Estimating brain microvascular blood flows from partial two-photon microscopy data by computation with a circuit model

Abstract

The cortical microvasculature plays a key role in cortical tissue health by transporting important molecules via blood. Disruptions to blood flow in the microvasculature due to events such as stroke can thus induce damage to the cortex. Recent developments in two-photon microscopy have enabled in vivo imaging of anesthetized rat cortex in three dimensions. The microscopy data provide information about the geometry of the cortical microvasculature, length and diameter of the vessels in the imaged microvasculature network, and blood flow through a subset of those vessels. We demonstrate a model that achieves three goals. First, given a network of interconnected vessels and flow measurements on a subset of those vessels, we can estimate the flows in the remaining vessels. Second, we can determine which and how many vessels should have blood flow measurements taken to provide sufficient information to predict the unmeasured flows. Finally, the model enables us to predict effects of blockages in one or more vessels, indicating which vessels are most important to overall flow in the network.

Model‐based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach

“…Other approaches to constrain boundary conditions include the use of literature values for boundary conditions, ensuring identifiability by searching for a “minimum‐norm solution”, and constraining boundary conditions by minimizing the deviance between simulated segment pressures and shear stresses and literature values . Exact literature boundary conditions could easily be incorporated into the probabilistic analysis framework by defining corresponding boundary prior distributions as Dirac delta functions located at the exact literature values.…”

“…This is an important feature in microvascular modeling since model inputs and parameters (eg, pressure and hematocrit boundary conditions) are typically not directly observable but at the same time have profound impact on the simulation model's performance . Furthermore, this parameter uncertainty can be propagated through the simulation model to quantify uncertainty related to the model's predictions. Although being computationally expensive compared to existing analysis methodologies, the Bayesian analysis coupled with MCMC sampling requires a rather reasonable runtime on a standard computer, ie, the analysis will not be a significant bottleneck in the microcirculatory data acquisition and processing chain. Exploration of high‐dimensional parameter spaces by MCMC is challenging .…”

“…23 Least-squares estimation has indeed proven useful in a series of studies focused on combining microcirculatory measurements and literature knowledge with model simulations. 9,13,17,24 However, in the presence of incomplete and imperfect experimental data, this optimization problem may become underdetermined and further (strong) assumptions are required, eg, to search for a solution that minimizes the Euclidean norm of the residuals 17 or to impose exact literature boundary conditions. 24 Furthermore, optimization leads to a single estimate of the best parameter values, and the uncertainties of the model's predictions are therefore not directly available.…”

“…• Although being computationally expensive compared to existing analysis methodologies, 13,15,17,24 the Bayesian analysis coupled with MCMC sampling requires a rather reasonable runtime on a standard computer, ie, the analysis will not be a significant bottleneck in the microcirculatory data acquisition and processing chain. Exploration of high-dimensional parameter spaces by MCMC is challenging.…”

“…9,15 Recent approaches determine pressure boundary conditions by minimizing the difference between observed and modeled flow directions or velocity, or between literature and modeled pressures and vessel wall shear stresses. 13,16,17 The information which can be obtained by combining model simulations with experimental measurements in a network-oriented analysis is limited by the uncertainties which inevitably arise from measurement errors and uncertainties regarding vascular topology, morphology, and model structural and parameter uncertainty. In this study, we present a Bayesian probabilistic approach to address this challenge.…”