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Abstract BackgroundOropharyngeal cancer (OPC) exhibits varying responses to chemoradiation therapy, making treatment outcome prediction challenging. Traditional imaging‐based methods often fail to capture the spatial heterogeneity within tumors, which influences treatment resistance and disease progression. Advances in modeling techniques allow for more nuanced analysis of this heterogeneity, identifying distinct tumor regions, or habitats, that drive patient outcomes. PurposeTo interrogate the association between treatment‐induced changes in spatial heterogeneity and chemoradiation resistance of oropharyngeal cancer (OPC) based on a novel tumor habitat analysis. MethodsA mathematical model was used to estimate tumor time dynamics of patients with OPC based on the applied analysis of partial differential equations. The position and momentum of each voxel was propagated according to Fokker‐Planck dynamics, that is, a common model in statistical mechanics. The boundary conditions of the Fokker‐Planck equation were solved based on pre‐ and intra‐treatment (i.e., after 2 weeks of therapy)¹⁸F‐FDG‐PET SUV images of patients (n = 56) undergoing definitive (chemo)radiation for OPC as part of a previously conducted prospective clinical trial. Tumor‐specific time dynamics, measured based on the solution of the Fokker‐Planck equation, were generated for each patient. Tumor habitats (i.e., non‐overlapping subregions of the primary tumor) were identified by measuring vector similarity in voxel‐level time dynamics through a fuzzy c‐means clustering algorithm. The robustness of our habitat construction method was quantified using a mean silhouette metric to measure intra‐habitat variability. Fifty‐four habitat‐specific radiomic texture features were extracted from pre‐treatment SUV images and normalized by habitat volume. Univariate Kaplan‐Meier analyses were implemented as a feature selection method, where statistically significant features (p < 0.05, log‐rank) were used to construct a multivariate Cox proportional‐hazards model. Parameters from the resulting Cox model were then used to construct a risk score for each patient, based on habitat‐specific radiomic expression. The patient cohort was stratified by median risk score value and association with recurrence‐free survival (RFS) was evaluated via log‐rank tests. ResultsDynamic tumor habitat analysis partitioned the gross disease of each patient into three spatial subregions. Voxels within each habitat suggested differential response rates in different compartments of the tumor. The minimum mean silhouette value was 0.57 and maximum mean silhouette value was 0.8, where values above 0.7 indicated strong intra‐habitat consistency and values between 0.5 and 0.7 indicated reasonable intra‐habitat consistency. Nine radiomic texture features (three GLRLM, two GLCOM, and three GLSZM) and SUVmax were found to be prognostically significant and were used to build the multivariate Cox model. The resulting risk score was associated with RFS (p = 0.032). By contrast, potential confounding factors (primary tumor volume and mean SUV) were not significantly associated with RFS (p = 0.286 andp = 0.231, respectively). ConclusionWe interrogated spatial heterogeneity of oropharyngeal tumors through the application of a novel algorithm to identify spatial habitats on SUV images. Our habitat construction technique was shown to be robust and habitat‐specific feature spaces revealed distinct underlying radiomic expression patterns. Radiomic features were extracted from dynamic habitats and used to build a risk score which demonstrated prognostic value. 

Abstract BackgroundDelta radiomics is a high‐throughput computational technique used to describe quantitative changes in serial, time‐series imaging by considering the relative change in radiomic features of images extracted at two distinct time points. Recent work has demonstrated a lack of prognostic signal of radiomic features extracted using this technique. We hypothesize that this lack of signal is due to the fundamental assumptions made when extracting features via delta radiomics, and that other methods should be investigated. PurposeThe purpose of this work was to show a proof‐of‐concept of a new radiomics paradigm for sparse, time‐series imaging data, where features are extracted from a spatial‐temporal manifold modeling the time evolution between images, and to assess the prognostic value on patients with oropharyngeal cancer (OPC). MethodsTo accomplish this, we developed an algorithm to mathematically describe the relationship between two images acquired at time and . These images serve as boundary conditions of a partial differential equation describing the transition from one image to the other. To solve this equation, we propagate the position and momentum of each voxel according to Fokker–Planck dynamics (i.e., a technique common in statistical mechanics). This transformation is driven by an underlying potential force uniquely determined by the equilibrium image. The solution generates a spatial‐temporal manifold (3 spatial dimensions + time) from which we define dynamic radiomic features. First, our approach was numerically verified by stochastically sampling dynamic Gaussian processes of monotonically decreasing noise. The transformation from high to low noise was compared between our Fokker–Planck estimation and simulated ground‐truth. To demonstrate feasibility and clinical impact, we applied our approach to¹⁸F‐FDG‐PET images to estimate early metabolic response of patients (n = 57) undergoing definitive (chemo)radiation for OPC. Images were acquired pre‐treatment and 2‐weeks intra‐treatment (after 20 Gy). Dynamic radiomic features capturing changes in texture and morphology were then extracted. Patients were partitioned into two groups based on similar dynamic radiomic feature expression via k‐means clustering and compared by Kaplan–Meier analyses with log‐rank tests (p < 0.05). These results were compared to conventional delta radiomics to test the added value of our approach. ResultsNumerical results confirmed our technique can recover image noise characteristics given sparse input data as boundary conditions. Our technique was able to model tumor shrinkage and metabolic response. While no delta radiomics features proved prognostic, Kaplan–Meier analyses identified nine significant dynamic radiomic features. The most significant feature was Gray‐Level‐Size‐Zone‐Matrix gray‐level variance (p = 0.011), which demonstrated prognostic improvement over its corresponding delta radiomic feature (p = 0.722). ConclusionsWe developed, verified, and demonstrated the prognostic value of a novel, physics‐based radiomics approach over conventional delta radiomics via data assimilation of quantitative imaging and differential equations.