We present a dynamic microcirculation PIPE model for functional neuroimaging, non-neuroimaging, and coherent hemodynamics spectroscopy. The temporal evolution of the concentration and oxygen saturation of hemoglobin in tissue, comprised of the contributions from the arterioles, capillaries, and venules of microvasculature, is determined by time-resolved hemodynamic and metabolic variations in blood volume, flow velocity, and oxygen consumption with a fluid mechanics treatment. Key parameters regarding microcirculation can be assessed, including the effective blood transit times through the capillaries and the venules, and the rate constant of oxygen release from hemoglobin to tissue. The vascular autoregulation can further be quantified from the relationship between the resolved blood volume and flow velocity variations. The PIPE model shows excellent agreement with the experimental cerebral and cutaneous coherent hemodynamics spectroscopy (CHS) and fMRI-BOLD data. It further identifies the impaired cerebral autoregulation distinctively in hemodialysis patients compared to healthy subjects measured by CHS. This new dynamic microcirculation PIPE model provides a valuable tool for brain and other functional studies with hemodynamic-based techniques. It is instrumental in recovering physiological parameters from analyzing and interpreting the signals measured by hemodynamic-based neuroimaging and non-neuroimaging techniques such as functional near-infrared spectroscopy (fNIRS) and functional magnetic resonance imaging (fMRI) in response to brain activation, physiological challenges, or physical maneuvers.
Metabolic Signaling in a Theoretical Model of the Human Retinal Microcirculation
Impaired blood flow and oxygenation contribute to many ocular pathologies, including glaucoma. Here, a mathematical model is presented that combines an image-based heterogeneous representation of retinal arterioles with a compartmental description of capillaries and venules. The arteriolar model of the human retina is extrapolated from a previous mouse model based on confocal microscopy images. Every terminal arteriole is connected in series to compartments for capillaries and venules, yielding a hybrid model for predicting blood flow and oxygenation throughout the retinal microcirculation. A metabolic wall signal is calculated in each vessel according to blood and tissue oxygen levels. As expected, a higher average metabolic signal is generated in pathways with a lower average oxygen level. The model also predicts a wide range of metabolic signals dependent on oxygen levels and specific network location. For example, for high oxygen demand, a threefold range in metabolic signal is predicted despite nearly identical PO2 levels. This whole-network approach, including a spatially nonuniform structure, is needed to describe the metabolic status of the retina. This model provides the geometric and hemodynamic framework necessary to predict ocular blood flow regulation and will ultimately facilitate early detection and treatment of ischemic and metabolic disorders of the eye.
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- Award ID(s):
- 1654019
- NSF-PAR ID:
- 10331080
- Date Published:
- Journal Name:
- Photonics
- Volume:
- 8
- Issue:
- 10
- ISSN:
- 2304-6732
- Page Range / eLocation ID:
- 409
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019 ; Lee et al., 2020 ). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.more » « less
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Abstract Purpose To review retinal vein occlusion (RVO) and its relationship with retinal oxygen saturation via automated retinal oximetry in eyes with RVO.
Methods A literature review was performed in PubMed and Medline until October 2021 utilizing specific keywords and cross‐matched reference lists.
Results This review found RVO to be associated with risk factors including age, hypertension, cardiovascular and metabolic conditions, male gender, and glaucoma. These may be attributed to a breakdown of regulatory processes in the retina. Retinal venous oxygen saturation (SvO2) and arteriovenous difference in eyes with central RVO have been found to be reduced and elevated, respectively. The literature indicates variable and contradictory findings in regard to branch RVO and retinal oxygenation. Additionally, ischaemic eyes have been found to have elevated retinal arterial oxygen saturation; however, the literature reports variable results regarding SvO2levels. Medications have been suggested to increase SvO2in RVO eyes, which may represent an important mechanism for disease management. Ranibizumab is currently the most studied drug for retinal oxygenation in RVO and has been suggested to increase SvO2in RVO eyes. In comparison, dexamethasone was found to decrease SvO2.
Conclusion The current literature on retinal oxygenation in ischaemic subtypes of RVO and in drug therapies is minimal, and further work is required to expand upon our understanding of how ischaemia and drugs influence retinal oxygenation and clinical outcomes.
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/photonics8100409
