Parametric and nonparametric modeling of cerebral hemodynamics

2016-08-08This manuscript focuses on the application of mathematical modeling to the study of cerebral hemodynamics. The central goal is to contribute to the pursuit of providing a reliable and practical approach to the management of clinical conditions relating to cerebral vascular and cognitive dysfunction. In particular, we study two fundamental processes of cerebral hemodynamics, cerebral autoregulation (CA) and vasomotor reactivity (VR) to CO₂ tension, using modeling techniques that provide quantitative information about the two processes. Quantitative assessment of CA and VR in humans serves as an important modeling goal, due to the observed association between cerebrovascular structure and function in the outcome of head injury, hypertension, stroke, vascular dementia, Alzheimer’s disease, and other forms of cognitive impairment. The availability of non-invasive measurements of relevant hemodynamic data has provided a means to obtain objective measures of CA and VR. It is believed that the relationship between time variations in cerebral perfusion pressure (CPP) and cerebral blood flow velocity can reflect relevant information about the status of CA in humans. In addition, it is well-known that CO₂ tension significantly influences the cerebral vasculature under physiological conditions, and the relationship between variations in CO₂ tension and cerebral perfusion is accepted as an approximation of the status of VR. Mathematical models of various forms have been employs as the methodological framework in which information about cerebral vascular status is summarized, analyzed, and interpreted. These models can be classified generally as “hypothesis-based” (or mechanistic) and “data-based” (or inductive). In the hypothesis-based approach, parametric models are constructed in the form of differential and/or algebraic equations from first hemodynamic principles in attempt to explicate the observed data. The main benefit of these models is the ability to derive physiological meaning, since the parameters which characterize the model are given meaning a priori. However, one important challenge is the virtually unavoidable oversimplification of the true depth of system, risking an incomplete and superficial picture of the actual system. This disadvantage can be supplemented by the use of inductive models, which are not hindered by simplifying assumptions about the system, but are instead obtained directly from measured data. Thus the data-based models are nonparametric in nature and their depth of the system depends on the richness of the data. These models are typically much easier to obtain (using a computer), and knowledge about the system is not required. However, the challenge of the data-based approach is the difficulty in achieving clear physiological interpretation for the model, which says nothing explicitly about the system