The Problem of Estimating Tissue Perfusion from Observations of Microvascular Flow

Abstract

The perfusion of a tissue region is defined as the blood flow rate to the region divided by its volume. For a whole organ, this definition is unambiguous, but a problem arises for small tissue regions, with many microvessels crossing the boundaries. The total inflow rate is approximately proportional to the surface area of the region. If this inflow rate is used to estimate the perfusion, the result is approximately proportional to the surface‐area‐to‐volume ratio, and yields unrealistically high estimates for small regions. How, then, should tissue perfusion be estimated from observations or simulations of blood flow in small tissue regions? The discrepancy arises because any flow pathway that passes through a small tissue region also contributes to perfusion of regions upstream and/or downstream. Therefore, the flow on that pathway should be only partially attributed to the given region. Here, a method is proposed for estimating perfusion in a region of tissue. The blood flow on any pathway through the region is attributed to the region in proportion to the decline in blood oxygen content that occurs in the region, divided by the overall decline from arterial to venous oxygen content. If the chosen region is representative of the tissue with regard to oxygen consumption rate, then the local perfusion computed by this method is equal to the overall tissue perfusion. Implementation of this method requires simulation of oxygen transport in the microvascular network supplying the region, which can be done efficiently using a Green’s function method. In these simulations, boundary segments are classified as arterioles, capillaries and venules, and outflow oxygen levels in each category are used to define inflow oxygen boundary conditions. When applied to a network from the mouse cortex containing 4908 segments, this method yields estimates of perfusion consistent with whole‐organ values, resolving the discrepancy between microscale and macroscale estimates. Tissue perfusion is closely related to the oxygen extraction ratio, which is a key determinant of tissue oxygen levels. Therefore, the estimation of tissue perfusion is an important step towards realistic assessment of the effects of microvascular network structure and blood flow on tissue oxygenation.Support or Funding InformationSupported by NIH grant HL133362.