Perivascular pumping in the mouse brain: Realistic boundary conditions reconcile theory, simulation, and experiment

We measured hydraulic resistance and compliance using bolus injection, an approach introduced by Marmarou et al. (1). We injected fluid briefly and rapidly, measuring the resulting change in intracranial pressure (ICP), to estimate an impulse response, approximating the CSF pathway as a linear RC system. All experiments were approved by the University Committee on Animal Resources of the University of Rochester Medical Center (Protocol No. 2011-023), and an effort was made to minimize the number of animals used. We used 8- to 12-week-old male C57BL/6 mice acquired from Charles River Laboratories (Wilmington, MA, USA). In all experiments, animals were anesthetized with a combination of ketamine (100 mg/kg) and xylazine (10 mg/kg) administered intraperitoneally. Depth of anesthesia was determined by the pedal reflex test. Body temperature was maintained at 37.5C with a rectal probe-controlled heated platform, and ECG and respiratory rate were monitored using a small animal physiological monitoring system (Harvard Apparatus). Anesthetized mice were fixed in a stereotaxic frame, and two cannulae were implanted into the right lateral ventricle (0.85 mm lateral, 2.10 mm ventral and 0.22 mm caudal to bregma) and the cisterna magna, as previously described (2). Using a computer-controlled syringe pump (Harvard Apparatus Pump 11 Elite), we injected V = 5 μL of artificial CSF (126 mM NaCl, 2.5 mM KCl, 1.25 mM NaH2PO4, 2 mM MgSO4, 2 mM CaCl2, 10 mM glucose, 26 mM NaHCO3; pH 7.4 when gassed with 95% O2 and 5% CO2) at 1 μL/s into the right lateral ventricle. We monitored ICP via the cisterna magna cannulation connected to a transducer attached to a pressure monitor (BP-1, World Precision Instruments Inc., Sarasota, FL). We have verified that the results do not change appreciably if we instead inject into the cisterna magna and measure ICP in the ventricle. We calculated the compliance C from the pressure-volume index (PVI): C = 0.4343·PVI/P0. The PVI is defined as the volume of fluid required to cause a tenfold pressure increase during bolus injection: PVI=V/(log10⁡[P_max/P_0]) The resistance R can be estimated as: R=(t·P_0)/(PVI·log10[P(t)·(P_max-P_0 )/(P_max·(P(t)-P_0))]) where P(t) is the pressure measured at time t. We expect R to be nearly constant, but to increase accuracy, we estimate R for each animal by averaging the results of the above equation to five evenly-spaced times during the experiment. 1. Marmarou A, Shulman K, Rosende RM (1978) A nonlinear analysis of the cerebrospinal fluid system and intracranial pressure dynamics. J Neurosurg 48(3):332–344. 2. Xavier AL, et al. (2018) Cannula implantation into the cisterna magna of rodents. JoVE (Journal of Visualized Experiments) (135):e57378.本研究采用弹丸式注射（bolus injection）方法测定液压阻力与顺应性，该方法由Marmarou等人(1)提出。我们以短暂快速的方式注射流体，同时记录由此引发的颅内压（intracranial pressure, ICP）变化，以此估算脉冲响应，并将脑脊液通路（cerebrospinal fluid pathway, CSF pathway）近似为线性RC系统。所有实验均经罗切斯特大学医学中心动物资源委员会批准（实验方案编号：2011-023），并尽可能减少实验动物的使用数量。本研究使用的实验动物为8~12周龄雄性C57BL/6小鼠，购自美国马萨诸塞州威尔明顿市查尔斯河实验室（Charles River Laboratories）。所有实验中，实验动物均采用氯胺酮（ketamine，100 mg/kg）与甲苯噻嗪（xylazine，10 mg/kg）复合制剂进行腹腔内（intraperitoneally）麻醉。麻醉深度通过足趾反射试验（pedal reflex test）判定。通过直肠探头控温加热台将动物体温维持在37.5℃，并采用小型动物生理监测系统（small animal physiological monitoring system，哈佛仪器公司Harvard Apparatus）监测心电图与呼吸频率。将麻醉后的小鼠固定于立体定位仪（stereotaxic frame）中，按照此前报道的方法(2)，向右侧侧脑室（相对于囟门（bregma）：外侧0.85 mm、腹侧2.10 mm、尾侧0.22 mm）与小脑延髓池（cisterna magna）分别植入两根套管。使用计算机控制的注射泵（syringe pump，哈佛仪器公司Pump 11 Elite型，Harvard Apparatus Pump 11 Elite）以1 μL/s的流速向右侧侧脑室注入5 μL人工脑脊液（artificial cerebrospinal fluid, artificial CSF），其配方为：126 mM NaCl、2.5 mM KCl、1.25 mM NaH₂PO₄、2 mM MgSO₄、2 mM CaCl₂、10 mM葡萄糖、26 mM NaHCO₃；在95% O₂与5% CO₂混合气下pH为7.4。通过连接至压力监测仪（pressure monitor，BP-1型，世界精密仪器公司World Precision Instruments Inc.，美国佛罗里达州萨拉索塔市）的传感器（transducer）的小脑延髓池套管监测ICP。本研究已验证，若改为向小脑延髓池注射并在侧脑室内测量ICP，实验结果无显著变化。 本研究通过压力容积指数（pressure-volume index, PVI）计算顺应性C：C = 0.4343·PVI/P₀。压力容积指数PVI被定义为弹丸式注射过程中使颅内压升高至初始值10倍所需的流体体积，计算公式为： $$ ext{PVI} = frac{V}{log_{10}left(frac{P_{ ext{max}}}{P_0} ight)}$$ 阻力R的估算公式如下： $$displaystyle R = frac{tcdot P_0}{ ext{PVI}cdotlog_{10}left( P(t)cdotfrac{P_{ ext{max}} - P_0}{P_{ ext{max}}cdot(P(t) - P_0)} ight)}$$ 其中$P(t)$为时刻$t$测得的颅内压。理论上R应近似为恒定值，为提升计算精度，本研究对每只动物均取实验过程中5个均匀分布的时间点的上述方程计算结果的平均值，以得到最终的R值。 参考文献： 1. Marmarou A, Shulman K, Rosende RM (1978) 脑脊液系统与颅内压动力学的非线性分析。《神经外科杂志》（*J Neurosurg*）48(3):332–344. 2. Xavier AL 等 (2018) 啮齿类动物小脑延髓池套管植入术。《JoVE（可视化实验杂志）》（*JoVE (Journal of Visualized Experiments)*）(135):e57378.