PREDICTING RECURRENT VENOUS THROMBOEMBOLISM THROUGH PATIENT-SPECIFIC SIMULATION OF BLOOD CLOT GROWTH USING A PARTIAL DIFFERENTIAL EQUATION MODEL

Recurrent Venous Thromboembolism (RVTE) is a leading cause of morbidity in patients with a history of thrombotic events. Despite the availability of several clinical scores, predicting recurrence remains challenging due to inter-patient variability in thrombus formation dynamics. While Machine Learning (ML) has shown promise, most models lack physiological interpretability. In contrast, mechanistic models based on differential equations can simulate clot growth but often ignore patient-specific biological variability. To improve prediction while preserving clinical transparency, this study proposes a physiologically interpretable framework that uses patient-specific kinetic parameters to simulate clot formation through a Partial Differential Equation (PDE) model, followed by binary classification of RVTE outcomes. To simulate patient-specific thrombus formation using a mechanistic PDE model, based on previously estimated kinetic parameters of the coagulation cascade, and to develop a binary ML classifier combining clot size with key clinical variables to predict RVTE recurrence. A retrospective cohort of 235 patients with a first episode of Venous Thromboembolism (VTE) was used. Patient-specific kinetic parameters were obtained from a previously optimized hybrid model, which combined an Artificial Neural Network (ANN) and a system of Ordinary Differential Equations (ODEs) to map clinical and hematological features to coagulation kinetics. These parameters were then used as inputs to a two-dimensional PDE model simulating clot growth under blood flow. The model incorporated platelet transport, biochemical reactions, and flow obstruction due to platelet aggregation. Thrombus size was computed as the proportion of simulated grid space occupied by bound platelets over a 10-minute simulation. A binary classifier was developed using four variables: patient age, D-dimer level, platelet count, and simulated clot size. Thirteen ML algorithms were evaluated using five-fold cross-validation, and model performance was assessed via area under the curve (AUC), accuracy, sensitivity, specificity, and F1-score. Simulations using patient-specific kinetic parameters significantly improved discrimination between RVTE and non-RVTE groups, as shown by clot size distributions (p = 0.0001, 95% confidence). Models using standard (non-personalized) parameters showed no significant outcome separation. Among ML algorithms tested, the ANN classifier with architecture (4-2-6-1) and activation functions (satlins–tansig–satlins) achieved the highest AUC (0.956), accuracy (0.886), and F1-score (0.789) on the test set. Shapley Additive Explanations (SHAP) analysis revealed that thrombus size and platelet count were the most important predictors for diagnosing RVTE, while D- dimer levels and age were more relevant in ruling out non-RVTE cases. Results show that physiological modeling improves accuracy and clinical insight. This study introduces a novel framework that links clinical data to thrombus growth through a patient-specific PDE model, enabling physiologically grounded RVTE prediction. By combining simulated clot size with routine clinical markers, the proposed classifier outperformed traditional ML approaches. Moreover, SHAP-based analysis ensured interpretability, reinforcing its clinical relevance. This model enables accurate recurrence risk stratification and supports personalized prevention.