标题： 基于固定预算的生长细胞群体模拟方法 显示英文标题

标题： Fixed-budget simulation method for growing cell populations

摘要： 研究增长细胞群体的动力学对于揭示生物体中的关键生物学机制至关重要，在治疗和生物化学工程中有许多重要的应用。 经典基于代理的模拟算法对于这些系统通常效率低下，因为它们跟踪每个单独的细胞，使得它们在快速（甚至指数级）增长的细胞群体中不切实际。 为了解决这个挑战，我们引入了一种基于种群动力学的类似费曼-卡克表示的新颖随机模拟方法。 这种方法被称为费曼-卡克启发的吉尔皮斯随机模拟算法（FKG-SSA），它始终使用固定数量的独立模拟细胞进行蒙特卡罗计算，从而无论种群大小如何，计算复杂度都保持恒定。 此外，我们从理论上证明了所提出方法的统计一致性，表明其准确性和可靠性。 最后，给出几个生物学相关的数值例子来说明该方法。 总体而言，提出的FKG-SSA有效解决了模拟增长细胞群体的挑战，为更好地分析这些系统提供了坚实的基础。 显示英文摘要

摘要： Investigating the dynamics of growing cell populations is crucial for unraveling key biological mechanisms in living organisms, with many important applications in therapeutics and biochemical engineering. Classical agent-based simulation algorithms are often inefficient for these systems because they track each individual cell, making them impractical for fast (or even exponentially) growing cell populations. To address this challenge, we introduce a novel stochastic simulation approach based on a Feynman-Kac-like representation of the population dynamics. This method, named the Feynman-Kac-inspired Gillespie's Stochastic Simulation Algorithm (FKG-SSA), always employs a fixed number of independently simulated cells for Monte Carlo computation of the system, resulting in a constant computational complexity regardless of the population size. Furthermore, we theoretically show the statistical consistency of the proposed method, indicating its accuracy and reliability. Finally, a couple of biologically relevant numerical examples are presented to illustrate the approach. Overall, the proposed FKG-SSA effectively addresses the challenge of simulating growing cell populations, providing a solid foundation for better analysis of these systems.