Effect of fractional blood flow on plasma skimming in the microvasculature

Abstract

Although redistribution of red blood cells at bifurcated vessels is highly dependent on flow rate, it is still challenging to quantitatively express the dependency of flow rate in plasma skimming due to nonlinear cellular interactions. We suggest a plasma skimming model that can involve the effect of fractional blood flow at each bifurcation point. For validating the new model, it is compared with in vivo data at single bifurcation points, as well as microvascular network systems. In the simulation results, the exponential decay of plasma skimming parameter, M , along fractional flow rate shows the best performance in both cases.Red blood cells (RBCs) in microvessels are concentrated on the vessel core. Subsequently, a cell-free layer (CFL) with a few micrometer thickness is observed on the vessel wall. The CFL leads asymmetric redistribution of hematocrit at each bifurcation, called plasma skimming effect. As a continuous process of plasma skimming in microvascular networks, the average hematocrit in capillary beds is lower than the systemic hematocrit as reported in many previous studies [1][2][3][4][5][6][7][8]. Interestingly, the plasma skimming is recently revisited to develop new microchannels for detecting specific DNAs, proteins and cells by efficiently separating plasma from whole blood [9][10][11]. Also, it has been highlighted to accurately predict drug carrier distribution in the microvasculature [12][13][14][15][16][17][18]. For utilizing the plasma skimming to new applications in vitro and in vivo, it is crucial to quantitatively predict the redistribution of RBCs and plasma at bifurcations.From the early 70s, several experiments for quantifying the plasma skimming were performed [2,[19][20][21][22][23] In this paper, we aim to mathematically model fractional blood flow in a simple and generalized manner in order to computationally study its significance in plasma skimming, and also to accurately predict plasma skimming in the microvasculature. For this task, a recently developed plasma skimming model [26] is taken, and extended to take into account the effect of fractional blood flow. This new model is then validated with experimental data at single bifurcation level, and also at microvascular network level.While there are other plasma skimming models [25,27], the model developed by Gould and Linninger [26] is considered due to its easy extensibility. The model is as follows:where H is the hematocrit, M is the plasma skimming parameter, ζ is the hematocrit change coefficient due to plasma skimming, Q is the flow rate, A is the crosssectional area of each vessel, and subscript 0, 1, and 2 indicate the parent, and two daughter vessels, respectively. Specifically, the plasma skimming parameter M is related to the cross-sectional distribution of RBCs near bifurcation. Small M represents that RBCs are highly concentrated on the vessel core. In other words, plasma dominant region, or CFL, is developed on the near wall region. The two separated regions, expressed as RBCs and plasma areas, lead to strong...

Abnormal morphology biases haematocrit distribution in tumour vasculature and contributes to heterogeneity in tissue oxygenation

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