PERFORM Centre, Concordia University, Montreal, Canada; Electrical and Computer Engineering Department, Concordia University, Montreal, Canada.
University of Rennes, INSERM, LTSI-UMR 1099, F-35000, Rennes, France.
J Theor Biol. 2023 Nov 7;575:111648. doi: 10.1016/j.jtbi.2023.111648. Epub 2023 Oct 21.
Emerging evidence emphasizes lactate's involvement in both physiological processes (energy metabolism, memory, etc.) and disease (traumatic brain injury, epilepsy, etc.). Furthermore, the usefulness of mathematical modeling in deciphering underlying dynamics of the brain to investigate lactate roles and mechanisms of action has been well established. Here, we analyze a novel mathematical model of brain lactate exchanges between four compartments: neurons, astrocytes, capillaries, and extracellular space. A system of four ordinary differential equations is proposed to explain interactions between these compartments. We first optimize and analyze the model's parameters under normal, resting state conditions, and then use it to simulate changes linked to elevated arterial lactate. Our results show that even though increased arterial lactate results in increased uptake by astrocytes and release to the extracellular space, it cannot strongly recover the initial drop in neuronal lactate concentration. Also, we show that the direction of lactate transport between the compartments is influenced by the maximum astrocyte production rate and the transport rate between astrocytes and extracellular space.
新出现的证据强调了乳酸在生理过程（能量代谢、记忆等）和疾病（创伤性脑损伤、癫痫等）中的作用。此外，数学建模在揭示大脑潜在动力学以研究乳酸作用和作用机制方面的有用性已得到充分证实。在这里，我们分析了一个新的大脑乳酸在四个隔室（神经元、星形胶质细胞、毛细血管和细胞外空间）之间交换的数学模型。提出了一个四阶常微分方程组来解释这些隔室之间的相互作用。我们首先在正常、休息状态下优化和分析模型的参数，然后使用它来模拟与动脉乳酸升高相关的变化。我们的结果表明，尽管动脉乳酸增加会导致星形胶质细胞摄取增加和向细胞外空间释放增加，但它不能强烈恢复神经元乳酸浓度的初始下降。此外，我们还表明，隔室之间乳酸转运的方向受星形胶质细胞最大生成率和星形胶质细胞与细胞外空间之间转运率的影响。
