Calculated dispersion of capillary transit times: significance for oxygen exchange

1981 ◽  
Vol 240 (2) ◽  
pp. H199-H208 ◽  
Author(s):  
C. R. Honig ◽  
C. L. Odoroff
Keyword(s):  
Transit Time ◽  
Probability Distributions ◽  
Release Time ◽  
Capillary Length ◽  
Mean Velocity ◽  
Capillary Recruitment ◽  
Lack Of Information ◽  
Gamma Distributions ◽  
Transit Times ◽  
Probability Densities

Probability densities for red cell velocity (V) and capillary length (L) in dog gracilis muscles were computed from mean length and mean velocity assuming two-parameter gamma distributions [Honig, Feldstein, and Frierson, Am. J. Physiol. 233 (Heart Circ. Physiol. 2): H122-H129, 1977]. The distribution of capillary transit times (L/V) was obtained from the ratio of the two gamma distributions. The lower tails of transit time distributions were compared with times thought required for O2 release from capillaries. Results indicate the following. 1) Transit time exceeds O2 release time at rest in all capillaries, regardless of assumptions in the calculation. 2) Transit time appears long enough even in moderate exercise provided mean L is about 1,000 microns and release time is about 100 ms. 3) Capillary recruitment prevents a functional O2 shunt during work at one- to two-thirds maximum O2 uptake (VO2max). 4) Recruitment is insufficient to prevent O2 shunting during exercise to VO2max. 5) Quantitative analysis of O2 transport is severely limited by lack of information about a) microvascular geometry, b) the probability distributions of parameters, and c) the kinetics of O2 release from capillaries.

Cell flow path influences transit time through striated muscle capillaries

1986 ◽  
Vol 250 (6) ◽  
pp. H899-H907 ◽  
Author(s):  
I. H. Sarelius
Keyword(s):  
Transit Time ◽  
Striated Muscle ◽  
Average Distance ◽  
Flow Path ◽  
Capillary Length ◽  
Capillary Networks ◽  
Transit Times ◽  
Total Cell Population ◽  
Path Lengths ◽  
Flow Variables

Indirect estimates of erythrocyte transit time across capillary beds incorporate two assumptions, that the anatomically defined capillary length correctly describes the functional flow path taken by cells across the network, and that the distribution of perfused flow path lengths does not change during hyperemia. Direct measurements of cell flow paths through capillary networks, cell transit times, and associated blood flow variables, have been made using fluorescent erythrocytes as tracers of the total cell population. Observations were made in cremaster muscles from juvenile or adult anesthetized golden hamsters; these tissues have capillary networks of differing degrees of branching. In the juvenile (more branching) networks, mean functional flow path (Lf) was 351 +/- 6 (SE) micron, about twice the average distance from terminal arteriole to collecting venule (172 +/- 37 microns). In the less branching adult networks, Lf = 438 +/- 9 microns compared with the anatomically defined distance of 372 +/- 33 microns. In both groups, Lf distribution was unchanged during hyperemia produced by 10(-4) M adenosine. Directly measured cell transit times across the networks were longer than expected from previous indirect estimates: means were 3.2 +/- 0.1 s in juveniles and 4.2 +/- 0.2 s in adults, with decreases to 2.2 +/- 0.1 and 2.3 +/- 0.1 s, respectively, in hyperemia.

scholarly journals Blood flow, capillary transit times, and tissue oxygenation: the centennial of capillary recruitment

2020 ◽  
Vol 129 (6) ◽  
pp. 1413-1421
Author(s):  
Leif Østergaard
Keyword(s):  
Blood Flow ◽  
Transit Time ◽  
Tissue Oxygenation ◽  
Plasma Viscosity ◽  
Capillary Endothelium ◽  
External Compression ◽  
Capillary Recruitment ◽  
Transit Times ◽  
Vascular Origin ◽  
Open Capillaries

