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Cardiovascular Engineering

Cardiovascular Engineering - Poster Session A

Poster H7 - A Mathematical Model of the Myogenic Response in Cerebral Arterioles

Thursday, October 24, 2024
10:00 AM - 11:00 AM EST
Location: Exhibit Hall E, F & G

Introduction:  The microcirculation responds rapidly and precisely to different stimuli in the brain to adjust local blood perfusion based on demands. This process is critical for brain functioning and its dysregulation contributes to pathological conditions. In response to an increase in blood pressure cerebral arteries constrict. At a macroscale this allows for a stable blood supply to the brain independently of pressure fluctuations (myogenic autoregulation). At a microscale, myogenic responses in small penetrating arterioles may regulate blood distribution in the brain and localized changes in blood supply. Pressure increases are sensed by Vascular Smooth Muscle Cells (SMC) that respond by elevating cytosolic Ca2+ levels, engaging the contractile apparatus yielding an increase in circumferential stress and constriction. Non-Selective Cation channels (NSCs) may play a primary role as sensors of the pressure elevations. Their opening depolarizes the cell membrane, opens Voltage-Operated Calcium channels (VOCCs) leading to an increase in transmembrane Ca2+ influx. Mathematical modeling can assist experimentation in elucidating the mechanisms underlying the microvascular control of cerebral blood flow (CBF). In this study, we developed an SMC model of electrophysiology and Ca2+ dynamics and integrated it with a minimal model of arteriole biomechanics. The model can capture the dynamics of Ca2+ and membrane potential in SMCs and the diameter response of arterioles as pressure changes.

Materials and

Methods:  The SMC model accounts for cell membrane electrophysiology and calcium dynamics as previously described (Kapela et al, 2008). It accounts for main components of the cell membrane and intracellular Ca2+ stores (Fig.1). Several ion channels (including calcium-activated K+ (BKCa), non-selective cation (NSC), inward rectifying K+ (Kir), voltage-operated Ca2+ (VOCC)), ion pumps and exchangers determine ionic balances and Membrane potential (Vm) at test and during stimulation. Intracellular stores with IP3 (IP3R) and ryanodine (RyR) receptor channels are included.
A minimal biomechanics model relates cytosolic Ca2+ in SMCs with the circumferential stress of the arteriole (Fig.2). An exponential stress-strain relationship accounts for the passive elastic properties of the vessel wall. A bell-shaped dependence of the maximum active SMC force on length is assumed. The degree of SMC activation (Atone), is assumed to have a sigmoidal relationship with [Ca2+]i (Eq. 1), where KMCa is the [Ca2+]i at half maximal active tone and ntone is the Hill coefficient. Active stress (σa) dependence on SMC Ca2+ is assumed to follow a Hill equation. Laplace law relates total stress (active σa and passive σp) to pressure (P), diameter (D) and arteriolar wall thickness (h). We assume that the open probability of NSC channels depends on σtot effectively accounting for the opening of NSC as pressure increases. By activating NSC channels, which induce Ca2+ influx and enhance contractility, thereby recapitulating myogenic autoregulation.
σ_tot= PD/2h= σ_p+A_tone σ_a A_tone= ([Ca^(2+) ]_i^(n_tone ))/([Ca^(2+) ]_i^(n_tone )+K_MCa^(n_tone ) ) (Eq. 1)

Results, Conclusions, and Discussions: The model can satisfactorily capture experimental data for the changes in SMC Ca2+, Vm and the constriction of arteriolar diameter as pressure increases (Fig. 3). In the absence of active tone (i.e. passive vessel biomechanics, dotted blue line) the model predicts SMC dilation as pressure values increase, consistent with experiments under zero extracellular Ca2+ concentration. The model supports a central role of NSC channels in this process. Stress-induced opening of NSC channels can substantially increase transmembrane Ca2+ influx, directly through the open NSCs or by opening of VOCCs following the NSC-induced membrane depolarization. The level of Ca2+ elevation can yield physiologically relevant constrictions to maintain global perfusion levels or to tightly regulate local blood supply. This model will serve as a basis to develop integrated models of blood flow control in the brain that will incorporate realistic network reconstructions, detailed description of network hemodynamics and biotransport model of oxygen delivery to tissue.

Acknowledgements (Optional):  This work is supported by the National Institute of Neurological Disorders and Stroke and the National Institute of Aging of the NIH under award number R01NS19971.