Radiomics on spatial-temporal manifolds via Fokker-Planck dynamics

Delta 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.

The 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).

To 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 to ¹⁸F-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.

Numerical 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).

We 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.