Simulation of post-prandial pharmacokinetics, such as muscle protein synthesis (MPS) through mTORC1 and insulin-induced glucose uptake, is often challenging due to the computational intensity of the multi-compartmental approach. In this study, I introduce an in silico metabolic simulator that uses bi-compartmental Bateman kinetic processes, gamma-variate distributions, and finite state machine reasoning to solve temporal differential equations instantaneously, generating metabolic curves and predictions depending on input meals. The novel underlying algorithm was custom-built entirely independent of third-party libraries or external services. This original computational engine, bridging the gap between academia and the digital health sector, is integrated within a web dashboard and provided as a service via REST APIs. The average response time is approximately 135 ms with a maximum below 750 ms. The multi-dimensional model was calibrated using a Landmark Validation approach across diverse dietary conditions (Whey Protein, mixed meal, OGTT) and optimized via Grid Search. Ultimately, the system achieved a global physiologically optimal Mean Absolute Percentage Error (MAPE) of $\sim18\%$ while maintaining an algorithmic complexity of $O(n \log n)$.

翻译：餐后药代动力学（如通过mTORC1途径的肌肉蛋白质合成（MPS）及胰岛素介导的葡萄糖摄取）的模拟常因多室模型的计算强度而面临挑战。本研究提出一种基于计算生物学的代谢模拟器，该模拟器通过双室Bateman动力学过程、伽马变异分布及有限状态机推理，可瞬时求解时间微分方程，并根据输入膳食生成代谢曲线与预测。其核心算法完全自主构建，不依赖任何第三方库或外部服务。这一原创性计算引擎架起了学术界与数字健康产业之间的桥梁，已集成于网页仪表盘，并通过REST API以服务形式提供。系统平均响应时间约135毫秒，最大响应时间低于750毫秒。该多维模型采用标志性验证方法在不同膳食条件（乳清蛋白、混合餐、口服葡萄糖耐量试验）下完成校准，并通过网格搜索实现优化。最终，该系统在保持算法复杂度为O(n log n)的前提下，实现了全局生理学最优平均绝对百分比误差（MAPE）约18%。