The transport of oxygen between blood and tissue is limited by blood’s capillary transit time, understood as the time available for diffusion exchange before blood returns to the heart. If all capillaries contribute equally to tissue oxygenation at all times, this physical limitation would render vasodilation and increased blood flow insufficient means to meet increased metabolic demands in the heart, muscle, and other organs. In 1920, Danish physiologist August Krogh was awarded the Nobel Prize in Physiology or Medicine for his mathematical and quantitative, experimental demonstration of a solution to this conceptual problem: capillary recruitment, the active opening of previously closed capillaries to meet metabolic demands. Today, capillary recruitment is still mentioned in textbooks. When we suspect symptoms might represent hypoxia of a vascular origin, however, we search for relevant, flow-limiting conditions in our patients and rarely ascribe hypoxia or hypoxemia to short capillary transit times. This review describes how natural changes in capillary transit-time heterogeneity (CTH) and capillary hematocrit (HCT) across open capillaries during blood flow increases can account for a match of oxygen availability to metabolic demands in normal tissue. CTH and HCT depend on a number of factors: on blood properties, including plasma viscosity, the number, size, and deformability of blood cells, and blood cell interactions with capillary endothelium; on anatomical factors including glycocalyx, endothelial cells, basement membrane, and pericytes that affect the capillary diameter; and on any external compression. The review describes how risk factor- and disease-related changes in CTH and HCT interfere with flow-metabolism coupling and tissue oxygenation and discusses whether such capillary dysfunction contributes to vascular disease pathology.

scholarly journals Towards the Dependence on Parameters for the Solution of the Thermostatted Kinetic Framework

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 59
Author(s):  
Bruno Carbonaro ◽  
Marco Menale
Keyword(s):  
Complex System ◽  
Continuous Dependence ◽  
Social Role ◽  
Probability Distributions ◽  
Functional Dependence ◽  
Transition Probability ◽  
Classical Mechanics ◽  
Human Society ◽  
Wide Range ◽  
Probability Densities

A complex system is a system involving particles whose pairwise interactions cannot be composed in the same way as in classical Mechanics, i.e., the result of interaction of each particle with all the remaining ones cannot be expressed as a sum of its interactions with each of them (we cannot even know the functional dependence of the total interaction on the single interactions). Moreover, in view of the wide range of its applications to biologic, social, and economic problems, the variables describing the state of the system (i.e., the states of all of its particles) are not always (only) the usual mechanical variables (position and velocity), but (also) many additional variables describing e.g., health, wealth, social condition, social rôle ⋯, and so on. Thus, in order to achieve a mathematical description of the problems of everyday’s life of any human society, either at a microscopic or at a macroscpoic scale, a new mathematical theory (or, more precisely, a scheme of mathematical models), called KTAP, has been devised, which provides an equation which is a generalized version of the Boltzmann equation, to describe in terms of probability distributions the evolution of a non-mechanical complex system. In connection with applications, the classical problems about existence, uniqueness, continuous dependence, and stability of its solutions turn out to be particularly relevant. As far as we are aware, however, the problem of continuous dependence and stability of solutions with respect to perturbations of the parameters expressing the interaction rates of particles and the transition probability densities (see Section The Basic Equations has not been tackled yet). Accordingly, the present paper aims to give some initial results concerning these two basic problems. In particular, Theorem 2 reveals to be stable with respect to small perturbations of parameters, and, as far as instability of solutions with respect to perturbations of parameters is concerned, Theorem 3 shows that solutions are unstable with respect to “large” perturbations of interaction rates; these hints are illustrated by numerical simulations that point out how much solutions corresponding to different values of parameters stay away from each other as t→+∞.

scholarly journals Simulating a Ground Truth for Transit Time Analysis of Indicator Dilution Curves

2020 ◽  
Vol 6 (3) ◽  
pp. 268-271
Author(s):  
Michael Reiß ◽  
Ady Naber ◽  
Werner Nahm
Keyword(s):  
Transit Time ◽  
Sampling Rate ◽  
Ground Truth ◽  
Indicator Dilution ◽  
Cross Sectional ◽  
In Vivo Measurements ◽  
Multiple Indicator Dilution ◽  
Transit Times ◽  
Dilution Curves

