Domogo Andrei A, Reinstrup Peter, Ottesen Johnny T
Department of Mathematics and Computer Science, University of the Philippines Baguio, Baguio City 2600, Philippines; IMFUFA, Department of Science and Environment, Roskilde University, 4000 Roskilde, Denmark.
Intensive and Perioperative Care, Skåne University Hospital, Lund, Sweden.
J Theor Biol. 2023 May 7;564:111451. doi: 10.1016/j.jtbi.2023.111451. Epub 2023 Mar 11.
The intracranial pressure (ICP) curve with its different peaks has been comprehensively studied, but the exact physiological mechanisms behind its morphology has not been revealed. If the pathophysiology behind deviations from the normal ICP curve form could be identified, it could be vital information to diagnose and treat each single patient. A mathematical model of the hydrodynamics in the intracranial cavity over single heart cycles was developed. A Windkessel model approach was generalized but the unsteady Bernoulli equation was utilized for blood flow and CSF flow. This is a modification of earlier models using the extended and simplified classical Windkessel analogies to a model that is based on mechanisms rooted in the laws of physics. The improved model was calibrated with patient data for cerebral arterial inflow, venous outflow, cerebrospinal fluid (CSF), and ICP over one heart cycle from 10 neuro-intensive care unit patients. A priori model parameter values were obtained by considering patient data and values taken from earlier studies. These values were used as an initial guess for an iterated constrained-ODE (ordinary differential equation) optimization problem with cerebral arterial inflow data as input into the system of ODEs. The optimization routine found patient-specific model parameter values that produced model ICP curves that showed excellent agreement with clinical measurements while model venous and CSF flow were within a physiologically acceptable range. The improved model and the automated optimization routine gave better model calibration results compared to previous studies. Moreover, patient-specific values of physiologically important parameters like intracranial compliance, arterial and venous elastance, and venous outflow resistance were determined. The model was used to simulate intracranial hydrodynamics and to explain the underlying mechanisms of the ICP curve morphology. Sensitivity analysis showed that the order of the three main peaks of the ICP curve was affected by a decrease in arterial elastance, a large increase in resistance to arteriovenous flow, an increase in venous elastance, or a decrease in resistance to CSF flow in the foramen magnum; and the frequency of oscillations were notably affected by intracranial elastance. In particular, certain pathological peak patterns were caused by these changes in physiological parameters. To the best of our knowledge, there are no other mechanism-based models associating the pathological peak patterns to variation of the physiological parameters.
颅内压（ICP）曲线及其不同的峰值已得到全面研究，但其形态背后的确切生理机制尚未揭示。如果能够确定偏离正常ICP曲线形态背后的病理生理学，这对于诊断和治疗每一位患者而言可能是至关重要的信息。我们建立了一个单心动周期内颅腔内流体动力学的数学模型。采用了广义的风箱模型方法，但利用非稳态伯努利方程来描述血流和脑脊液流动。这是对早期模型的一种改进，早期模型使用扩展和简化的经典风箱类比，而改进后的模型基于物理定律的机制。利用10名神经重症监护病房患者一个心动周期内的脑动脉流入、静脉流出、脑脊液（CSF）和ICP的患者数据对改进后的模型进行校准。通过考虑患者数据和早期研究中的取值获得先验模型参数值。这些值被用作迭代约束常微分方程（ODE）优化问题的初始猜测值，将脑动脉流入数据作为ODE系统的输入。优化程序找到了患者特异性的模型参数值，这些值生成的模型ICP曲线与临床测量结果显示出极佳的一致性，同时模型静脉和脑脊液流动处于生理可接受范围内。与先前的研究相比，改进后的模型和自动优化程序给出了更好的模型校准结果。此外，还确定了生理重要参数的患者特异性值，如颅内顺应性、动脉和静脉弹性以及静脉流出阻力。该模型用于模拟颅内流体动力学，并解释ICP曲线形态的潜在机制。敏感性分析表明，ICP曲线三个主要峰值的顺序受动脉弹性降低、动静脉血流阻力大幅增加、静脉弹性增加或枕骨大孔处脑脊液流动阻力降低的影响；振荡频率尤其受颅内弹性的显著影响。特别是，这些生理参数的变化导致了某些病理性峰值模式。据我们所知，没有其他基于机制的模型将病理性峰值模式与生理参数的变化联系起来。
