Benchmarking off-the-shelf statistical shape modeling tools in clinical applications

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Introduction: Statistical shape modeling (SSM) is a valuable and powerful tool to generate a detailed representation of complex anatomy that enables quantitative analysis of shapes and their variations. SSM applies mathematics, statistics, and computing to parse the shape into some quantitative representation (such as correspondence points or landmarks) which can be used to study the covariance patterns of the shapes and answer various questions about the anatomical variations across the population. Complex anatomical structures have many diverse parts with varying interactions or intricate architecture. For example, the heart is a four-chambered organ with several shared boundaries between chambers. Subtle shape changes within the shared boundaries of the heart can indicate potential pathologic changes such as right ventricular overload. Early detection and robust quantification could provide insight into ideal treatment techniques and intervention timing. However, existing SSM methods do not explicitly handle shared boundaries which aid in a better understanding of the anatomy of interest. If shared boundaries are not explicitly modeled, it restricts the capability of the shape model to identify the pathological shape changes occurring at the shared boundary. Hence, this paper presents a general and flexible data-driven approach for building statistical shape models of multi-organ anatomies with shared boundaries that explicitly model contact surfaces.Methods: This work focuses on particle-based shape modeling (PSM), a state-of-art SSM approach for building shape models by optimizing the position of correspondence particles. The proposed PSM strategy for handling shared boundaries entails (a) detecting and extracting the shared boundary surface and contour (outline of the surface mesh/isoline) of the meshes of the two organs, (b) followed by a formulation for a correspondence-based optimization algorithm to build a multi-organ anatomy statistical shape model that captures morphological and alignment changes of individual organs and their shared boundary surfaces throughout the population.Results: We demonstrate the shared boundary pipeline using a toy dataset of parameterized shapes and a clinical dataset of the biventricular heart models. The shared boundary model for the cardiac biventricular data achieves consistent parameterization of the shared surface (interventricular septum) and identifies the curvature of the interventricular septum as pathological shape differences.

Section: Introductionmentioning

confidence: 99%

Statistical shape modeling of multi-organ anatomies with shared boundaries

Iyer

Morris²,

Zenger³

et al. 2023

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“…These approaches avoid complex parameterization construction steps and the limitations inherent in parametric representations, such as restriction to specific topologies and bias resulting from the choice of basis or template. The non-parametric techniques have been shown to produce more robust and compact models that better retain clinically relevant shape characteristics (Goparaju et al (2018); Goparaju et al (2022)). In this work, we utilize the entropy-based approach to PDM optimization formulated in Cates et al (2007), a. k.a.…”

Section: Introductionmentioning

confidence: 99%

Learning spatiotemporal statistical shape models for non-linear dynamic anatomies

Adams

Khan

Morris

et al. 2023

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Numerous clinical investigations require understanding changes in anatomical shape over time, such as in dynamic organ cycle characterization or longitudinal analyses (e.g., for disease progression). Spatiotemporal statistical shape modeling (SSM) allows for quantifying and evaluating dynamic shape variation with respect to a cohort or population of interest. Existing data-driven SSM approaches leverage information theory to capture population-level shape variations by learning correspondence-based (landmark) representations of shapes directly from data using entropy-based optimization schemes. These approaches assume sample independence and thus are unsuitable for sequential dynamic shape observations. Previous methods for adapting entropy-based SSM optimization schemes for the spatiotemporal case either utilize a cross-sectional design (ignoring within-subject correlation) or impose other limiting assumptions, such as the linearity of shape dynamics. Here, we present a principled approach to spatiotemporal SSM that relaxes these assumptions to correctly capture population-level shape variation over time. We propose to incorporate modeling the underlying time dependency into correspondence optimization via a regularized principal component polynomial regression. This approach is flexible enough to capture non-linear temporal dynamics while encoding population-specific spatial regularity. We demonstrate our method’s efficacy on synthetic data and left atrium segmented from cardiac MRI scans. Our approach better captures the population modes of variation and a statistically significant time dependency than existing methods.

“…These mappings should be learned from the study population in a data-driven manner to capture the underlying population-specific morphological variability Kulis et al (2013) . Approaches for establishing such mappings that rely on pairwise comparisons (e.g., Styner et al (2006) and Jenkinson et al (2012) ] typically require a predefined atlas for initialization, leading to biased and suboptimal models Goparaju et al (2022) . Group-wise approaches [e.g., Durrleman et al (2014) and Cates et al (2017a) ], on the other hand, observe the entire population to quantify the quality of shape correspondences, and hence better reflect the underlying population variability Goparaju et al (2022) .…”

Section: Introductionmentioning

confidence: 99%

“…Approaches for establishing such mappings that rely on pairwise comparisons (e.g., Styner et al (2006) and Jenkinson et al (2012) ] typically require a predefined atlas for initialization, leading to biased and suboptimal models Goparaju et al (2022) . Group-wise approaches [e.g., Durrleman et al (2014) and Cates et al (2017a) ], on the other hand, observe the entire population to quantify the quality of shape correspondences, and hence better reflect the underlying population variability Goparaju et al (2022) . Particle-based shape modeling (PSM) Cates et al (2007) and Cates et al (2017a) , in particular, is a state-of-the-art computational approach for constructing point distribution models (PDM) via automatically placing a dense set of corresponding landmarks on a set of shapes.…”

Section: Introductionmentioning

confidence: 99%

Statistical multi-level shape models for scalable modeling of multi-organ anatomies

Khan

Peterson²,

Aubert³

et al. 2023

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Statistical shape modeling is an indispensable tool in the quantitative analysis of anatomies. Particle-based shape modeling (PSM) is a state-of-the-art approach that enables the learning of population-level shape representation from medical imaging data (e.g., CT, MRI) and the associated 3D models of anatomy generated from them. PSM optimizes the placement of a dense set of landmarks (i.e., correspondence points) on a given shape cohort. PSM supports multi-organ modeling as a particular case of the conventional single-organ framework via a global statistical model, where multi-structure anatomy is considered as a single structure. However, global multi-organ models are not scalable for many organs, induce anatomical inconsistencies, and result in entangled shape statistics where modes of shape variation reflect both within- and between-organ variations. Hence, there is a need for an efficient modeling approach that can capture the inter-organ relations (i.e., pose variations) of the complex anatomy while simultaneously optimizing the morphological changes of each organ and capturing the population-level statistics. This paper leverages the PSM approach and proposes a new approach for correspondence-point optimization of multiple organs that overcomes these limitations. The central idea of multilevel component analysis, is that the shape statistics consists of two mutually orthogonal subspaces: the within-organ subspace and the between-organ subspace. We formulate the correspondence optimization objective using this generative model. We evaluate the proposed method using synthetic shape data and clinical data for articulated joint structures of the spine, foot and ankle, and hip joint.