Modeling Continuous Bladder Size Dynamics Using Ultrasound Tomography for Pediatric Assessment

Neurogenic bladder disorder assessment in young patients is constrained by invasive testing and scarce, irregular time-series data. We present a reproducible, symptom-aware heuristic, non-linear function-based framework that generates continuous bladder dynamics and paired ultrasound-tomography (UST) data across three conditions: healthy, incontinence, and retention. Filling is modeled with logistic or linear growth; voiding with quadratic or logistic decay. Incontinence adds stochastic leakage (half-sine or logistic drops) and pauses; retention enforces asymmetric voiding with high post-void residual. We simulate 150 virtual patients per condition, each across 100 steps, yielding 45,000 time-indexed UST frames with measurement vectors and per-patient metadata (initial/max radius, residual, $\beta $ , $\gamma $ , filling/voiding steps and methods, global/patient seeds) to ensure exact reproducibility and auditability. Clinical plausibility was quantified by matching two real pediatric time series per condition (8 sparse points each) to their nearest simulated trajectories under bladder-size constraints and computing error/similarity metrics. Healthy cases showed strong agreement (RMSE 9–15 px, MAE 7–11 px, R ${}^{2}~0.97$ –0.98; NCC 0.72– 0.90; DTW $\approx 0.9$ – $3.3\times 10 ^{3}$ ). Retention also aligned well (RMSE 20–27 px, MAE 17–24 px, R ${}^{2}~0.93$ –0.97; NCC $\approx 0.99$ ; DTW $\approx 1.2$ – $1.6\times 10 ^{3}$ ) with larger max radius and residuals captured by the model. Incontinence, which is intrinsically irregular, exhibited higher errors yet preserved shape similarity (RMSE 29–30 px, MAE 26–27 px, R ${}^{2}~0.39$ –0.76; NCC 0.74–0.88; DTW $\approx 2.2$ – $2.4\times 10 ^{3}$ ). These results demonstrate that the model reproduces interpretable bladder dynamics and class-specific behaviors while exposing expected variability in incontinence. The resulting dataset constitutes a pragmatic strength for translational AI, providing a scalable, clinically grounded foundation for training and benchmarking machine-learning models for non-invasive, time-dependent bladder assessment in children.