AbstractTransit times of a bolus through an organ can provide valuable information for researchers, technicians and clinicians. Therefore, an indicator is injected and the temporal propagation is monitored at two distinct locations. The transit time extracted from two indicator dilution curves can be used to calculate for example blood flow and thus provide the surgeon with important diagnostic information. However, the performance of methods to determine the transit time Δt cannot be assessed quantitatively due to the lack of a sufficient and trustworthy ground truth derived from in vivo measurements. Therefore, we propose a method to obtain an in silico generated dataset of differently subsampled indicator dilution curves with a ground truth of the transit time. This method allows variations on shape, sampling rate and noise while being accurate and easily configurable. COMSOL Multiphysics is used to simulate a laminar flow through a pipe containing blood analogue. The indicator is modelled as a rectangular function of concentration in a segment of the pipe. Afterwards, a flow is applied and the rectangular function will be diluted. Shape varying dilution curves are obtained by discrete-time measurement of the average dye concentration over different cross-sectional areas of the pipe. One dataset is obtained by duplicating one curve followed by subsampling, delaying and applying noise. Multiple indicator dilution curves were simulated, which are qualitatively matching in vivo measurements. The curves temporal resolution, delay and noise level can be chosen according to the requirements of the field of research. Various datasets, each containing two corresponding dilution curves with an existing ground truth transit time, are now available. With additional knowledge or assumptions regarding the detection-specific transfer function, realistic signal characteristics can be simulated. The accuracy of methods for the assessment of Δt can now be quantitatively compared and their sensitivity to noise evaluated.

scholarly journals Random numbers from the tails of probability distributions using the transformation method

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Daniel Fulger ◽  
Enrico Scalas ◽  
Guido Germano
Keyword(s):  
Probability Distributions ◽  
Transformation Method ◽  
Fractional Diffusion ◽  
Random Numbers ◽  
Stochastic Solution ◽  
Probability Densities ◽  
Speed Up ◽  
Time Fractional Diffusion Equation ◽  
Transformation Methods ◽  
Very High

AbstractThe speed of many one-line transformation methods for the production of, for example, Lévy alpha-stable random numbers, which generalize Gaussian ones, and Mittag-Leffler random numbers, which generalize exponential ones, is very high and satisfactory for most purposes. However, fast rejection techniques like the ziggurat by Marsaglia and Tsang promise a significant speed-up for the class of decreasing probability densities, if it is possible to complement them with a method that samples the tails of the infinite support. This requires the fast generation of random numbers greater or smaller than a certain value. We present a method to achieve this, and also to generate random numbers within any arbitrary interval. We demonstrate the method showing the properties of the transformation maps of the above mentioned distributions as examples of stable and geometric stable random numbers used for the stochastic solution of the space-time fractional diffusion equation.

Validation of cerebral arteriovenous malformation hemodynamics assessed by DSA using quantitative magnetic resonance angiography: preliminary study

2017 ◽  
Vol 10 (2) ◽  
pp. 156-161 ◽  
Author(s):  
Sophia F Shakur ◽  
Denise Brunozzi ◽  
Ahmed E Hussein ◽  
Andreas Linninger ◽  
Chih-Yang Hsu ◽  
...  
Keyword(s):  
Magnetic Resonance ◽  
Magnetic Resonance Angiography ◽  
Transit Time ◽  
Internal Carotid ◽  
Flow Measurements ◽  
Quantitative Magnetic Resonance ◽  
Transit Times ◽  
Before And After ◽  
Preliminary Study ◽  
The Difference

