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Research Papers

# Numerical Study on Flows of Red Blood Cells With Liposome-Encapsulated Hemoglobin at Microvascular Bifurcation

[+] Author and Article Information
Toru Hyakutake1

Okayama University, 3-1-1, Tsushimanaka, Okayama 700-8530, Japanhyaku@mech.okayama-u.ac.jp

Shouko Tominaga, Shinichiro Yanase

Okayama University, 3-1-1, Tsushimanaka, Okayama 700-8530, Japan

Takeshi Matsumoto

Osaka University, 1-3, Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan

1

Corresponding author.

J Biomech Eng 130(1), 011014 (Feb 12, 2008) (7 pages) doi:10.1115/1.2838024 History: Received December 11, 2006; Revised June 14, 2007; Published February 12, 2008

## Abstract

Flow analysis at microvascular bifurcation after partial replacement of red blood cell (RBC) with liposome-encapsulated hemoglobin (LEH) was performed using the lattice Boltzmann method. A two-dimensional symmetric Y bifurcation model with a parent vessel diameter of $20μm$ and daughter branch diameters of $20μm$ was considered, and the distributions of the RBC, LEH, and oxygen fluxes were calculated. When only RBCs flow into the daughter branches with unevenly distributed flows, plasma separation occurred and the RBC flow to the lower-flow branch was disproportionately decreased. On the other hand, when half of RBC are replaced by LEH, the biasing of RBC flow was enhanced whereas LEH flowed favorably into the lower-flow branch, because many LEH within the parent vessel are suspended in the plasma layer, where no RBCs exist. Consequently, the branched oxygen fluxes became nearly proportional to flows. These results indicate that LEH facilitates oxygen supply to branches that are inaccessible to RBCs.

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Copyright © 2008 by American Society of Mechanical Engineers
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## Figures

Figure 5

Relationship between fractional RBC flux (N1R∕NpR) and fractional flow (Q1∕Qp) into the daughter branch b1. The hematocrit HtR is 0.30. The open circles denote the plasma layer thickness ht=4.7μm, and the filled circles denote ht=2.4μm. The solid line is obtained by Pries’ model, and the dotted line denotes the condition whereby N1R∕NpR is equal to Q1∕Qp.

Figure 4

Images of RBCs passing through the bifurcation at three time points. The hematocrit HtR is 0.30, and the plasma layer thickness in the parent vessel is 2.4μm. The upper figure (a) shows the case of the fractional flow into daughter branch b1, Q1∕Qp=0.15, and the lower figure (b) shows the case of Q1∕Qp=0.50. The red filled circles denote RBCs.

Figure 3

Distributions of RBCs flowing through the bifurcation and profiles of plasma velocity contours. The hematocrit HtR is 0.30 and the plasma layer thickness ht is 2.4μm. The upper figure (a) shows the case of the fractional flow into daughter branch b1, Q1∕Qp=0.15, and the lower figure (b) shows the case of Q1∕Qp=0.50. Contours are normalized as ∣u∣∕um, where um is the mean entrance velocity in the parent vessel. The black filled circles denote RBCs.

Figure 2

(a) Lattice grids surrounding a RBC and a closed surface S. The gray domain denotes the wall of the RBC. (b) Binary collision between particles m and n. Particles m and n collide when surface Sm touches surface Sn.

Figure 1

A two-dimensional symmetric Y bifurcation geometry showing the relationship between the parent vessel and two daughter branches, b1 and b2. Superscripts R and L indicate RBC and LEH, respectively.

Figure 6

Images of RBCs passing through the bifurcation at three time points. The hematocrit HtR is 0.15, and the volume fraction of LEH HtL is 0.15. The plasma layer thickness in the parent vessel is 2.4μm. The upper figure (a) shows the case in which the fractional flow into daughter branch b1 is Q1∕Qp=0.15, and the lower figure (b) shows the case in which Q1∕Qp=0.50. The red filled circles denote RBCs, and the green dots denote LEHs.

Figure 7

Relationship between fractional RBC or LEH fluxes (N1R∕NpR or N1L∕NpL) and fractional flow (Q1∕Qp) into the daughter branch b1. The hematocrit HtR is 0.15, and the volume fraction of LEH HtL is 0.15. The upper figure shows that the plasma layer thickness in the parent vessel ht is 2.4μm, and the lower figure shows that ht is 4.7μm. The filled triangles and open triangles denote N1R∕NpR and N1L∕NpL, respectively. The crosses denote N1R∕NpR of hemodilution without LEH (HtR=0.15, HtL=0).

Figure 8

Fractional oxygen supply into daughter branch b1 under the assumption that the oxygen carrying capacity per unit area of LEH is identical to that of RBC

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