Computational singular perturbation analysis of brain lactate metabolism

Lactate in the brain is considered an important fuel and signalling molecule for neuronal activity, especially during neuronal activation. Whether lactate is shuttled from astrocytes to neurons or from neurons to astrocytes leads to the contradictory Astrocyte to Neuron Lactate Shuttle (ANLS) or Neuron to Astrocyte Lactate Shuttle (NALS) hypotheses, both of which are supported by extensive, but indirect, experimental evidence. This work explores the conditions favouring development of ANLS or NALS phenomenon on the basis of a model that can simulate both by employing the two parameter sets proposed by Simpson et al. (J Cereb. Blood Flow Metab., 27:1766, 2007) and Mangia et al. (J of Neurochemistry, 109:55, 2009). As most mathematical models governing brain metabolism processes, this model is multi-scale in character due to the wide range of time scales characterizing its dynamics. Therefore, we utilize the Computational Singular Perturbation (CSP) algorithm, which has been used extensively in multi-scale systems of reactive flows and biological systems, to identify components of the system that (i) generate the characteristic time scale and the fast/slow dynamics, (ii) participate to the expressions that approximate the surfaces of equilibria that develop in phase space and (iii) control the evolution of the process within the established surfaces of equilibria. It is shown that a decisive factor on whether the ANLS or NALS configuration will develop during neuronal activation is whether the lactate transport between astrocytes and interstitium contributes to the fast dynamics or not. When it does, lactate is mainly generated in astrocytes and the ANLS hypothesis is realised, while when it doesn’t, lactate is mainly generated in neurons and the NALS hypothesis is realised. This scenario was tested in exercise conditions

CH4/air homogeneous autoignition: A comparison of two chemical kinetics mechanisms

Reactions contributing to the generation of the explosive time scale that characterise autoignition of homogeneous stoichiometric CH4/air mixture are identified using two different chemical kinetics models; the well known GRI-3.0 mechanism (53/325 species/reactions with N-chemistry) and the AramcoMech mechanism from NUI Galway (113/710 species/reactions without N-chemistry; Combustion and Flame 162:315-330, 2015). Although the two mechanisms provide qualitatively similar results (regarding ignition delay and profiles of temperature, of mass fractions and of explosive time scale), the 113/710 mechanism was shown to reproduce the experimental data with higher accuracy than the 53/325 mechanism. The present analysis explores the origin of the improved accuracy provided by the more complex kinetics mechanism. It is shown that the reactions responsible for the generation of the explosive time scale differ significantly. This is reflected to differences in the length of the chemical and thermal runaways and in the set of the most influential species

Comparative investigation of homogeneous autoignition of DME/air and EtOH/air mixtures at low initial temperatures

The dynamics of homogeneous isochoric explosions of dimethylether (DME)/air and ethanol (EtOH)/air mixtures were studied and compared at relatively low initial temperatures (≤ 700 K) using algorithmic tools derived from the methodology of computational singular perturbation. In the DME case, it is shown that the low-temperature oxidation is dominated by reactions involving heavy carbonaceous species, in contrast to the high-temperature case where oxidation is dominated by reactions involving light carbonaceous species. Moreover, it is demonstrated that the outcome of the competition between two specific reactions is the cause of the exhibited negative temperature coefficient (NTC). In the EtOH case, the analysis points to the importance of carbonaceous species and in particular acetaldehyde, which is different from what happens at elevated initial temperatures (above 1000 K), where hydrogen chemistry dominates the entirety of the oxidation process. The autoignition dynamics of both mixtures are shown to be pretty much independent of initial pressure, with the exception of the NTC behaviour of DME

H2/Air Autoignition Dynamics around the Third Explosion Limit

This paper examines the influence of wall reactions on the generation of the explosive time scale that characterizes ignition delay around the third explosion limit of a stoichiometric H2/air homogeneous mixture. The only wall reactions exhibiting a sizeable influence are HO2→HO2(w) and H2O2→H2O2(w)—in both cases opposing the ignition process. The opposing influence of the former wall reaction complements that of 2HO2→H2O2+O2 in opposing H2O2+H←H2+HO2, which promotes ignition. However, the combined influence of these three reactions is not practically affected when the third explosion limit is crossed by increasing the initial pressure for a given initial temperature. The latter wall reaction opposes 2OH(+M)←H2O2(+M), which also promotes ignition. The combined influence of these reactions increases substantially as the third explosion limit is crossed, leading to significantly lower ignition delays. It is shown that around the third explosion limit the temperature has a strong influence on the explosive mode that leads to ignition. This influence is stronger when the wall reactions are accounted for

