On Empirical Scrutiny of the Bohmian Model Using a Spin Rotator and the Arrival/Transit Time Distribution

Abstract. Baseflow recession analysis and groundwater dating have up to now developed as two distinct branches of hydrogeology and have been used to solve entirely different problems. We show that by combining two classical models, namely the Boussinesq equation describing spring baseflow recession, and the exponential piston-flow model used in groundwater dating studies, the parameters describing the transit time distribution of an aquifer can be in some cases estimated to a far more accurate degree than with the latter alone. Under the assumption that the aquifer basis is sub-horizontal, the mean transit time of water in the saturated zone can be estimated from spring baseflow recession. This provides an independent estimate of groundwater transit time that can refine those obtained from tritium measurements. The approach is illustrated in a case study predicting atrazine concentration trend in a series of springs draining the fractured-rock aquifer known as the Luxembourg Sandstone. A transport model calibrated on tritium measurements alone predicted different times to trend reversal following the nationwide ban on atrazine in 2005 with different rates of decrease. For some of the springs, the actual time of trend reversal and the rate of change agreed extremely well with the model calibrated using both tritium measurements and the recession of spring discharge during the dry season. The agreement between predicted and observed values was however poorer for the springs displaying the most gentle recessions, possibly indicating a stronger influence of continuous groundwater recharge during the summer months.

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State vector models of the cell cycle II: The first three moments of the transit time distribution

Journal of Theoretical Biology ◽

10.1016/0022-5193(79)90144-9 ◽

1979 ◽

Vol 77 (1) ◽

pp. 141-160 ◽

Cited By ~ 5

Author(s):

R. Allen White ◽

H.D. Thames

Keyword(s):

Cell Cycle ◽

Transit Time ◽

State Vector ◽

Time Distribution ◽

Transit Time Distribution

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Random paths through a convex region

Journal of Applied Probability ◽

10.1017/s0021900200105662 ◽

1978 ◽

Vol 15 (01) ◽

pp. 144-152 ◽

Cited By ~ 14

Author(s):

E. G. Enns ◽

P. F. Ehlers

Keyword(s):

Transit Time ◽

Time Distribution ◽

Convex Region ◽

Transit Time Distribution ◽

Straightforward Approach

The distribution of the length of random secants through a convex region is formulated in terms of the intersection volume of the convex region with its translated self. This method allows a more straightforward approach to calculating secant-length distributions for various measures of randomness. The results are applied to calculating the transit-time distribution of particles traversing a convex region. Several examples are given.

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Transit time distribution of aerosols in 3-D lung bifurcations

Journal of Aerosol Science ◽

10.1016/0021-8502(96)00374-6 ◽

1996 ◽

Vol 27 ◽

pp. S603-S604 ◽

Cited By ~ 1

Author(s):

T. Heistracher ◽

W. Hofmann ◽

I. Balásházy

Keyword(s):

Transit Time ◽

Time Distribution ◽

Transit Time Distribution ◽

Lung Bifurcations

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

Journal of Cerebral Blood Flow & Metabolism ◽

10.1038/jcbfm.2014.254 ◽

2015 ◽

Vol 35 (5) ◽

pp. 806-817 ◽

Cited By ~ 36

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.

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