Radiomics On Spatial-Temporal Manifolds Via Fokker-Planck Dynamics
J Stevens1*, J Je2, Y Gao3, C Wang4, Y Mowery5, D Brizel6, F Yin7, J Liu8, K Lafata9, (1) Duke University, Durham, NC, (2) Duke University, ,,(3) Purdue University, ,,(4) Duke University Medical Center, Durham, NC, (5) Duke University Medical Center, Durham, ,(6) Duke University Medical Center, Durham, ,(7) Duke University Medical Center, Chapel Hill, NC, (8) Duke University, ,,(9) Duke University, Durham, NC
Presentations
SU-H330-IePD-F9-5 (Sunday, 7/10/2022) 3:30 PM - 4:00 PM [Eastern Time (GMT-4)]
Exhibit Hall | Forum 9
Purpose: To develop 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.
Methods: We developed an algorithm to model the temporal evolution between two images, ImageA and ImageB, acquired at t=0 and t>0, respectively. Images serve as no-flux boundary conditions of the Fokker-Planck partial differential equation, where ImageA is an excited-state and ImageB is an equilibrium-state. To model in-between timeframes, we propagate pixels according to Fokker-Planck dynamics. This transformation is driven by an underlying potential force uniquely determined by the equilibrium. It generates a spatial-temporal manifold (4th-order tensor; 3 spatial dimensions + time), from which radiomic features are characterized by their continuous rate-of-change. 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 Fokker-Planck estimation and simulated ground-truth. Second, we conducted a patient study to estimate early metabolic response of patients undergoing definitive radiotherapy for oropharyngeal cancer. 18F-FDG PET images from 57 patients were acquired pre-treatment (ImageA) and two-weeks intra-treatment after 20Gy (ImageB). Each patient’s metabolic time-evolution was modeled, from which image energy and entropy were calculated as a function-of-time and compared to 5-year cancer recurrence.
Results: Numerical results confirmed our technique can recover image noise characteristics given sparse input data as boundary conditions. Compared to ground-truth, the estimated impulse response of energy and entropy achieved cross-correlations of 0.82 and 0.94, respectively. Our patient study demonstrated a measurable difference in energy rate-of-change between patients with-and-without recurrence (RMSE=2.9%). Recurrent tumor energy changed faster than non-recurrent tumor energy, suggesting early metabolic response is linked to how quickly disease becomes metabolically homogenous.
Conclusion: We developed, verified, and applied a new approach to sparse, time-series image characterization via data assimilation of radiomics with partial differential equations.
Funding Support, Disclosures, and Conflict of Interest: DOD\CDMRP W81XWH2110248
Keywords
Modeling, Nonlinear Dynamics, PET
Taxonomy
IM/TH- Image Analysis (Single Modality or Multi-Modality): Imaging biomarkers and radiomics
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