A Computational Study of the Effect of Capillary Network Anastomoses and Tortuosity on Oxygen Transport

Goldman, Daniel; Popel, Aleksander S.

doi:10.1006/jtbi.2000.2113

Cited by 181 publications

(224 citation statements)

References 31 publications

(44 reference statements)

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“…Under standard physiological conditions, V max is about 2.5 × 10 −6 mol min −1 g −1 and K m about 7 × 10 −7 M (which corresponds to about 0.5 mmHg in the units of partial pressure as α O 2 = 1.46 × 10 −6 M mmHg −1 . 17,31,51 The estimate of K m about 0.7 μM is a functional one that makes excellent sense relative to myoglobin about 2.39 mmHg. Furthermore, the K m value from in vitro measurements on isolated mitochondria are generally found to be 0.…”

Section: Michaelis-menten Kinetics For Oxygen Consumptionmentioning

confidence: 95%

“…"The value of R rbc is about 0.69 [13][14][15]31,38 . Multiplying [CO 2 ] bl by 22.256 converts the units of molar to ml of CO 2 per ml of blood.…”

Section: Correctionmentioning

confidence: 99%

“…Other models based on non-cylindrical geometry have been designed or proposed to reflect the morphological and anatomical structures of the specific tissues. [16][17][18]31,34,61 There have been previous studies on simultaneous or dynamic transport and exchange of O 2 and CO 2 in the microcirculation. Hill et al [39][40][41] and Salathe et al 58 studied the kinetics of O 2 and CO 2 exchange through compartmental modeling by accounting for physical and biochemical processes including the acid-base balance.…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Dash

Bassingthwaighte

2006

Ann Biomed Eng

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A detailed nonlinear four-region (red blood cell, plasma, interstitial fluid, and parenchymal cell) axially distributed convection-diffusion-permeation-reaction-binding computational model is developed to study the simultaneous transport and exchange of oxygen (O 2 ) and carbon dioxide (CO 2 ) in the blood-tissue exchange system of the heart. Since the pH variation in blood and tissue influences the transport and exchange of O 2 and CO 2 (Bohr and Haldane effects), and since most CO 2 is transported as (bicarbonate) via the CO 2 hydration (buffering) reaction, the transport and exchange of and H + are also simulated along with that of O 2 and CO 2 . Furthermore, the model accounts for the competitive nonlinear binding of O 2 and CO 2 with the hemoglobin inside the red blood cells (nonlinear O 2 -CO 2 interactions, Bohr and Haldane effects), and myoglobin-facilitated transport of O 2 inside the parenchymal cells. The consumption of O 2 through cytochrome-c oxidase reaction inside the parenchymal cells is based on MichaelisMenten kinetics. The corresponding production of CO 2 is determined by respiratory quotient (RQ), depending on the relative consumption of carbohydrate, protein, and fat. The model gives a physiologically realistic description of O 2 transport and metabolism in the microcirculation of the heart. Furthermore, because model solutions for tracer transients and steady states can be computed highly efficiently, this model may be the preferred vehicle for routine data analysis where repetitive solutions and parameter optimization are required, as is the case in PET imaging for estimating myocardial O 2 consumption.

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Section: Michaelis-menten Kinetics For Oxygen Consumptionmentioning

confidence: 95%

“…"The value of R rbc is about 0.69 [13][14][15]31,38 . Multiplying [CO 2 ] bl by 22.256 converts the units of molar to ml of CO 2 per ml of blood.…”

Section: Correctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Dash

Bassingthwaighte

2006

Ann Biomed Eng

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“…The parameter values used in our model are given in Table II, based upon numerous reports in the literature Christoforides et al, 1969;Ellsworth & Pittman, 1984;Ellsworth et al, 1988;Honig & Gayeski, 1982;Jürgens et al, 1994;Mahler et al, 1985;Meng et al, 1993;Sullivan & Pittman, 1984;Goldman & Popel, 2000;Eggleton et al, 1998;Wüst et al, 2009b). The lengthscale, L, is derived by assuming that capillaries in the circular simulation domain have a dimensional density of the rat EDL muscle cross section in Fig.…”

