RESUMEN
A groundwater monitoring network surrounding a pumping well (such as a public water supply) allows for early contaminant detection and mitigation where possible contaminant source locations are often unknown. This numerical study investigates how the contaminant detection probability of a hypothetical sentinel-well monitoring network consisting of one to four monitoring wells is affected by aquifer spatial heterogeneity and dispersion characteristics, where the contaminant source location is randomized. This is achieved through a stochastic framework using a Monte Carlo approach. A single production well is considered that results in converging non-uniform flow close to the well. Optimal network arrangements are obtained by maximizing a weighted risk function that considers true and false positive detection rates, sampling frequency, early detection, and contaminant travel time uncertainty. Aquifer dispersivity is found to be the dominant parameter for the quantification of network performance. For the range of parameters considered, a single monitoring well screening the full aquifer thickness is expected to correctly and timely identify at least 12% of all incidents resulting in contaminants reaching the production well. This proportion increases to a global maximum of 96% for a network consisting of four wells and very dispersive transport conditions. Irrespective of network size and sampling frequency, more dispersive transport conditions result in higher detection rates. Increasing aquifer heterogeneity and decreasing aquifer spatial continuity also lead to higher detection rates, though these effects are diminished for networks of 3 or more wells. Statistical anisotropy has no effect on the network performance. Earlier detection, which is critical for remedial action and supply safety, comes with a significant cost in terms of detection rate, and should be carefully considered when a monitoring network is being designed.
Asunto(s)
Agua Subterránea , Contaminantes Químicos del Agua , Monitoreo del Ambiente/métodos , Incertidumbre , Contaminantes Químicos del Agua/análisis , Pozos de AguaRESUMEN
Neuronal activity evokes a localised increase in cerebral blood flow through neurovascular coupling (NVC), a communication system between a group of cells known as a neurovascular unit (NVU). Dysfunctional NVC can lead to pathologies such as cortical spreading depression (CSD), characterised by a slowly propagating wave of neuronal depolarisation and high extracellular potassium (K+) levels. CSD is associated with several neurological disorders such as migraine, stroke, and traumatic brain injury. Insight into the spatial dynamics of CSD in humans is mainly deduced from animal experiments on the smooth lissencephalic brain (in particular murine experiments), however the human cortex is gyrencephalic (highly folded) and is considered likely to exhibit different and more complex patterns of CSD. In this study a large scale numerical NVC model of multiple NVUs is coupled to a vascular tree simulating a two-dimensional cerebral tissue slice. This model is extended with a spatial Gaussian curvature mapping that can simulate the highly folded nature of the human cortex. For a flat surface comparable to a lissencephalic cortex the model can simulate propagating waves of high extracellular K+ travelling radially outwards from a stimulated area at approximately 6.7â¯mm/min, corresponding well with multiple experimental results. The high K+ concentration induces a corresponding wave of vasoconstriction (with decreased blood flow) then slight vasodilation, achieved through cellular communication within the NVU. The BOLD response decreases below baseline by approximately 10% followed by an increase of 1%. For a surface with spatially varied curvature comparable to a section of gyrencephalic cortex, areas of positive Gaussian curvature inhibit wave propagation due to decreased extracellular diffusion rate. Whereas areas of negative curvature promote propagation. Consequently extracellular K+ is observed travelling as wave segments (as opposed to radial waves) through flat or negatively curved "valleys" corresponding to folds (sulci) in the cortex. If the wave size (defined as the activated area of high K+ concentration) is too small or diffusion rate too low then wave segments can cease propagation. If the diffusion rate is high enough the wave segments can grow from open ends forming loose spiral waves. These results may provide some insight into the differences seen between human and animal experiments.
Asunto(s)
Corteza Cerebral/anatomía & histología , Depresión de Propagación Cortical/fisiología , Simulación por Computador , Humanos , Modelos Anatómicos , Potasio/metabolismoRESUMEN
Neuronal activity evokes a localised increase in cerebral blood flow in a response known as neurovascular coupling (NVC), achieved through communication between a group of cells known as a neurovascular unit (NVU). Dysfunctional NVC can lead to pathologies such as cortical spreading depression (CSD), characterised by a slow moving wave of neuronal depolarisation and high extracellular K+ levels. This phenomenon can be affected by the presence of an astrocytic gap junction network which is able to transport K+ away from areas of high concentrations, however the precise role of these gap junctions remains controversial. In this study, a large scale numerical NVC model of a vascular tree coupled with multiple NVUs comprising a two-dimensional cerebral tissue slice is extended through extracellular K+ and Na+ electrodiffusion and K+ transport via an astrocytic gap junction network. An updated NVU model has been utilised that contains complex neuronal and extracellular dynamics and is able to simulate various pathologies such as CSD and the effect on the vascular response. Under pathological conditions (determined by model parameters) and with extracellular electrodiffusion the model is able to simulate a propagating wave of high extracellular K+ travelling at 6.7â¯mm/min as can occur in CSD. This wave travels outward from the neuronally stimulated area and is followed by a wave of vasoconstriction (with corresponding decreased blood flow) then slight vasodilation in agreement with multiple experimental results. The vasoconstrictive wave peaks after the K+ wave due to the delayed vascular response. Increasing the density of astrocytic gap junctions reduces the duration and amplitude of the vasoconstrictive wave and for high enough density the vasoconstrictive behaviour outside the stimulated area is eliminated. Gap junctions also reduce the area that is initially affected by vasoconstriction. This in silico model provides a complex and experimentally validated test bed for a variety of neurological phenomena.
