scholarly journals Study of capillary transit time distribution in coherent hemodynamics spectroscopy

2015 ◽  
Vol 08 (02) ◽  
pp. 1550025 ◽  
Author(s):  
Angelo Sassaroli ◽  
Jana Kainerstorfer ◽  
Sergio Fantini
Keyword(s):  
Blood Flow ◽  
Transit Time ◽  
Time Distribution ◽  
Mean Value ◽  
Original Model ◽  
Extended Model ◽  
Transit Times ◽  
Sinusoidal Input ◽  
The Mean ◽  
Transit Time Distribution

A recently proposed analytical hemodynamic model1 [S. Fantini, NeuroImage85, 202–221 (2014)] is able to predict the changes of oxy, deoxy, and total hemoglobin concentrations (model outputs) given arbitrary changes in blood flow, blood volume, and rate of oxygen consumption (model inputs). One assumption of this model is that the capillary compartment is characterized by a single blood transit time. In this work, we have extended the original model by considering a distribution of capillary transit times and we have compared the outputs of both models (original and extended) for the case of sinusoidal input signals at different frequencies, which realizes the new technique of coherent hemodynamics spectroscopy (CHS). For the calculations with the original model, we have used the mean value of the distribution of capillary transit times considered in the extended model. We have found that, for distributions of capillary transit times having mean values around 1 s and a standard deviation less than about 45% of the mean value, the original and extended models yield the same CHS spectra (i.e., model outputs versus frequency of oscillation) within typical experimental errors. For wider capillary transit time distributions, the two models yield different CHS spectra. By assuming that Poiseuille's law is valid in the capillary compartment, we have related the distribution of capillary transit times to the distributions of capillary lengths and capillary speed of blood flow to calculate the average capillary and venous saturations. We have found that, for standard deviations of the capillary transit time distribution that are less than about 80% of the mean value, the average capillary saturation is always larger than the venous saturation. By contrast, the average capillary saturation may be less than the venous saturation for wider distributions of the capillary transit times.

scholarly journals Nonparametric lower bounds to mean transit times

2017 ◽  
Author(s):  
Earl Bardsley
Keyword(s):  
Lower Bound ◽  
Transit Time ◽  
Time Distribution ◽  
Mean Transit Time ◽  
Mean Value ◽  
System A ◽  
Lumped Parameter ◽  
Transit Times ◽  
Lumped Parameter Models ◽  
Transit Time Distribution

Abstract. Mean transit time μT, also called mean residence time, has been used widely in hydrological studies as an indicator of catchment water storage characteristics. Typically μT is estimated by the nature of catchment transformation of a natural input tracer time series. For example, increased damping and delaying of 18O seasonal isotopic variation may be taken to indicate longer mean transit times. Part of a μT estimation process involves specification of a lumped parameter flow model which provides the basis for a parametric transit time distribution. However, μT estimation has been called into question because catchment flow systems have a degree of complexity which may not justify use of simple parametric distributions. Moving toward a related index, the question is raised here as to the extent to which an arbitrary transit time distribution might enable a model mean transit time to be minimized before the fit to catchment output tracer data becomes unacceptably poor. This minimized mean value μ* represents a lower bound to μT, whatever the true transit time distribution might be. The lower bound is not necessarily an approximation to μT but might serve as an index for catchment comparisons or detect when μT is large. For a linear catchment system a simple nonparametric linear programming (LP) approach can be utilised to obtain μ*, which is conditional on a user-specified acceptable level of data fit. The LP method presented is applicable to both steady state and time-varying catchment systems and has the advantage of not requiring specification of lumped parameter models or use of explicit transit time distributions.

scholarly journals The Wavelets show it – the transit time of water varies in time

2018 ◽  
Vol 66 (3) ◽  
pp. 295-302 ◽  
Author(s):  
Milan Onderka ◽  
Vladimír Chudoba
Keyword(s):  
Transit Time ◽  
Time Distribution ◽  
Conceptual Modeling ◽  
Flow Paths ◽  
Transit Times ◽  
The Mean ◽  
Transit Time Distribution ◽  
Mathematical Techniques ◽  
Time Invariant