Section: Parameter Valuesmentioning

confidence: 99%

Modelling capillary oxygen supply capacity in mixed muscles: Capillary domains revisited

Alshammari

Gaffney

Egginton

2014

Journal of Theoretical Biology

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Developing effective therapeutic interventions for pathological conditions associated with abnormal oxygen transport to muscle fibres critically depends on the objective characterisation of capillarity. Local indices of capillary supply have the potential to identify the onset of fine-scale tissue pathologies and dysregulation. Detailed tissue geometry, such as muscle fibre size, has been incorporated into such measures by considering the distribution of Voronoi polygons (VP) generated from planar capillary locations as a representation of capillary supply regions. Previously, detailed simulations have predicted that this is generally accurate for muscle tissue with uniform oxygen uptake. Here we extend this modelling framework to heterogeneous muscle for the assessment of capillary supply capacity under maximal sustainable oxygen consumption. We demonstrate for muscle with heterogeneous fibre properties that VP theoretically provide a computationally simple but often accurate representation of trapping regions (TR), which are predicted from biophysical transport models to represent the areas of tissue supplied by individual capillaries. However, this use of VP may become less accurate around large fibres, and at the interface of fibres of largely different oxidative capacities. In such cases, TR may provide a more robust representation of capillary supply regions. Additionally, given VP can only approximate oxygen delivery by capillaries, we show that their generally close relationship to TR suggests that (1) fibre type distribution may be tightly regulated to avoid large fibres with high oxidative capacities, (2) the anatomical fibre distribution is also tightly regulated to prevent large surface area of interaction between metabolically dissimilar fibres, and (3) in chronically hypoxic tissues capillary distribution is more important in determining oxygen supply than the spatial heterogeneity of fibre demand.

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“…Type I is also of practical significance in relation to arteriovenous malformations (cerebral abnormalities in which a blood vessel subdivides over a relatively short distance into many subvessels; Hademenos et al 1996;Smith & Jones 2003) and to emerging issues, including increased mass flux and an apparent absence of flow reversal. Several theoretical conjectures remain largely untested, while direct computation has only given solutions either accurately over a few generations or with limited detail over more generations (see Hademenos et al 1996;Pries et al 1998;Goldman & Popel 2000;Smith & Jones 2003). Related branching or network studies have been conducted with some success by Handa et al (1993), Miyasaka et al (1993), Pedley et al (1994), Gatlin et al (1995), Young et al (1996), Gao et al (1997), Hademenos & Massoud (1997), Wilquem & Degrez (1997), Zhai et al (1997), Pries et al (1998), Brada & Kitchen (2000), Kassab et al (2000), Lorthois et al (2000), McEvoy et al (2000), Cassidy et al (2001) and Comer et al (2001).…”

Section: Introductionmentioning

confidence: 99%

Multi-branching flows from one mother tube to many daughters or to a network

Bowles

Dennis

Purvis

et al. 2005

Phil. Trans. R. Soc. A.

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Multiply branching fluid flows are modelled in two contexts. The first (type I) is for oneto-many branching. Computations are described for flow through a channel, with fully developed motion upstream, which branches abruptly into a number of subchannels downstream. The differences in pressure between the upstream end of the channel and the downstream ends of the subchannels are substantial. Comparisons with recent analytical predictions show fair agreement for Reynolds numbers in the low tens and above. The second context (type II) has successive generations of bifurcation in a network. Modelling, computations and analysis include the effects of many bifurcations.

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A Computational Study of the Effect of Capillary Network Anastomoses and Tortuosity on Oxygen Transport

Cited by 181 publications

References 31 publications

Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Simultaneous Blood–Tissue Exchange of Oxygen, Carbon Dioxide, Bicarbonate, and Hydrogen Ion

Modelling capillary oxygen supply capacity in mixed muscles: Capillary domains revisited

Multi-branching flows from one mother tube to many daughters or to a network

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