Article

Oxygen advection and diffusion in a three-dimensional vascular anatomical network

Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts 02129, USA.
Optics Express (Impact Factor: 3.49). 11/2008; 16(22):17530-41. DOI: 10.1364/OE.16.017530
Source: PubMed

ABSTRACT

There is an increasing need for quantitative and computationally affordable models for analyzing tissue metabolism and hemodynamics in microvascular networks. In this work, we develop a hybrid model to solve for the time-varying oxygen advection-diffusion equation in the vessels and tissue. To obtain a three-dimensional temporal evolution of tissue oxygen concentration for realistic complex vessel networks, we used a graph-based advection model combined with a finite-element based diffusion model and an implicit time-advancing scheme. We validated this algorithm for both static and dynamic conditions. We also applied it to a complex vascular network obtained from a rodent somatosensory cortex. Qualitative agreement was found with in-vivo experiments.

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Available from: Sava Sakadzic, Dec 20, 2013
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    • "However, this model was extremely complex, including many parameters that necessitated a much more intricate fitting procedure; moreover, this model still relied on a venous dilation effects. Also, a 3D convection–diffusion model was developed for direct application to the complex measured topology of the vascular network (Fang et al., 2008). This model was then applied and expanded with multiple imaging techniques (two-photon microscopy, confocal microscopy, and fMRI) to consider the effect of individual vascular compartments on the BOLD signal (Gagnon et al., 2015). "
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    ABSTRACT: The blood oxygen level dependent (BOLD) signal evoked by brief neural stimulation, the hemodynamic response function (HRF), is a critical feature of neurovascular coupling. The HRF is directly related to local transient changes in oxygen supplied by cerebral blood flow (CBF) and oxygen demand, the cerebral metabolic rate of oxygen (CMRO2). Previous efforts to explain the HRF have relied upon the hypothesis that CBF produces a non-linear venous dilation within the cortical parenchyma. Instead, the observed dynamics correspond to prompt arterial dilation without venous volume change. This work develops an alternative biomechanical model for the BOLD response based on the hypothesis that prompt upstream dilation creates an arterial flow impulse amenable to linear description. This flow model is coupled to a continuum description of oxygen transport. Measurements using high-resolution fMRI demonstrate the efficacy of the model. The model predicts substantial spatial variations of the oxygen saturation along the length of capillaries and veins, and fits the varied gamut of measured HRFs by the combined effects of corresponding CBF and CMRO2 responses. Three interesting relationships among the hemodynamic parameters are predicted. First, there is an offset linear correlation with approximately unity slope between CBF and CMRO2 responses. Second, the HRF undershoot is strongly correlated to the corresponding CBF undershoot. Third, late-time-CMRO2 response can contribute to a slow recovery to baseline, lengthening the HRF undershoot. The model provides a powerful mathematical framework to understand the dynamics of neurovascular and neurometabolic responses that form the BOLD HRF.
    Preview · Article · Sep 2015 · NeuroImage
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    • "The distribution of dissolved oxygen in the brain has proven difficult to examine at the microvascular level under baseline conditions let alone after selective flow alterations due to methodological shortcomings of classical oximetry techniques. Empirical measurements are often still made outside the vascular lumen of large vessels through invasive Clark electrodes [1,2] from which mathematical models of oxygen delivery have been developed following the theory of advection-diffusion [3,4]. More recently, three-dimensional optical imaging techniques have been shown to provide hemodynamic characterization of microvascular beds with greater sensitivity and accessibility without significant physiological perturbation [5]. "
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    • "In animals, the emergence of new optical imaging techniques has provided unprecedented access to vascular anatomy and tissue perfusion [5]. Two photon microscopy (TPM) using labelled markers allows high resolution imaging of vascular networks. "
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