Williams Nakeya D, Brady Renee, Gilmore Steven, Gremaud Pierre, Tran Hien T, Ottesen Johnny T, Mehlsen Jesper, Olufsen Mette S
Mathematical Sciences Department, United States Military Academy, West Point, NY, USA.
Department of Integrated Mathematical Oncology, H Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA.
J Math Biol. 2019 Aug;79(3):987-1014. doi: 10.1007/s00285-019-01386-9. Epub 2019 May 31.
This study develops non-pulsatile and pulsatile models for the prediction of blood flow and pressure during head-up tilt. This test is used to diagnose potential pathologies within the autonomic control system, which acts to keep the cardiovascular system at homeostasis. We show that mathematical modeling can be used to predict changes in cardiac contractility, vascular resistance, and arterial compliance, quantities that cannot be measured but are useful to assess the system's state. These quantities are predicted as time-varying parameters modeled using piecewise linear splines. Having models with various levels of complexity formulated with a common set of parameters, allows us to combine long-term non-pulsatile simulations with pulsatile simulations on a shorter time-scale. We illustrate results for a representative subject tilted head-up from a supine position to a [Formula: see text] angle. The tilt is maintained for 5 min before the subject is tilted back down. Results show that if volume data is available for all vascular compartments three parameters can be identified, cardiovascular resistance, vascular compliance, and ventricular contractility, whereas if model predictions are made against arterial pressure and cardiac output data alone, only two parameters can be estimated either resistance and contractility or resistance and compliance.
本研究开发了非搏动性和搏动性模型，用于预测头高位倾斜期间的血流和压力。该测试用于诊断自主控制系统内的潜在病变，自主控制系统的作用是使心血管系统保持稳态。我们表明，数学建模可用于预测心脏收缩力、血管阻力和动脉顺应性的变化，这些量无法测量，但有助于评估系统状态。这些量被预测为使用分段线性样条建模的时变参数。拥有用一组通用参数制定的具有不同复杂程度的模型，使我们能够将长期非搏动性模拟与较短时间尺度上的搏动性模拟相结合。我们展示了一名代表性受试者从仰卧位到头高位倾斜至[公式：见正文]角度的结果。在受试者再倾斜回来之前，倾斜状态保持5分钟。结果表明，如果所有血管腔室的容积数据可用，则可以识别三个参数，即心血管阻力、血管顺应性和心室收缩力，而如果仅根据动脉压和心输出量数据进行模型预测，则只能估计两个参数，即阻力和收缩力或阻力和顺应性。
