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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. 

Purpose To develop a method of biologically guided deep learning for post-radiation 18 FDG-PET image outcome prediction based on pre-radiation images and radiotherapy dose information. Methods Based on the classic reaction–diffusion mechanism, a novel biological model was proposed using a partial differential equation that incorporates spatial radiation dose distribution as a patient-specific treatment information variable. A 7-layer encoder–decoder-based convolutional neural network (CNN) was designed and trained to learn the proposed biological model. As such, the model could generate post-radiation 18 FDG-PET image outcome predictions with breakdown biological components for enhanced explainability. The proposed method was developed using 64 oropharyngeal patients with paired 18 FDG-PET studies before and after 20-Gy delivery (2 Gy/day fraction) by intensity-modulated radiotherapy (IMRT). In a two-branch deep learning execution, the proposed CNN learns specific terms in the biological model from paired 18 FDG-PET images and spatial dose distribution in one branch, and the biological model generates post-20-Gy 18 FDG-PET image prediction in the other branch. As in 2D execution, 718/233/230 axial slices from 38/13/13 patients were used for training/validation/independent test. The prediction image results in test cases were compared with the ground-truth results quantitatively. Results The proposed method successfully generated post-20-Gy 18 FDG-PET image outcome prediction with breakdown illustrations of biological model components. Standardized uptake value (SUV) mean values in 18 FDG high-uptake regions of predicted images (2.45 ± 0.25) were similar to ground-truth results (2.51 ± 0.33). In 2D-based Gamma analysis, the median/mean Gamma Index (<1) passing rate of test images was 96.5%/92.8% using the 5%/5 mm criterion; such result was improved to 99.9%/99.6% when 10%/10 mm was adopted. Conclusion The developed biologically guided deep learning method achieved post-20-Gy 18 FDG-PET image outcome predictions in good agreement with ground-truth results. With the breakdown biological modeling components, the outcome image predictions could be used in adaptive radiotherapy decision-making to optimize personalized plans for the best outcome in the future.