Abstract The ways how water from rain or melting snow flows over and beneath the Earth‘s surface affects the timing and intensity at which the same water leaves a catchment. Several mathematical techniques have been proposed to quantify the transit times of water by e.g. convolving the input-output tracer signals, or constructing frequency response functions. The primary assumption of these techniques is that the transit time is regarded time-invariant, i.e. it does not vary with temporarily changing e.g. soil saturation, evaporation, storage volume, climate or land use. This raises questions about how the variability of water transit time can be detected, visualized and analyzed. In this paper we present a case study to show that the transit time is a temporarily dynamic variable. Using a real-world example from the Lower Hafren catchment, Wales, UK, and applying the Continuous Wavelet Transform we show that the transit time distributions are time-variant and change with streamflow. We define the Instantaneous Transit Time Distributions as a basis for the Master Transit Time Distribution. We show that during periods of elevated runoff the transit times are exponentially distributed. A bell-shaped distribution of travel times was observed during times of lower runoff. This finding is consistent with previous investigations based on mechanistic and conceptual modeling in the study area according to which the diversity of water flow-paths during wet periods is attributable to contributing areas that shrink and expand depending on the duration of rainfall. The presented approach makes no assumptions about the shape of the transit time distribution. The mean travel time estimated from the Master Transit Time Distribution was ~54.3 weeks.

Morphological controls on groundwater residence times of shallow aquifers

2020 ◽  
Author(s):  
Alexandre Gauvain ◽  
Sarah Leray ◽  
Jean Marçais ◽  
Camille Vautier ◽  
Luc Aquilina ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Transit Time ◽  
Time Distribution ◽  
Residence Times ◽  
Shallow Aquifers ◽  
Transit Times ◽  
Tracking Model ◽  
The Mean ◽  
Transit Time Distribution ◽  
Groundwater Body

<p>In shallow aquifers, including weathered zones characteristic of crystalline geologic basements, subsurface flows strongly depend on the geomorphological evolution of landscapes as well as on the geological heterogeneity structures. Yet, it remains largely unknown how geomorphology and geology shape the residence times in the aquifers and the transit times  in the receiving stream water bodies.</p><p>We investigate this issue with 3D synthetic models of free aquifers. Aquifer models represent hillslopes from the river to the catchment divide with constant slopes, evolving widths and depths. They are submitted to uniform and constant recharge. All flows end up in the river either through the aquifer or through the surface as return flows and saturation excess overland flows. Steady-state flows and transit times to the river are simulated with Modflow and Modpath (Niswonger et al., 2011; Pollock, 2016). The mean and standard deviation of the transit time distribution are systematically determined as functions of the hillslope shapes (convergent or divergent to the river, thinning or thickening to the river) and the ratio of recharge to hydraulic conductivity.</p><p>We show that the mean transit time distribution is a function of the geology through the volume of the aquifer divided by the recharge rate even in the presence of seepage areas. The standard deviation of the transit time distribution is a function of the geomorphology through the bulk organization of the groundwater body from the river to the catchment divide. Without seepage, the organization of the groundwater body is efficiently characterized by its barycenter. When seepage occurs, the standard deviation becomes also sensitive to the extent of the seepage zone.</p><p>We conclude that mean of the transit time distribution is primarily determined by geology through the accessible aquifer volume while the ratio of the standard deviation to the mean (coefficient of variation) is rather determined by geomorphology through the profile of the aquifer from the river to the catchment divide. We discuss how geophysical data might help to determine the groundwater body and assess the transit time distribution. We illustrate these findings on natural aquifers in the crystalline basements of Brittany-Normandy (France).</p><p><strong>References</strong></p><p>Niswonger, R.G., Panday, S., Ibaraki, M., 2011. MODFLOW-NWT, A Newton formulation for MODFLOW-2005.</p><p>Pollock, D.W., 2016. User guide for MODPATH Version 7—A particle-tracking model for MODFLOW (Report No. 2016–1086), Open-File Report. Reston, VA. https://doi.org/10.3133/ofr20161086</p>

scholarly journals The Effects of Capillary Transit Time Heterogeneity (CTH) on Brain Oxygenation

