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Differentiating radionecrosis from tumor recurrence non\u2010invasively remains a major clinical challenge, as conventional imaging techniques often necessitate surgical biopsy for accurate diagnosis. Machine learning and deep learning models have shown potential in distinguishing radionecrosis from tumor recurrence. However, their clinical adoption is hindered by a lack of explainability, limiting understanding and trust in their diagnostic decisions.<\/jats:p><\/jats:sec><jats:sec><jats:title>Purpose<\/jats:title><jats:p>To utilize a novel neural ordinary differential equation (NODE) model for discerning BM post\u2010SRS radionecrosis from recurrence. This approach integrates image\u2010deep features, genomic biomarkers, and non\u2010image clinical parameters within a synthesized latent feature space. The trajectory of each data sample towards the diagnosis decision can be visualized within this feature space, offering a new angle on radiogenomic data analysis foundational for AI explainability.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>By hypothesizing that deep feature extraction can be modeled as a spatiotemporally continuous process, we designed a novel model based on heavy ball NODE (HBNODE) in which deep feature extraction was governed by a second\u2010order ODE. This approach enabled tracking of deep neural network (DNN) behavior by solving the HBNODE and observing the stepwise derivative evolution. Consequently, the trajectory of each sample within the Image\u2010Genomic\u2010Clinical (I\u2010G\u2010C) space became traceable. A decision\u2010making field (<jats:bold><jats:italic>F<\/jats:italic><\/jats:bold>) was reconstructed within the feature space, with its gradient vectors directing the data samples\u2019 trajectories and intensities showing the potential. The evolution of <jats:bold><jats:italic>F<\/jats:italic><\/jats:bold> reflected the cumulative feature contributions at intermediate states to the final diagnosis, enabling quantitative and dynamic comparisons of the relative contribution of each feature category over time. A velocity curve was designed to determine key intermediate states (locoregional \u2207<jats:bold><jats:italic>F\u00a0<\/jats:italic><\/jats:bold>=<jats:bold>\u00a0<\/jats:bold>0) that are most predictive. Subsequently, a non\u2010parametric model aggregated the optimal solutions from these key states to predict outcomes.<\/jats:p><jats:p>Our dataset included 90 BMs from 62 NSCLC patients, and 3\u2010month post\u2010SRS T1+c MR image features, seven NSCLC genomic features, and seven clinical features were analyzed. An 8:2 train\/test assignment was employed, and five independent models were trained to ensure robustness. Performance was benchmarked in sensitivity, specificity, accuracy, and ROC<jats:sub>AUC<\/jats:sub>, and results were compared against (1) a DNN using only image\u2010based features, and (2) a combined \u201cI+G+C\u201d features without the HBNODE model.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>The temporal evolution of gradient vectors and potential fields in <jats:bold><jats:italic>F<\/jats:italic><\/jats:bold> suggested that clinical features contribute the most during the initial stages of the HBNODE implementation, followed by imagery features taking dominance in the latter ones, while genomic features contribute the least throughout the process. The HBNODE model successfully identified and assembled key intermediate states, exhibiting competitive performance with an ROC<jats:sub>AUC<\/jats:sub> of 0.88\u00a0\u00b1\u00a00.04, sensitivity of 0.79\u00a0\u00b1\u00a00.02, specificity of 0.86\u00a0\u00b1\u00a00.01, and accuracy of 0.84\u00a0\u00b1\u00a00.01, where the uncertainties represent standard deviations. For comparison, the image\u2010only DNN model achieved an ROC<jats:sub>AUC<\/jats:sub> of 0.71\u00a0\u00b1\u00a00.05 and sensitivity of 0.66\u00a0\u00b1\u00a00.32 (<jats:italic>p<\/jats:italic><jats:bold>\u00a0<\/jats:bold><jats:italic>=<\/jats:italic>\u00a00.086), while the \u201cI+G+C\u201d model without HBNODE reported an ROC<jats:sub>AUC<\/jats:sub> of 0.81\u00a0\u00b1\u00a00.02 and sensitivity of 0.58\u00a0\u00b1\u00a00.11 (<jats:italic>p<\/jats:italic><jats:bold>\u00a0<\/jats:bold><jats:italic>=<\/jats:italic>\u00a00.091).<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>The HBNODE model effectively identifies BM radionecrosis from recurrence, enhancing explainability within XAI frameworks. Its performance encourages further exploration in clinical settings and suggests potential applicability across various XAI domains.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.17635","type":"journal-article","created":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T09:39:56Z","timestamp":1738143596000},"page":"2661-2674","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Radiogenomic explainable AI with neural ordinary differential equation for identifying post\u2010SRS brain metastasis radionecrosis"],"prefix":"10.1002","volume":"52","author":[{"given":"Jingtong","family":"Zhao","sequence":"first","affiliation":[{"name":"Deparment of Radiation Oncology Duke University  Durham North Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eugene","family":"Vaios","sequence":"additional","affiliation":[{"name":"Deparment of Radiation Oncology Duke University  Durham North Carolina 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