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Amiri FA, Zhang J. Numerical analysis of oxygen uptake processes by red blood cells in stopped-flow measurements: Effects of cell shape, membrane permeability and unstirred layer. Med Eng Phys 2023; 121:104057. [PMID: 37985019 DOI: 10.1016/j.medengphy.2023.104057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Revised: 09/12/2023] [Accepted: 10/02/2023] [Indexed: 11/22/2023]
Abstract
The transport process of oxygen and other gas species across red blood cell (RBC) membrane is of great importance for better understanding the critical biological functions of RBCs, and the stopped-flow experiments have often been employed for such investigations. In previous stopped-flow analyses, the RBC had usually been represented by a spherical capsule based on the RBC volume, and an assumed unstirred layer (USL) thickness had been used to determine the membrane permeability. In this research, unlike these previous studies, we simulate the oxygen uptake process with different RBC shapes (shperical, ellipsoidal and biconcave) and examine the effects of USL thickness and membrane permeability over broad ranges based on literature values. Our results show that the excess membrane area can greatly improve the oxygen transport efficiency, and a same uptake half-time can be obtained using different combinations of USL thickness and membrane permeability. These findings raise concerns on the reliability and uncertainty for the results and conclusions in previous studies, and also call for more complete numerical models, for example, with the fluid flow and cell deformation considered, and more in-depth investigations on the oxygen transport processes.
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Affiliation(s)
- Farhad A Amiri
- Bharti School of Engineering and Computer Science, Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario, P3E 2C6, Canada
| | - Junfeng Zhang
- Bharti School of Engineering and Computer Science, Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario, P3E 2C6, Canada.
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Amiri FA, Zhang J. Oxygen transport across tank-treading red blood cell: Individual and joint roles of flow convection and oxygen-hemoglobin reaction. Microvasc Res 2023; 145:104447. [PMID: 36270419 DOI: 10.1016/j.mvr.2022.104447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Revised: 10/04/2022] [Accepted: 10/13/2022] [Indexed: 11/06/2022]
Abstract
Gas, especially oxygen, transport in the microcirculation is a complex phenomenon, however, of critical importance for maintaining normal biological functions, and the cytoplasm fluid in red blood cells (RBCs) is the major vehicle for transporting oxygen from lungs to tissues via the circulatory system. Existing theoretical and numerical studies have neglected the cytoplasm convection effect by treating RBCs as rigid particles undergoing a constant translation velocity. As a consequence, the influence and mechanism of the cytoplasm flow on oxygen transport are still not clear in microcirculation research. In this study, we consider a tank-treading capsule in shear flow, which is generated with two parallel plates moving in opposite directions: the top plate of a higher oxygen pressure (PO2) representing the RBC core in the central region of a microvessel and the bottom plate of a lower PO2 representing the microvessel wall. Numerical simulations are conducted to investigate the individual and combined effects of cytoplasm convection and oxygen-hemoglobin (O2-Hb) reaction on the oxygen transport efficiency across the tank-treading capsule, and different PO2 situations and shear rates are also tested. Due to the lower oxygen diffusivity in cytoplasm, the presence of the capsule reduces the oxygen transfer flux across the gap by 7.34 % in the pure diffusion system where the flow convection and O2-Hb reaction are both neglected. Including the flow convection or the O2-Hb reaction has little influence on the oxygen flux; however, when they act together as in real microcirculation situations, the enhancement in oxygen transport could be significant, especially in the low PO2 and high shear rate situations. In particular, with the respective PO2 at 60 and 30 mmHg on the top and bottom plates and a 400 s-1 shear rate, the oxygen flux reduction is only 0.02 %, suggesting that the cytoplasm convection can improve the oxygen transport across RBCs considerably. The simulation results are scrutinized to explore the underlying mechanism for the enhancement, and a new nondimensional parameter is introduced to characterize the importance of cytoplasm convection in oxygen transport. These simulation results, discussion and analysis could be helpful for a better understanding of the complex oxygen transport process and therefor valuable for relevant studies.
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Affiliation(s)
- Farhad A Amiri
- Bharti School of Engineering and Computer Science, Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario P3E 2C6, Canada
| | - Junfeng Zhang
- Bharti School of Engineering and Computer Science, Laurentian University, 935 Ramsey Lake Road, Sudbury, Ontario P3E 2C6, Canada.