2015 ◽  
Vol 35 (5) ◽  
pp. 806-817 ◽  
Author(s):  
Hugo Angleys ◽  
Leif Østergaard ◽  
Sune N Jespersen
Keyword(s):  
Blood Flow ◽  
Diffusion Equation ◽  
Oxygen Tension ◽  
Transit Time ◽  
Time Distribution ◽  
Ischemia Reperfusion ◽  
Oxygen Metabolism ◽  
Tissue Oxygen Tension ◽  
Tissue Oxygen ◽  
Transit Time Distribution

We recently extended the classic flow–diffusion equation, which relates blood flow to tissue oxygenation, to take capillary transit time heterogeneity ( CTH) into account. Realizing that cerebral oxygen availability depends on both cerebral blood flow ( CBF) and capillary flow patterns, we have speculated that CTH may be actively regulated and that changes in the capillary morphology and function, as well as in blood rheology, may be involved in the pathogenesis of conditions such as dementia and ischemia-reperfusion injury. The first extended flow–diffusion equation involved simplifying assumptions which may not hold in tissue. Here, we explicitly incorporate the effects of oxygen metabolism on tissue oxygen tension and extraction efficacy, and assess the extent to which the type of capillary transit time distribution affects the overall effects of CTH on flow–metabolism coupling reported earlier. After incorporating tissue oxygen metabolism, our model predicts changes in oxygen consumption and tissue oxygen tension during functional activation in accordance with literature reports. We find that, for large CTH values, a blood flow increase fails to cause significant improvements in oxygen delivery, and can even decrease it; a condition of malignant CTH. These results are found to be largely insensitive to the choice of the transit time distribution.

Distribution of pulmonary capillary red blood cell transit times

1995 ◽  
Vol 79 (2) ◽  
pp. 382-388 ◽  
Author(s):  
R. G. Presson ◽  
J. A. Graham ◽  
C. C. Hanger ◽  
P. S. Godbey ◽  
S. A. Gebb ◽  
...  
Keyword(s):  
Red Blood Cells ◽  
Transit Time ◽  
Blood Cells ◽  
Time Distribution ◽  
Capillary Networks ◽  
Transit Times ◽  
Pulmonary Capillary ◽  
Capillary Bed ◽  
Transit Time Distribution ◽  
Pass Through

In theory, red blood cells can pass through the pulmonary capillaries too rapidly to be completely saturated with oxygen during exercise. This idea has not been directly tested because the transit times of the fastest red blood cells are unknown. We report the first measurements of the entire transit time distribution for red blood cells crossing single subpleural capillary networks of canine lung using in vivo fluorescence videomicroscopy and compare those times with the distribution of plasma transit times in the same capillary networks. On average, plasma took 1.4 times longer than red blood cells to pass through the capillary bed. Decreased transit times with increased cardiac output were mitigated by both capillary recruitment and a narrowing of the transit time distribution. This design feature of the pulmonary capillary bed kept the shortest times from falling below the theoretical minimum time for complete oxygenation.

scholarly journals The Transit-Time Distribution from the Northern Hemisphere Midlatitude Surface

2016 ◽  
Vol 73 (10) ◽  
pp. 3785-3802 ◽  
Author(s):  
Clara Orbe ◽  
Darryn W. Waugh ◽  
Paul A. Newman ◽  
Stephen Steenrod
Keyword(s):  
Northern Hemisphere ◽  
Transit Time ◽  
Time Distribution ◽  
Transport Model ◽  
Fundamental Property ◽  
Spectral Width ◽  
The Arctic ◽  
Transit Times ◽  
Fast Transport ◽  
Transit Time Distribution

