CALCULATIONS OF OXYGEN TRANSPORT BY RED BLOOD CELLS AND HEMOGLOBIN SOLUTIONS IN CAPILLARIES

Figures & data

Figure 1. Schematic of computational domain with subregions RBC, plasma, vascular wall, interstitium and tissue.

Table 1. List of Model Parameters

Parameter	Value	Units	Source (Ref no.)
Tissue
α	3.88×10 ^−5	mlO 2 cm ^−3 mmHg ^−1	[[31]]
D O	2.41×10 ^−5	cm ^2/s	[[32]]
[Mb]	4×10 ^2	nmole/cm ^3	[[33]]
D Mb	6×10 ^−7	cm ^2/s	[[24]]
P 50 ^Mb	5.3	mm Hg	[[34]]
M t	1.58×10 ^−4	mlO 2ml ^−1s ^−1	[[15]]
Interstitium
α	2.81×10 ^−5	mlO 2 cm ^−3 mmHg ^−1	[[35]]
D O	2.18×10 ^−5	cm ^2/s	[[36]]
R i–R w	0.35×10 ^−4	cm	[[37]]
Wall
α	3.89×10 ^−5	mlO 2 cm ^−3 mmHg ^−1	[[31]]
D O	8.73×10 ^−6	cm ^2/s	[[38]]
M w	1×10 ^−4	mlO 2ml ^−1s ^−1	[[23]]
R w–R p	0.3×10 ^−4	cm	[[37]]
Plasma
[Hb] s	0, 4, 7, 10	g/dl	Model parameter
α	2.81×10 ^−5	mlO 2 cm ^−3 mmHg ^−1	[[39]]
D O		cm ^2/s	[[27]]
D Hb		cm ^2/s	[[27]]
k s	44	s ^−1	[[40]]
P 50,s ^Hb	10, 20, 29.3, 40, 50	mm Hg	Model parameter
n s	1, 2.2, 3.5		Model parameter
μ s	0.012	cP	[[21]]
R p	2.0×10 ^−4	cm	[[15]]
RBC
[Hb] c	34.0	g/dl	Model parameter
α	3.38×10 ^−5	mlO 2 cm ^−3 mmHg ^−1	[[35]]
D O		cm ^2/s	[[27]]
D Hb		cm ^2/s	[[27]]
k c	44	s ^−1	[[40]]
P 50,s ^Hb	29.3	mm Hg	[[15]]
n c	2.2		[[15]]
v c	150×10 ^−4	cm/s	[[41]]
V RBC	6.9×10 ^−11	cm ^3	[[35]]

Figure 2. Comparison of k_o, for different initial PO₂. P_50,c^Hb=P_50,s^Hb=29.3 Torr, n_c=n_s=2.2, [Hb]_s=7g/dl, H_c=0.2.

Figure 3. (A) Comparison of k _o for different values of HBOC oxygen affinities. P _50,c^Hb=29.3 Torr, n_c=n_s=2.2. H_c=0.2, [Hb] _s=7 g/dl. (B) Comparison of k_cell for different values of HBOC oxygen affinities. P_50,c^Hb=29.3 Torr, n_c=n_s=2.2, H_c=0.2, [Hb] _s=7 g/dl.

Figure 4. (A) Comparison of k _o for different values of HBOC oxygen cooperatives. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=2.2, H _c=0.2, [Hb] _s=7 g/dl. (B) Comparison of k _cell for different values of HBOC oxygen cooperatives. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=2.2, H _c=0.2, [Hb] _s=7 g/dl.

Figure 5. (A) Comparison of k _o for different values of HBOC concentrations. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=n _s=2.2, H _c=0.2. (B) Comparison of k _cell for different values of HBOC concentrations. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=n _s=2.2, H _c=0.2.

Figure 6. (A) Tissue PO ₂ distribution along capillary length for different HBOC oxygen affinities. P _50,c ^Hb=29.3 Torr, n _c=n _s=2.2, H _c=0.2, [Hb] _s=7 g/dl. (B) Radial tissue PO ₂ distribution profiles for different HBOC oxygen affinities. P _50,c ^Hb=29.3 Torr, n _c=n _s=2.2, H _c=0.2, [Hb] _s=7 g/dl. The vertical line shows the plasma-wall interface. A-arteriolar end, M-midcap, V-venular end. –·–·–·–· P _50,s ^Hb=10 Torr, ------- P _50,s ^Hb=29.3 Torr, ——— P _50,s ^Hb=50 Torr.

Figure 7. Tissue PO ₂ distribution along capillary length for different HBOC oxygen cooperatives. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=2.2, H _c=0.2, [Hb] _s=7 g/dl.