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Reproducing the Hemoglobin Saturation Profile, a Marker of the Blood Oxygenation Level Dependent (BOLD) fMRI Effect, at the Microscopic Level. PLoS One 2016; 11:e0149935. [PMID: 26939128 PMCID: PMC4777512 DOI: 10.1371/journal.pone.0149935] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2015] [Accepted: 02/06/2016] [Indexed: 11/29/2022] Open
Abstract
The advent of functional MRI in the mid-1990s has catalyzed progress pertaining to scientific discoveries in neuroscience. With the prospect of elucidating the physiological aspect of the Blood Oxygenation Level Dependent (BOLD) effect we present a computational capillary-tissue system capable of mapping venous hemoglobin saturation— a marker of the BOLD hemodynamic response. Free and facilitated diffusion and convection for hemoglobin and oxygen are considered in the radial and axial directions. Hemoglobin reaction kinetics are governed by the oxyhemoglobin dissociation curve. Brain activation, mimicked by dynamic transitions in cerebral blood velocity (CBv) and oxidative metabolism (CMRO2), is simulated by normalized changes in m = (ΔCBv/CBv)/(ΔCMRO2/CMRO2) of values 2, 3 and 4. Venous hemoglobin saturation profiles and peak oxygenation results, for m = 2, based upon a 50% and a 25% increase in CBv and CMRO2, respectively, lie within physiological limits exhibiting excellent correlation with the BOLD signal, for short-duration stimuli. Our analysis suggests basal CBv and CMRO2 values of 0.6 mm/s and 200 μmol/100g/min. Coupled CBv and CMRO2 responses, for m = 3 and m = 4, overestimate peak hemoglobin saturation, confirming the system’s responsiveness to changes in hematocrit, CBv and CMRO2. Finally, factoring in neurovascular effects, we show that no initial dip will be observed unless there is a time delay in the onset of increased CBv relative to CMRO2.
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Roy TK, Secomb TW. Theoretical analysis of the determinants of lung oxygen diffusing capacity. J Theor Biol 2014; 351:1-8. [PMID: 24560722 DOI: 10.1016/j.jtbi.2014.02.009] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2013] [Revised: 02/06/2014] [Accepted: 02/10/2014] [Indexed: 10/25/2022]
Abstract
The process of pulmonary oxygen uptake is analyzed to obtain an explicit equation for lung oxygen diffusing capacity in terms of hematocrit and pulmonary capillary diameter. An axisymmetric model with discrete cylindrical erythrocytes is used to represent radial diffusion of oxygen from alveoli through the alveolar-capillary membrane into pulmonary capillaries, through the plasma, and into erythrocytes. Analysis of unsteady diffusion due to the passage of the erythrocytes shows that transport of oxygen through the alveolar-capillary membrane occurs mainly in the regions adjacent to erythrocytes, and that oxygen transport through regions adjacent to plasma gaps can be neglected. The model leads to an explicit formula for diffusing capacity as a function of geometric and oxygen transport parameters. For normal hematocrit and a capillary diameter of 6.75 μm, the predicted diffusing capacity is 102 ml O₂ min⁻¹ mmHg⁻¹. This value is 30-40% lower than values estimated previously by the morphometric method, which considers the total membrane area and the specific uptake rate of erythrocytes. Diffusing capacity is shown to increase with increasing hematocrit and decrease with increasing capillary diameter and increasing thickness of the membrane. Simulations of pulmonary oxygen uptake in humans under conditions of exercise or hypoxia based show closer agreement with experimental data than previous models, but still overestimate oxygen uptake. The remaining discrepancy may reflect effects of heterogeneity of perfusion and ventilation in the lung.
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Affiliation(s)
- Tuhin K Roy
- Department of Anesthesiology, Mayo Clinic, 200 First Street SW, Rochester, MN 55905, USA.
| | - Timothy W Secomb
- Department of Physiology, University of Arizona, Tucson, AZ 85724-5051, USA
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Liu B, Kim MM, Zhu TC. A theoretical comparison of macroscopic and microscopic modeling of singlet oxygen during Photofrin and HPPH mediated-PDT. PROCEEDINGS OF SPIE--THE INTERNATIONAL SOCIETY FOR OPTICAL ENGINEERING 2013; 8568:856805. [PMID: 25999642 PMCID: PMC4437727 DOI: 10.1117/12.2002489] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
Mathematic models were developed to simulate the complex dynamic process of photodynamic therapy (PDT). Macroscopic or microscopic modeling of singlet oxygen (1O2) is particularly of interest because it is the major cytotoxic agent causing biological effects during PDT. Our previously introduced macroscopic PDT model incorporates the diffusion equation for the light propagation in tissue and the macroscopic kinetic equations for the production of the 1O2. The distance-dependent distribution of 3O2 and reacted 1O2 can be numerically calculated using finite-element method (FEM). We recently improved the model to include microscopic kinetic equations of oxygen diffusion from uniformly distributed blood vessels and within tissue. In the model, the cylindrical blood capillary has radius in the range of 2-5 μm and a mean length of 300 μm, and supplies oxygen into tissue. The blood vessel network is assumed to form a 2-D square grid perpendicular to a linear light source. The spacing of the grid is 60 μm. Oxygen can also diffuse along the radius and the longitudinal axial of the cylinder within tissue. The oxygen depletion during Photofrin-PDT can be simulated using both macroscopic and microscopic approaches. The comparison of the simulation results have reasonable agreements when velocity of blood flow is reduced during PDT.
