Microbioreactors are a promising technology to accelerate biologic drug development. In aerobic cellular respiration, a potential limit to the productivity of such systems is the transport of oxygen from an external gas to the most oxygen-deficient cells, and the potential for excessive spatially localized dissolved oxygen which can result in cellular damage. This article analytically solves a mechanistic model for the spatiotemporal transport of oxygen through a gas-permeable membrane to the cells within a microbioreactor. An analytical solution to the partial differential equations for oxygen transport is derived using the finite Fourier transform method. A parameter-adaptive extended Kalman filter is shown to produce highly accurate estimates of the oxygen uptake rate of the cells, with some fluctuation in estimates of the specific cell growth rate and the specific oxygen uptake rate. The estimates are fed to a model predictive control formulation that improves the spatial control of dissolved oxygen during cell growth by more than 30% compared to a PID controller.

微生物反应器是加速生物药物开发的有前途的技术。在有氧细胞呼吸中，这种系统的生产率的潜在限制是氧气从外部气体向最缺氧的细胞的运输，以及在空间上局部溶解的氧气过多的潜力，这可能导致细胞损伤。本文分析性地解决了一种机制模型，该模型用于将氧通过透气膜时空传输到微生物反应器中的细胞。使用有限傅里叶变换法导出了用于氧气传输的偏微分方程的解析解。展示了一个参数自适应扩展卡尔曼滤波器，可以产生细胞氧吸收率的高精度估算值，特定细胞生长速率和特定氧气吸收速率的估算值会有一些波动。估计值将输入到模型预测控制公式中，与PID控制器相比，该模型将细胞生长过程中溶解氧的空间控制提高了30％以上。