[Paper Review] Radiologic Image-based Statistical Shape Analysis of Brain Tumors

Karthik Bharath, Sebastian Kurtek+2 more|arXiv (Cornell University)|Feb 3, 2017

Morphological variations and asymmetry35 references4 citations

TL;DR

This paper proposes a Riemannian-geometric, curve-based framework for statistical shape analysis of brain tumors using radiologic MRI images. By modeling tumor shapes on a manifold with an elastic metric, it enables shape comparison, PCA, clustering, and survival modeling—demonstrating that tumor shape significantly improves survival prediction beyond clinical and genomic variables in glioblastoma patients.

ABSTRACT

We propose a curve-based Riemannian-geometric approach for general shape-based statistical analyses of tumors obtained from radiologic images. A key component of the framework is a suitable metric that (1) enables comparisons of tumor shapes, (2) provides tools for computing descriptive statistics and implementing principal component analysis on the space of tumor shapes, and (3) allows for a rich class of continuous deformations of a tumor shape. The utility of the framework is illustrated through specific statistical tasks on a dataset of radiologic images of patients diagnosed with glioblastoma multiforme, a malignant brain tumor with poor prognosis. In particular, our analysis discovers two patient clusters with very different survival, subtype and genomic characteristics. Furthermore, it is demonstrated that adding tumor shape information into survival models containing clinical and genomic variables results in a significant increase in predictive power.

Motivation & Objective

• To develop a rigorous, mathematically sound method for statistical shape analysis of brain tumors from 2D MRI slices.
• To overcome limitations of subjective, non-reproducible shape descriptors used in clinical practice.
• To integrate tumor shape into survival modeling to enhance prognostic accuracy in glioblastoma multiforme (GBM).
• To identify biologically meaningful shape patterns linked to survival, subtype, and genomic profiles.
• To provide a generalizable framework for shape-based analysis applicable to other cancers and imaging modalities.

Proposed method

• The method models tumor contours as closed curves in the plane, embedded in a pre-shape space of square-integrable functions on the unit circle.
• It employs a Riemannian metric based on elastic shape analysis, enabling geodesic distances and intrinsic shape comparisons.
• Principal component analysis (PCA) is performed on the shape manifold to identify dominant modes of shape variation.
• Tumor shapes are represented via square-root velocity functions (SRVF), enabling efficient computation of shape deformations and alignment.
• Survival models incorporate principal coefficients of shape as predictors alongside clinical and genomic variables.
• Clustering and hypothesis testing are performed on the shape manifold to detect biologically distinct tumor subtypes.

Experimental results

Research questions

• RQ1 Can a Riemannian-geometric framework effectively model and compare tumor shapes from 2D MRI slices?
• RQ2 Does tumor shape, independent of size and volume, carry significant prognostic information in glioblastoma?
• RQ3 Can shape-based clustering reveal biologically and clinically distinct subtypes of GBM?
• RQ4 To what extent does adding shape information improve survival prediction models?
• RQ5 Are there detectable associations between tumor shape patterns and underlying genomic or pathological subtypes?

Key findings

• The framework successfully identified two distinct patient clusters with markedly different survival outcomes, subtype characteristics, and genomic profiles.
• Tumor shape, when added to models with clinical and genomic variables, significantly improved predictive power for survival.
• The principal components of shape variation revealed biologically plausible deformations, such as increasing spiculation with decreasing survival.
• The mean shape along the direction of decreased survival showed increased irregularity and spiculation, consistent with aggressive tumor behavior.
• The method uncovered potential associations between tumor shape coefficients and driver genes, suggesting shape as a biomarker for molecular subtypes.
• The survival model incorporating shape coefficients demonstrated improved discrimination and calibration compared to models without shape features.