt;h2 id="methodology">Methodology&lt;/h2>
&lt;h3 id="finite-element-mesh-construction">Finite Element Mesh Construction&lt;/h3>
&lt;p>Each lung is represented by a finite element mesh with a fixed topology (225 nodes in this study). To ensure an accurate and smooth representation, the mesh is fitted to imaging data by minimizing an energy functional that balances data fidelity against surface smoothness.&lt;/p>
&lt;h4 id="energy-model-formulation">Energy Model Formulation&lt;/h4>
&lt;p>The energy function is defined as:&lt;/p>
&lt;p>$$
T(u) = \sum_{i=1}^{N} \gamma_i \left| z(\xi_i) - z_d \right|^2 + \int_{\Omega} g(u(\xi)), d\xi,
$$&lt;/p>
&lt;p>where:&lt;/p>
&lt;ul>
&lt;li>$u$ is the vector of shape (or nodal displacement) parameters.&lt;/li>
&lt;li>$z(\xi_i)$ represents the geometric position of a node in local parametric coordinates $\xi_i$.&lt;/li>
&lt;li>$z_d$ is the target data point from the segmented lung surface.&lt;/li>
&lt;li>$\gamma_i$ is a weight factor controlling data matching for each node.&lt;/li>
&lt;li>$g(u(\xi))$ is the smoothness (regularization) term that penalizes rapid or non-physical deformations.&lt;/li>
&lt;li>$\Omega$ denotes the domain over which the mesh is defined.&lt;/li>
&lt;/ul>
&lt;p>This formulation ensures that the FE mesh adapts to the lung&amp;rsquo;s surface while preserving a biologically plausible smooth geometry.&lt;/p>
&lt;h4 id="pseudo-code-for-mesh-fitting">Pseudo-code for Mesh Fitting&lt;/h4>
&lt;pre>&lt;code>for each subject:
// Step 1: Initialize template mesh
Initialize template_mesh with 225 nodes
// Step 2: Define anatomical landmarks
Define landmarks:
- Apices
- Diaphragm
- Lung base edges
- Anterior segments
// Step 3: Optimize node positions using energy minimization
Optimize node positions by minimizing the energy function T(u):
T(u) = Σγ ||z(ξ₁, ξ₂) - z_d||² + ∫ g(u(ξ)) dξ
// where:
// z = nodal coordinates (x, y, z)
// g = smoothness constraint (curvature regularization)
// γ = data matching weight factor
&lt;/code>&lt;/pre>
&lt;p>&lt;em>Mean fitting error: 5.2 ± 2.3 mm&lt;/em>&lt;/p>
&lt;h3 id="data-alignment-and-statistical-shape-modeling">Data Alignment and Statistical Shape Modeling&lt;/h3>
&lt;p>Prior to PCA, lung shapes are aligned using General Procrustes Analysis (GPA) to eradicate variations due to
translation, rotation, and, in the case of the size-exclusive model, scaling.&lt;/p>
&lt;h4 id="alignment-equation">Alignment Equation&lt;/h4>
&lt;p>The alignment is expressed as:&lt;/p>
&lt;p>$$
\bar{S} = \alpha R S + T,
$$&lt;/p>
&lt;p>where:&lt;/p>
&lt;ul>
&lt;li>$S$ is the original shape vector,&lt;/li>
&lt;li>$R$ is the rotation matrix,&lt;/li>
&lt;li>$T$ is the translation vector,&lt;/li>
&lt;li>$\alpha$ is the scaling factor (applied only in size-inclusive models).&lt;/li>
&lt;/ul>
&lt;h3 id="principal-component-analysis-pca">Principal Component Analysis (PCA)&lt;/h3>
&lt;p>PCA is employed to reduce the high-dimensional shape vector into principal modes that capture the primary sources of variance.&lt;/p>
&lt;h4 id="pca-decomposition-via-svd">PCA Decomposition via SVD&lt;/h4>
&lt;p>The shape matrix $\mathbf{S}$ is decomposed using singular value decomposition (SVD):&lt;/p>
&lt;p>$$
\mathbf{S} = \mathbf{U} {\Sigma} \mathbf{V}^{T},
$$&lt;/p>
&lt;p>where:&lt;/p>
&lt;ul>
&lt;li>$\mathbf{U}$ contains the eigenvectors of $\mathbf{S} \mathbf{S}^{T}$,&lt;/li>
&lt;li>${\Sigma}$ is the diagonal matrix of singular values $\sigma_i$ (with $\lambda_i = \sigma_i^2$ being
the eigenvalues),&lt;/li>
&lt;li>$\mathbf{V}^{T}$ holds the principal directions in the data space.&lt;/li>
&lt;/ul>
&lt;p>Each lung shape is reconstructed as:&lt;/p>
&lt;p>$$
M_{l}(w) = \bar{S}_0 + w, u_{l},
$$&lt;/p>
&lt;p>with:&lt;/p>
&lt;ul>
&lt;li>$\bar{S}_0$ being the mean shape,&lt;/li>
&lt;li>$u_l$ the $l$th principal component,&lt;/li>
&lt;li>$w$ the corresponding weight factor.&lt;/li>
&lt;/ul>
&lt;p>The variance explained by each mode is:&lt;/p>
&lt;p>$$
\text{Variance Explained} = \frac{\sigma_l^2}{\sum_{i} \sigma_i^2} \times 100%.
$$&lt;/p>
&lt;h2 id="results">Results&lt;/h2>
&lt;ul>
&lt;li>
&lt;p>&lt;strong>Correlation with Age:&lt;/strong>&lt;br>
Specific principal shape modes display strong correlations with age (e.g., $R = -0.75, ; p &amp;lt; 0.001$),&lt;/p>
&lt;/li>
&lt;li>
&lt;p>indicating that lung geometries become more “pyramidal” as age increases.&lt;/p>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Sex and BMI Associations:&lt;/strong>&lt;br>
Differences in shape related to lung size manifest in the size-inclusive model, highlighting sex-related volumetric differences. In contrast, the size-exclusive model emphasizes purely geometric deformations, with moderate correlations observed for BMI.&lt;/p>
&lt;/li>
&lt;/ul>
&lt;img src="pca-lung.png" alt="drc-worfklow" width="800">
&lt;img src="pca-plot.png" alt="drc-worfklow" width="800">
&lt;h2 id="implications">Implications&lt;/h2>
&lt;ul>
&lt;li>
&lt;p>&lt;strong>Clinical Applications:&lt;/strong>&lt;br>
The detailed mathematical framework enables lung shape to be employed as a biomarker for aging and disease. Deviations from the normative PCA model may assist in early detection or staging of conditions like COPD and IPF.&lt;/p>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Technical Advancements:&lt;/strong>&lt;br>
The fusion of finite element modeling with PCA offers a versatile and robust method for analyzing complex organ shapes. This approach can be adapted to other anatomical structures requiring similar quantitative assessments.&lt;/p>
&lt;/li>
&lt;li>
&lt;p>&lt;strong>Future Directions:&lt;/strong>&lt;br>
Enhancing the energy model and incorporating dynamic imaging (e.g., covering breathing cycles) could further refine shape analysis. Additionally, exploring non-linear dimensionality reduction techniques may uncover further subtleties in lung morphology.&lt;/p>
&lt;/li>
&lt;/ul></description></item></channel></rss>