BackgroundThe hemodynamic evaluation of cerebral arteriovenous malformations (AVMs) using DSA has not been validated against true flow measurements.ObjectiveTo validate AVM hemodynamics assessed by DSA using quantitative magnetic resonance angiography (QMRA).Materials and methodsPatients seen at our institution between 2007 and 2016 with a supratentorial AVM and DSA and QMRA obtained before any treatment were retrospectively reviewed. DSA assessment of AVM flow comprised AVM arterial-to-venous time (A-Vt) and iFlow transit time. A-Vt was defined as the difference between peak contrast intensity in the cavernous internal carotid artery and peak contrast intensity in the draining vein. iFlow transit times were determined using syngo iFlow software. A-Vt and iFlow transit times were correlated with total AVM flow measured using QMRA and AVM angioarchitectural and clinical features.Results33 patients (mean age 33 years) were included. Nine patients presented with hemorrhage. Mean AVM volume was 9.8 mL (range 0.3–57.7 mL). Both A-Vt (r=−0.47, p=0.01) and iFlow (r=−0.44, p=0.01) correlated significantly with total AVM flow. iFlow transit time was significantly shorter in patients who presented with seizure but A-Vt and iFlow did not vary with other AVM angioarchitectural features such as venous stenosis or hemorrhagic presentation.ConclusionsA-Vt and iFlow transit times on DSA correlate with cerebral AVM flow measured using QMRA. Thus, these parameters may be used to indirectly estimate AVM flow before and after embolization during angiography in real time.

An anatomic and physiological model of hepatic vascular system

1995 ◽  
Vol 79 (3) ◽  
pp. 1008-1026 ◽  
Author(s):  
D. R. Fine ◽  
D. Glasser ◽  
D. Hildebrandt ◽  
J. Esser ◽  
R. E. Lurie ◽  
...  
Keyword(s):  
Blood Flow ◽  
Transit Time ◽  
Vascular System ◽  
Model Parameters ◽  
Activity Time ◽  
Mathematical Relationship ◽  
Portal Flow ◽  
Splenic Blood Flow ◽  
Liver Activity ◽  
Transit Times

Hepatic function can be characterized by the activity/time curves obtained by imaging the aorta, spleen, and liver. Nonparametric deconvolution of the activity/time curves is clinically useful as a diagnostic tool in determining organ transit times and flow fractions. The use of this technique is limited, however, because of numerical and noise problems in performing deconvolution. Furthermore, the interaction of part of the tracer with the spleen and gastrointestinal tract, before it enters the liver, further obscures physiological information in the deconvolved liver curve. In this paper, a mathematical relationship is derived relating the liver activity/time curve to portal and hepatic behavior. The mathematical relationship is derived by using transit time spectrum/residence time density theory. Based on this theory, it is shown that the deconvolution of liver activity/time curves gives rise to a complex combination of splenic, gastrointestinal, and liver dependencies. An anatomically and physiologically plausible parametric model of the hepatic vascular system has been developed. This model is used in conjunction with experimental data to estimate portal, splenic, and hepatic physiological blood flow parameters for eight normal volunteers. These calculated parameters, which include the portal flow fraction, the splenic blood flow fraction, and blood transit times are shown to adequately correspond to published values. In particular, the model of the hepatic vascular system identifies the portal flow fraction as 0.752 +/- 0.022, the splenic blood flow fraction as 0.180 +/- 0.023, and the liver mean transit time as 13.4 +/- 1.71 s. The model has also been applied to two portal hypertensive patients. The variation in some of the model parameters is beyond normal limits and is consistent with the observed pathology.