Figure 8. Tissue PO ₂ distribution along capillary length for different HBOC concentrations. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=n _s=2.2, H _c=0.2.

Figure 9. (A) Comparison of k _o for different values of hematocrits. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=n _s=2.2, [Hb] _s=7 g/dl. (B) Comparison of k _cell for different values of hematocrits. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=n _s=2.2, [Hb] _s=7 g/dl.

Figure 10. Comparison of kinetic parameter values with and without HBOC. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=n _s=2.2, [Hb] _s=7 g/dl.

Figure 11. Comparison of overall mass transfer coefficient for different HBOC diffusion coefficients. P _50,c ^Hb=P _50,s ^Hb=29.3 Torr, n _c=n _s=2.2, [Hb] _s=7 g/dl.

Mahler M., Louy C., Homsher E., Peskoff A. Reappraisal of diffusion, solubility, and consumption of oxygen in frog skeletal muscle, with applications to muscle energy balance. J. Gen. Physiol. 1985; 86(1)105–134

 PubMedGoogle Scholar

Bentley T. B., Meng H., Pittman R. N. Temperature dependence of oxygen diffusion and consumption in mammalian striated muscle. Am. J. Physiol. 1993; 264(6 Pt. 2)H1825–H1830

 Google Scholar

Meng H., Bentley T. B., Pittman R. N. Myoglobin content of hamster skeletal muscles. J. Appl. Physiol. 1993; 74(5)2194–2197

 PubMedGoogle Scholar

Wang D., Kreutzer U., Chung Y., Jue T. Myoglobin and hemoglobin rotational diffusion in the cell. Biophys. J. 1997; 73(5)2764–2770

 PubMedGoogle Scholar

Jurgens K. D., Peters T., Gros G. Diffusivity of myoglobin in intact skeletal muscle cells. Proc. Natl. Acad. Sci. U. S. A. 1994; 91(9)3829–3833

 PubMedGoogle Scholar

Ellsworth M. L., Popel A. S., Pittman R. N. Assessment and impact of heterogeneities of convective oxygen transport parameters in capillaries of striated muscle: experimental and theoretical. Microvasc. Res. 1988; 35(3)341–362

 PubMed Web of Science ®Google Scholar

Respiration and Circulation, P. L. Altman, D. S. Dittmer. Fed. Am. Soc. Exp. Biol., Bethesda, MD 1971

 Google Scholar

Goldstick T. K., Ciuryla V. T., Zuckerman L. Diffusion of oxygen in plasma and blood. Adv. Exp. Med. Biol. 1976; 75: 183–190

 PubMedGoogle Scholar

Kayar S. R., Hoppeler H., Hudlicka E., Uhlmann E., Tyler K. R. Capillary dimensions and barrier thickness from capillaries to muscles. Acta Anat. 1987; 128: 370

 Google Scholar

Liu C. Y., Eskin S. G., Hellums J. D. The oxygen permeability of cultured endothelial cell monolayers. Adv. Exp. Med. Biol. 1994; 345: 723–730

 PubMedGoogle Scholar

Vadapalli A., Pittman R. N., Popel A. S. Estimating oxygen transport resistance of the microvascular wall. Am. J. Physiol.: Heart Circ. Physiol. 2000; 279(2)H657–H671

 PubMed Web of Science ®Google Scholar

Christoforides C., Laasberg L. H., Hedley-Whyte J. Effect of temperature on solubility of O 2 in human plasma. J. Appl. Physiol. 1969; 26(1)56–60

 PubMedGoogle Scholar

Bouwer S. T., Hoofd L., Kreuzer F. Diffusion coefficients of oxygen and hemoglobin measured by facilitated oxygen diffusion through hemoglobin solutions. Biochim. Biophys. Acta 1997; 1338(1)127–136

 PubMedGoogle Scholar

Clark A., Jr., Federspiel W. J., Clark P. A., Cokelet G. R. Oxygen delivery from red cells. Biophys. J. 1985; 47(2 Pt. 1)171–181

 PubMedGoogle Scholar

Pries A. R., Secomb T. W., Gessner T., Sperandio M. B., Gross J. F., Gaehtgens P. Resistance to blood flow in microvessels in vivo. Circ. Res. 1994; 75(5)904–915

 PubMed Web of Science ®Google Scholar

Stein J. C., Ellsworth M. L. Capillary oxygen transport during severe hypoxia: role of hemoglobin oxygen affinity. J. Appl. Physiol. 1993; 75(4)1601–1607

 PubMedGoogle Scholar