Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral hemodynamics. In this work, a mathematical model of cerebral hemodynamics and intracranial pressure (ICP) dynamics, developed in previous years, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the ICP-volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular hemodynamics and cannot only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions.

We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions.

Based on the results, we believe the model would be useful to teach complex relationships of brain hemodynamics and study clinical research questions such as the optimal head-up position, the effects of intracranial hemorrhage on cerebral hemodynamics, as well as the best CO(2) concentration, to reach the optimal compromise between intracranial pressure and perfusion. With the ability to vary the model's complexity, we believe it would be useful for both beginners and advanced learners. The model could also be used by practicing clinicians to model individual patients (entering the effects of needed clinical manipulations and then running the model to test for optimal combinations of therapeutic maneuvers).

This work investigates the complex relationships between cerebrovascular dynamics, intracranial pressure (ICP), Cushing response, and short-term systemic regulation via an original mathematical model. The model has been used to analyze the effects of Cushing response on cardiovascular and cerebrovascular quantities during constant ICP elevation and during the occurrence of ICP plateau waves and to investigate the conditions leading to system instability with the formation of slow (0.05-0.1 Hz) arterial pressure waves. The model may be of value to assist clinicians in finding the balance between clinical benefits of Cushing response and its shortcomings.

Conditions characterized by a fall in cardiac output are associated with alterations in cardiopulmonary variables and activation of cardiovascular and respiratory control mechanisms. In order to study these complex relationships, we developed a comprehensive cardiopulmonary model consisting of a circulation, a respiration and a metabolism block. In this work, the model is used to simulate cardiovascular dynamics in pathological conditions with an acute decrease in heart function. In particular, two conditions are examined: the first is characterized by a decrease in heart contractility, simulated in the model via a reduction in the left ventricular end-systolic elastance. The second consists in an increase in pulmonary arterial resistance, associated with pulmonary embolism. In conclusion, the proposed model may be of value in clinical settings to illustrate the complex relationship among cardiovascular variables.