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Affiliation(s)
- Baochang Liu
- Department of Radiation Oncology, School of Medicine, University of Pennsylvania, Philadelphia, PA 19104
| | - Michele M Kim
- Department of Radiation Oncology, School of Medicine, University of Pennsylvania, Philadelphia, PA 19104
| | - Timothy C Zhu
- Department of Radiation Oncology, School of Medicine, University of Pennsylvania, Philadelphia, PA 19104
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Zhang J, Nolan TD, Zhang T, Griffith BP, Wu ZJ. Characterization of membrane blood oxygenation devices using computational fluid dynamics. J Memb Sci 2007. [DOI: 10.1016/j.memsci.2006.11.041] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Whiteley JP. Some factors affecting pulmonary oxygen transport. Math Biosci 2006; 202:115-32. [PMID: 16697423 DOI: 10.1016/j.mbs.2006.03.014] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2004] [Revised: 03/08/2006] [Accepted: 03/16/2006] [Indexed: 11/27/2022]
Abstract
Equations governing oxygen transport from alveolar gas to red blood cells flowing through pulmonary capillaries are written down. Some analytical predictions are made on factors affecting the rate at which this process takes place. Numerical simulations are carried out to investigate the effect of red blood cell shape, capillary dimensions, haematocrit and choice of oxygen dissociation curve on pulmonary oxygen transport. These factors all have an effect on pulmonary transport, with the effect being much more marked for simulations with low oxygen levels, typical of those seen in some subjects with respiratory disease.
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Affiliation(s)
- Jonathan P Whiteley
- Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom.
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Chakraborty S, Balakotaiah V, Bidani A. Diffusing capacity reexamined: relative roles of diffusion and chemical reaction in red cell uptake of O2, CO, CO2, and NO. J Appl Physiol (1985) 2004; 97:2284-302. [PMID: 15322062 DOI: 10.1152/japplphysiol.00469.2004] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
This paper presents an analytical expression for the diffusing capacity (Θt) of the red blood cell (RBC) for any reactive gas in terms of size and shape of the RBC, thickness of the unstirred plasma layer surrounding the RBC, diffusivities and solubilities of the gas in RBC and boundary layer, hematocrit, and the slope of the dissociation curve. The expression for Θthas been derived by spatial averaging of the fundamental convection-diffusion-reaction equation for O2in the RBC and has been generalized to all cell shapes and for other reactive gases such as CO, NO, and CO2. The effects of size and shape of the RBC, thickness of the unstirred plasma layer, hemoglobin concentration, and hematocrit on Θthave been analyzed, and the analytically obtained expression for Θthas been validated by comparison with different sets of existing experimental data for O2and CO2. Our results indicate that the discoidal shape of the human RBC with average dimensions of 1.6-μm thickness and 8-μm diameter is close to optimal design for O2uptake and that the true reaction velocity in the RBC is suppressed significantly by the mass transfer resistance in the surrounding unstirred layer. In vitro measurements using rapid-mixing technique, which measures Θtin the presence of artificially created large boundary layers, substantially underpredicts the in vivo diffusing capacity of the RBC in the diffusion-controlled regime. Depending on the conditions in the RBC, uptake of less reactive gases (such as CO) undergoes transition from reaction-limited to diffusion-limited regime. For a constant set of morphological parameters, the theoretical expression for Θtpredicts that Θt,NO> Θt,CO2> Θt,O2> Θt,CO.
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Affiliation(s)
- Saikat Chakraborty
- Pulmonary Critical Care and Sleep Medicine, Department of Internal Medicine, The University of Texas Medical School, Houston, TX 77030, USA
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Macey PM, Alger JR, Kumar R, Macey KE, Woo MA, Harper RM. Global BOLD MRI changes to ventilatory challenges in congenital central hypoventilation syndrome. Respir Physiol Neurobiol 2003; 139:41-50. [PMID: 14637309 DOI: 10.1016/j.resp.2003.09.006] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
We evaluated global blood oxygen level dependent (BOLD) signal changes in gray and white matter in 14 congenital central hypoventilation syndrome (CCHS) and 14 control subjects. One baseline image series with room air and three series with 30 s room air followed by 120 s hypercapnia (5% CO2/95% O2), hypoxia (15% O2/85% N2) or hyperoxia (100% O2) were collected. Hypercapnia and hyperoxia raised, and hypoxia lowered gray and white matter global signal in both groups, with smaller changes in white matter. Signal changes in CCHS cases were lower than control subjects for hypercapnia in gray and white matter, slightly more-enhanced in hypoxia, and, except for initial transient responses, were nearly comparable during hyperoxia. Initial signal rate or pattern changes emerged in all three challenges in gray or white matter in control, but not CCHS cases. Neural or vascular mechanisms mediate perfusion differently in CCHS; the aberrant initial transient responses may reflect deficiencies in rapidly-varying physiologic interactions in the syndrome.
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Affiliation(s)
- Paul M Macey
- Department of Neurobiology, David Geffen School of Medicine at UCLA, University of California, Los Angeles, CA 90095-1763, USA
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