Heterogeneity of gut capillary transit times and impaired gut oxygen extraction in endotoxemic pigs

1996 ◽  
Vol 81 (2) ◽  
pp. 895-904 ◽  
Author(s):  
M. F. Humer ◽  
P. T. Phang ◽  
B. P. Friesen ◽  
M. F. Allard ◽  
C. M. Goddard ◽  
...  
Keyword(s):  
Blood Volume ◽  
Transit Time ◽  
Volume Flow ◽  
Oxygen Extraction ◽  
Control Group ◽  
Total Blood Volume ◽  
Oxygen Extraction Ratio ◽  
Total Blood ◽  
Transit Times ◽  
Critical Oxygen

We tested the hypothesis that endotoxin increases the heterogeneity of gut capillary transit times and impairs oxygen extraction. The gut critical oxygen extraction ratio was determined by measuring multiple oxygen delivery-consumption points during progressive phlebotomy in eight control and eight endotoxin-infused anesthetized pigs. In multiple 1- to 2-g samples of small bowel, we measured blood volume (radiolabeled red blood cells) and flow (radiolabeled 15-microns microspheres) before and after critical oxygen extraction. Red blood cell transit time (= volume/flow) multiplied by morphologically determined capillary/total blood volume gave capillary transit time. During hemorrhage, capillary/total blood volume did not change in the endotoxin group (0.5 +/- 4.5%) but increased in the control group (17.6 +/- 2.5%; P < 0.05) due to a decrease in total gut blood volume. Flow decreased significantly in the endotoxin group (36 +/- 10%; P < 0.05) but not in the control group (12 +/- 10%). Capillary transit-time heterogeneity increased in the endotoxin group (12.3 +/- 4.9%) compared with the control group (-5.8 +/- 7.4%; P < 0.05), predicting a critical oxygen extraction ratio 0.14 lower in the endotoxin group than in the control group (K. R. Walley. J. Appl. Physiol. 81: 885–894, 1996). This matches the measured difference (endotoxin group, 0.60 +/- 0.04; control group, 0.74 +/- 0.03; P < 0.05). Increased heterogeneity of capillary transit times may be an important cause of impaired oxygen extraction.

scholarly journals Aggregation in environmental systems: seasonal tracer cycles quantify young water fractions, but not mean transit times, in spatially heterogeneous catchments

2015 ◽  
Vol 12 (3) ◽  
pp. 3059-3103 ◽  
Author(s):  
J. W. Kirchner
Keyword(s):  
Transit Time ◽  
Mean Transit Time ◽  
Strong Nonlinearity ◽  
Isotopic Tracers ◽  
Water Fraction ◽  
Benchmark Tests ◽  
Environmental Systems ◽  
Transit Times ◽  
Event Based ◽  
The Relationship

Abstract. Environmental heterogeneity is ubiquitous, but environmental systems are often analyzed as if they were homogeneous instead, resulting in aggregation errors that are rarely explored and almost never quantified. Here I use simple benchmark tests to explore this general problem in one specific context: the use of seasonal cycles in chemical or isotopic tracers (such as Cl−, δ18O, or δ2H) to estimate timescales of storage in catchments. Timescales of catchment storage are typically quantified by the mean transit time, meaning the average time that elapses between parcels of water entering as precipitation and leaving again as streamflow. Longer mean transit times imply greater damping of seasonal tracer cycles. Thus, the amplitudes of tracer cycles in precipitation and streamflow are commonly used to calculate catchment mean transit times. Here I show that these calculations will typically be wrong by several hundred percent, when applied to catchments with realistic degrees of spatial heterogeneity. This aggregation bias arises from the strong nonlinearity in the relationship between tracer cycle amplitude and mean travel time. I propose an alternative storage metric, the young water fraction in streamflow, defined as the fraction of runoff with transit times of less than roughly 0.2 years. I show that this young water fraction (not to be confused with event-based "new water" in hydrograph separations) is accurately predicted by seasonal tracer cycles within a precision of a few percent, across the entire range of mean transit times from almost zero to almost infinity. Importantly, this relationship is also virtually free from aggregation error. That is, seasonal tracer cycles also accurately predict the young water fraction in runoff from highly heterogeneous mixtures of subcatchments with strongly contrasting transit time distributions. Thus, although tracer cycle amplitudes yield biased and unreliable estimates of catchment mean travel times in heterogeneous catchments, they can be used reliably to estimate the fraction of young water in runoff.

Sign in / Sign up

Export Citation Format

Share Document