*Result*: Multivariable optimal control for hemodialysis: A physiologically-grounded simulation study.

*This study introduces a novel multivariable optimal control framework for hemodialysis, which uniquely integrates five physiological states (blood urea concentration, fluid volume, blood pressure, electrolytes, and hemoglobin) with three clinically adjustable inputs (ultrafiltration rate, blood flow, and dialysate composition). By employing the limited-memory Broyden-Fletcher-Goldfarb-Shanno-B (L-BFGS-B) algorithm with patient-specific box constraints, the model enforces patient-specific physiological safety limits while dynamically balancing clinical targets. Numerical simulations demonstrate the stabilization of key parameters within ±5% of clinical benchmarks (e.g., KDIGO guidelines), though deviations in the hemodynamic responses underscore the need for adaptive control in real-world scenarios. Urea clearance trajectories align with efficacy patterns observed in practice, while blood pressure fluctuations reveal systematic offsets that require protocol refinement. This work bridges control theory with hemodialysis dynamics, thus offering a simulation-driven foundation for future clinical validation and personalized treatment optimization.*