An integrated lumped-parameter model of the cardiovascular system for the simulation of acute ischemic stroke: description of instantaneous changes in hemodynamics

Lorenzo Civilla; Agnese Sbrollini; Laura Burattini; Micaela Morettini; Lorenzo Civilla; Agnese Sbrollini; Laura Burattini; Micaela Morettini

doi:10.3934/mbe.2021200

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 4: 3993-4010. doi: 10.3934/mbe.2021200

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An integrated lumped-parameter model of the cardiovascular system for the simulation of acute ischemic stroke: description of instantaneous changes in hemodynamics

Department of Information Engineering, UniversitȤ Politecnica delle Marche, Ancona 60131, Italy

^† The authors contributed equally to this work.
Academic Editor: Alena Talkachova

Received: 02 February 2021 Accepted: 21 April 2021 Published: 08 May 2021

Acute Ischemic Stroke (AIS) is defined as the acute condition of occlusion of a cerebral artery and is often caused by a Hypertensive Condition (HC). Due to its sudden occurrence, AIS is not observable the right moment it occurs, thus information about instantaneous changes in hemodynamics is limited. This study aimed to propose an integrated Lumped Parameter (LP) model of the cardiovascular system to simulate an AIS and describe instantaneous changes in hemodynamics. In the integrated LP model of the cardiovascular system, heart chambers have been modelled with elastance systems with controlled pressure inputs; heart valves have been modelled with static open/closed pressure-controlled valves; eventually, the vasculature has been modelled with resistor-inductor-capacitor (RLC) direct circuits and have been linked to the rest of the system through a series connection. After simulating physiological conditions, HC has been simulated by changing pressure inputs and constant RLC parameters. Then, AIS occurring in arteries of different sizes have been simulated by considering time-dependent RLC parameters due to the elimination from the model of the occluding artery; instantaneous changes in hemodynamics have been evaluated by Systemic Arteriolar Flow (Q_a) and Systemic Arteriolar Pressure (P_a) drop with respect to those measured in HC. Occlusion of arteries of different sizes leaded to an average Q_a drop of 0.38 ml/s per cardiac cycle (with minimum and maximum values of 0.04 ml/s and 1.93 ml/s) and average P_a drop of 0.39 mmHg, (with minimum and maximum values of 0.04 mmHg and 1.98 mmHg). In conclusion, hemodynamic variations due to AIS are very small with respect to HC. A direct relation between the inverse of the length of the artery in which the occlusion occurs and the hemodynamic variations has been highlighted; this may allow to link the severity of AIS to the length of the interested artery.
- lumped parameter model,
- acute ischemic stroke,
- cardiovascular system,
- hemodynamics,
- initial conditions,
- computational model,
- hypertension,
- cerebral arteries
Citation: Lorenzo Civilla, Agnese Sbrollini, Laura Burattini, Micaela Morettini. An integrated lumped-parameter model of the cardiovascular system for the simulation of acute ischemic stroke: description of instantaneous changes in hemodynamics[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3993-4010. doi: 10.3934/mbe.2021200

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Abstract

Acute Ischemic Stroke (AIS) is defined as the acute condition of occlusion of a cerebral artery and is often caused by a Hypertensive Condition (HC). Due to its sudden occurrence, AIS is not observable the right moment it occurs, thus information about instantaneous changes in hemodynamics is limited. This study aimed to propose an integrated Lumped Parameter (LP) model of the cardiovascular system to simulate an AIS and describe instantaneous changes in hemodynamics. In the integrated LP model of the cardiovascular system, heart chambers have been modelled with elastance systems with controlled pressure inputs; heart valves have been modelled with static open/closed pressure-controlled valves; eventually, the vasculature has been modelled with resistor-inductor-capacitor (RLC) direct circuits and have been linked to the rest of the system through a series connection. After simulating physiological conditions, HC has been simulated by changing pressure inputs and constant RLC parameters. Then, AIS occurring in arteries of different sizes have been simulated by considering time-dependent RLC parameters due to the elimination from the model of the occluding artery; instantaneous changes in hemodynamics have been evaluated by Systemic Arteriolar Flow (Q_a) and Systemic Arteriolar Pressure (P_a) drop with respect to those measured in HC. Occlusion of arteries of different sizes leaded to an average Q_a drop of 0.38 ml/s per cardiac cycle (with minimum and maximum values of 0.04 ml/s and 1.93 ml/s) and average P_a drop of 0.39 mmHg, (with minimum and maximum values of 0.04 mmHg and 1.98 mmHg). In conclusion, hemodynamic variations due to AIS are very small with respect to HC. A direct relation between the inverse of the length of the artery in which the occlusion occurs and the hemodynamic variations has been highlighted; this may allow to link the severity of AIS to the length of the interested artery.

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