Abstract The distribution of transit times from the Northern Hemisphere (NH) midlatitude surface is a fundamental property of tropospheric transport. Here, the authors present an analysis of the transit-time distribution (TTD) since air last contacted the NH midlatitude surface, as simulated by the NASA Global Modeling Initiative Chemistry Transport Model. Throughout the troposphere, the TTD is characterized by young modes and long tails. This results in mean transit times or “mean ages” Γ that are significantly larger than their corresponding modal transit times or “modal ages” τmode, especially in the NH, where Γ ≈ 0.5 yr, while τmode < 20 days. In addition, the shape of the TTD changes throughout the troposphere as the ratio of the spectral width Δ—the second temporal moment of the TTD—to the mean age decreases sharply in the NH from ~2.5 at NH high latitudes to ~0.7 in the Southern Hemisphere (SH). Decreases in Δ/Γ in the SH reflect a narrowing of the TTD relative to its mean and physically correspond to changes in the contributions of fast transport paths relative to slow eddy-diffusive recirculations. It is shown that fast transport paths control the patterns and seasonal cycles of idealized 5- and 50-day loss tracers in the Arctic and the tropics, respectively. The relationship between different TTD time scales and the idealized loss tracers, therefore, is conditional on the shape of the TTD.

scholarly journals The potential uses of tracer cycles for groundwater dating in heterogeneous aquifers

2016 ◽  
Author(s):  
Julien Farlin ◽  
Piotr Małoszewski
Keyword(s):  
Transit Time ◽  
Time Distribution ◽  
Mean Transit Time ◽  
Homogeneous Medium ◽  
Distribution Functions ◽  
Temperature Cycle ◽  
Groundwater Temperature ◽  
Groundwater Dating ◽  
The Mean ◽  
Transit Time Distribution

Abstract. The use of the annual cycles of stable isotopes to estimate the parameters of transit time distribution functions has been recently criticised by Kirchner (2016). The author shows that the mean residence time of heterogeneous catchments calculated from the damping of the amplitude of the input signal are very often over-estimates, sometimes by large factors. We show here that the overestimation depends on the relative time scales of the cycle’s frequency and the mean transit time and that tracer cycles can still be used, at least for groundwater systems sustained by baseflow. Firstly it appears that an exponential model is a good approximation for the transit time distribution of a heterogeneous groundwatershed if the subgroundwatersheds’ transit time distributions are themselves exponential and their mean transit times are in the same range or slightly higher than the period of the tracer cycle. Secondly, we suggest that tracer cycles can still be used as secondary data to test whether the degree of heterogeneity of the subsurface is small enough to warrant approximating it by a homogeneous medium. Lastly, we develop a model predicting the amplitude of groundwater temperature from the annual air temperature cycle, and show that even though temperature is not a conservative tracer, it can be useful for groundwater dating. The potential use of the temperature cycle is illustrated in the case-study of a sandstone aquifer drained by contact springs.

scholarly journals Retrieving the age of air spectrum from tracers: principle and method

2018 ◽  
Author(s):  
Aurélien Podglajen ◽  
Felix Ploeger
Keyword(s):  
Transit Time ◽  
Annual Cycle ◽  
Time Distribution ◽  
Small Dimension ◽  
Inversion Method ◽  
Radioactive Tracers ◽  
Linear Inverse Problem ◽  
Transit Times ◽  
Scale Structures ◽  
Transit Time Distribution

Abstract. Surface-emitted tracers with different dependencies on transit time (e.g., due to chemical loss or time-dependent boundary conditions) carry independent pieces of information on the age of air spectrum (the distribution of transit times from the surface). This paper investigates how and to what extent knowledge of tracer concentrations can be used to retrieve the age spectrum. Since the tracers considered depend linearly on the transit time distribution, the question posed can be formulated as a linear inverse problem of small dimension. An inversion methodology is introduced, which does not require any assumptions regarding the shape of the spectrum. The performance of the approach is first evaluated on a constructed set of artificial radioactive tracers derived from idealized spectra. Hereafter, the inversion method is applied to model output. The latter experiment highlights the limits of inversions using only parent radioactive tracers: they are unable to retrieve fine scale structures such as the annual cycle. Improvements can be achieved by including daughter decaying tracers and tracers with an annual cycle at the surface. This study demonstrates the feasibility of retrieving the age spectrum from tracers, and has implications for transport diagnosis in models and observations.

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.

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