Asunto(s)
Astrocitos/metabolismo , Circulación Cerebrovascular , Depresión de Propagación Cortical , Modelos Cardiovasculares , Modelos Neurológicos , Neuronas/metabolismo , Acoplamiento Neurovascular , Vasodilatación , AnimalesRESUMEN
A state-of-the-art integrated model of neurovascular coupling (NVC) (Dormanns et al., 2015b; Dormanns et al., 2016; Kenny et al., 2018) and the BOLD response (Mathias et al., 2017a; Mathias et al., 2017b) is presented with the ability to simulate the fMRI BOLD responses due to continuous neuronal spiking, bursting and cortical spreading depression (CSD) along with the underlying complex vascular coupling. Simulated BOLD responses are compared to experimental BOLD signals observed in the rat barrel cortex and in the hippocampus under seizure conditions showing good agreement. Bursting phenomena provides relatively clear BOLD signals as long as the time between bursts is not too short. For short burst periods the BOLD signal remains constant even though the neuron is in a predominantly bursting mode. Simulation of CSD exhibits large negative BOLD signals. Visco-elastic effects of the capillary bed do not seem to have a large effect on the BOLD signal even for relatively high values of oxygen consumption. While the results of the model suggests that potassium ions released during neural activity could act as the main mediator in NVC, it suggests the possibility of other mechanisms that can coexist and increase blood flow such as the arachidonic acid to epoxyeicosatrienoic acid (EET) pathway. The comparison with experimental cerebral blood flow (CBF) data indicates the possible existence of multiple neural pathways influencing the vascular response. Initial negative BOLD signals occur for all simulations due to the rate at which the metabolic oxygen consumption occurs relative to the dilation of the perfusing cerebro-vasculature. However it is unclear as to whether these are normally seen clinically due to the size of the magnetic field. Experimental comparisons for different animal experiments may very well require variation in the model parameters. The complex integrated model is believed to be the first of its kind to simulate both NVC and the resulting BOLD signal.
Asunto(s)
Encéfalo/irrigación sanguínea , Encéfalo/fisiología , Modelos Neurológicos , Neuronas/fisiología , Acoplamiento Neurovascular , Animales , Mapeo Encefálico , Depresión de Propagación Cortical , Hipocampo/fisiología , Humanos , Imagen por Resonancia Magnética , Ratas , Corteza Somatosensorial/fisiologíaRESUMEN
Neuronal activity evokes a localised change in cerebral blood flow in a response known as neurovascular coupling (NVC). Although NVC has been widely studied the exact mechanisms that mediate this response remain unclear; in particular the role of astrocytic calcium is controversial. Mathematical modelling can be a useful tool for investigating the contribution of various signalling pathways towards NVC and for analysing the underlying cellular mechanisms. The lumped parameter model of a neurovascular unit with both potassium and nitric oxide (NO) signalling pathways and comprised of neurons, astrocytes, and vascular cells has been extended to include the glutamate induced astrocytic calcium pathway with epoxyeicosatrienoic acid (EET) signalling and the stretch dependent TRPV4 calcium channel on the astrocytic endfoot. Results show that the potassium pathway governs the fast onset of vasodilation while the NO pathway has a delayed response, maintaining dilation longer following neuronal stimulation. Increases in astrocytic calcium concentration via the calcium signalling pathway and/or TRPV4 channel to levels consistent with experimental data are insufficient for inducing either vasodilation or constriction, in contrast to a number of experimental results. It is shown that the astrocyte must depolarise in order to produce a significant potassium flux through the astrocytic BK channel. However astrocytic calcium is shown to strengthen potassium induced NVC by opening the BK channel further, consequently allowing more potassium into the perivascular space. The overall effect is vasodilation with a higher maximal vessel radius.