Predicting retinal tissue oxygenation using an image-based theoretical model

Abstract

Impaired oxygen delivery and tissue perfusion have been identified as significant factors that contribute to the loss of retinal ganglion cells in glaucoma patients. This study predicts retinal blood and tissue oxygenation using a theoretical model of the retinal vasculature based on confocal microscopy images of the mouse retina. These images reveal a complex and heterogeneous geometry of vessels that are distributed non-uniformly into multiple distinct retinal layers at varying depths. Predicting oxygen delivery and distribution in this irregular arrangement of retinal microvessels requires the use of an efficient theoretical model. The model employed in this work utilizes numerical methods based on a Green's function approach to simulate the spatial distribution of oxygen levels in a network of retinal blood vessels and the tissue surrounding them. Model simulations also predict the blood flow rates and pressures in each of the microvessels throughout the entire network. As expected, the model predicts that average vessel PO decreases as oxygen demand is increased. However, the standard deviation of PO in the vessels nearly doubles as oxygen demand is increased from 1 to 8 cm O/100 cm/min, indicating a very wide spread in the predicted PO levels, suggesting that average PO is not a sufficient indicator of oxygenation in a heterogeneous vascular network. Ultimately, the development of this mathematical model will help to elucidate the important factors associated with blood flow and metabolism that contribute to the vision loss characteristic of glaucoma.

Metabolic Signaling in a Theoretical Model of the Human Retinal Microcirculation

“…To validate this mouse-to-man conversion process, it is noted that an assumed pressure drop of 16 mmHg along the human arteriolar network [2] corresponds to a total flow of 36,670 nL/min to the human retinal microcirculation, which is consistent with the flows measured in human retina [15,16]. [8,9], as described in [7]. (B) Heterogeneous human arteriolar network developed by modifying the mouse model in panel (A) in the following ways: reducing the number of main branches from six to four, rotating the four main branches according to oximetry images, and increasing vessel diameters and lengths by a scaling factor of 3.6 and 5.9, respectively.…”

“…where Q is the volumetric blood flow rate in an individual vessel segment, ∆P is the pressure drop along the vessel, D is the diameter of the blood vessel, L is the vessel length, and µ is the apparent viscosity, which was assumed dependent on the diameter and hematocrit of the blood vessel based on the diameter-dependent relationship previously established by Pries et al [18]. Conservation of mass was imposed at every junction in the network, which allows for the flow rate, hematocrit, and apparent viscosity to be calculated in each arteriole using an iterative scheme [19], described in detail in [7]. Initial pressure and flow conditions for the capillary compartment were obtained from the predictions in the terminal arterioles of the heterogeneous arteriolar network.…”

“…In the spatially heterogeneous arteriolar network, a Green's function method [23,24] was used to solve Equation (2), where the vessels were modeled as discrete oxygen sources, and the tissue points were represented as oxygen sinks [7,[23][24][25]. The resulting P O2 at a tissue point was then calculated as the superposition of the oxygen fields (Green's functions) produced by each of the surrounding sources and sinks.…”

Microcirculatory model predicts blood flow and autoregulation range in the human retina: in vivo investigation with laser speckle flowgraphy

“…Therefore, it might ignore local variations attributed to anatomy or to disease-related focal microvascular dropout, outside the ROI (17,93,146). A more accurate representation of the vasculature would contribute to the understanding of crucial phenomena, such as localized flow deficits or tissue oxygen extraction and diffusion (36). However, adapting more heterogeneous or three-dimensional theoretical models to account for individualized estimations in the human eye would require further improvements in visualization and quantification of the interconnectivity between different capillary plexus.…”

Neurodegenerative Disorders of the Eye and of the Brain: A Perspective on Their Fluid-Dynamical Connections and the Potential of Mechanism-Driven Modeling

“…As a result, only few mechanism-driven models are currently available to study the interaction among diverse biophysical aspects of ocular physiology. Examples include models coupling biomechanics and hemodynamics (Guidoboni et al, 2014a,b,c;Arciero et al, 2019;Sala, 2019) and models coupling hemodynamics and oxygenation (Arciero et al, 2013(Arciero et al, , 2019Causin et al, 2016;Carichino et al, 2016;Fry et al, 2018).…”