Autoignition dynamics of DME/air and EtOH/air homogeneous mixtures

The autoignition kinetics of DME/air and EtOH/air stoichiometric mixtures are compared with the use of algorithmic tools from the CSP method at a range of initial conditions that refers to the operation of reciprocating engines. DME and EtOH are two isomer fuels, with the potential for production from renewable sources, that have virtually identical thermochemistry; i.e. very closely equal heat of combustion and adiabatic flame temperature. These isomer fuels have drastically different ignition delays because of their different kinetics. In particular, the first and largest part of the ignition delay in the DME and EtOH cases is dominated by two different sets of components of carbon chemistry, while the last and shortest part is dominated by the same hydrogen chemistry. Considering sufficiently large initial temperatures, in the DME case the time scale that characterizes autoignition in the first part is promoted by single-carbon chemistry and is opposed mainly by recombination of CH3 radicals. On the contrary, in the EtOH case the two-carbon chain retains its bond in that part. Therefore, the hydrogen chemistry plays an important role in promoting the generation of the time scale that characterizes autoignition from the start of the process, while the reactions that oppose the generation of this time scale involve HO2 and H2O2 and they are not as effective as the reactions opposing ignition for DME. These features generate a substantially shorter ignition delay for EtOH. This situation is reversed for sufficiently low initial temperatures due to the shift in relative importance between internal and external H-abstraction that occurs as temperature increases

Ignition delay control of DME/air and EtOH/air homogeneous autoignition with the use of various additives

The effect of selected additives on the ignition delay of ethanol (EtOH)/air and dimethylether (DME)/air mixture is investigated. Computational Singular Perturbation (CSP) tools are utilized in an effort to determine algorithmically which species to select as additives and it is established that CSP can identify species whose addition to the mixture can affect ignition delay. However, this is not a necessary condition for additives to be effective. Additives that are not identified by CSP can have a substantial effect on ignition delay, provided that they drastically alter the prevailing chemistry, by altering the instant in time when the thermal runaway regime develops. Some of the additives that were studied computationally are unstable radicals whose injection in practical mixtures is unrealistic. However, chemically stable, relatively light species were also determined that can drastically affect ignition delay, such as hydrogen peroxide, formaldehyde and acetaldehyde

H2/Air Autoignition Dynamics around the Third Explosion Limit

This paper examines the influence of wall reactions on the generation of the explosive time scale that characterizes ignition delay around the third explosion limit of a stoichiometric H2/air homogeneous mixture. The only wall reactions exhibiting a sizeable influence are HO2→HO2(w) and H2O2→H2O2(w)—in both cases opposing the ignition process. The opposing influence of the former wall reaction complements that of 2HO2→H2O2+O2 in opposing H2O2+H←H2+HO2, which promotes ignition. However, the combined influence of these three reactions is not practically affected when the third explosion limit is crossed by increasing the initial pressure for a given initial temperature. The latter wall reaction opposes 2OH(+M)←H2O2(+M), which also promotes ignition. The combined influence of these reactions increases substantially as the third explosion limit is crossed, leading to significantly lower ignition delays. It is shown that around the third explosion limit the temperature has a strong influence on the explosive mode that leads to ignition. This influence is stronger when the wall reactions are accounted for

The mechanism by which CH2O and H2O2 additives affect the autoignition of CH4/air mixtures

When the fast dissipative time scales become exhausted, the evolution of reacting processes is characterized by slower time scales. Here the case where these slower time scales are of explosive character is considered. This feature allows for the acquisition of significant physical understanding; among others, the identification of intermediates in the reacting process that can be used as additives for the control of the ignition delay. The case of the homogeneous autoignition of CH4/air mixtures is analyzed here and the effects of adding the stable intermediates CH2O and H2O2 to the fuel. These two species are identified as those relating the most to the explosive mode that causes autoignition, throughout the largest part of the ignition delay. Small quantities of these species in the initial mixture decrease considerably the ignition delay, by expediting the development of the thermal runaway

Algorithmic determination of the mechanism through which H2O-dilution affects autoignition dynamics and NO formation in CH4/air mixtures

The Computational Singular Perturbation (CSP) algorithm is employed in order to determine how H2O-dilution influences ignition delay and chemical paths that generate NO during isochoric homogenous lean CH4/air autoignition. Regarding the ignition delay, it is shown that H2O-dilution enhances reactivity, mainly due to the increased OH production throughout the explosive stage via reaction H2O2 (+H2O) -> OH + OH(+H2O). With regard to NO generation, the relative importance of thermal and chemical effects are examined and it is concluded that both are important. The thermal effects result in a lower temperature at the end of the explosive stage, while the most notable chemical effect is the lower level of O after this stage, mainly due to the effect of H2O-dilution on the equilibrium of the reaction O + H2O OH + OH. The depletion of O, together with the thermal effect, causes a substantial decrease in final NO generation

Issues arising in the construction of QSSA mechanisms: the case of reduced n-heptane/air models for premixed flames

A model reduction methodology, based on the quasi steady-state approximation (QSSA), is employed for the construction of reduced mechanisms in the case of an n-heptane/air premixed flame. Several issues related to the construction of these reduced mechanisms are discussed; such as the influence of the size of the starting skeletal mechanism, the stiffness reduction, and the truncation/simplification of (i) the expressions of the global rates and (ii) the steady-state relations. The starting point for the reduction is two skeletal mechanisms that involve 177/768 and 66/326 species/reactions, respectively [J. Prager, H.N. Najm, M. Valorani, and D.A. Goussis, Skeletal mechanism generation with CSP and validation for premixed n-heptane flames, Proc. Combust. Inst. 32 (2009), pp. 509–517] and which were derived from the detailed mechanism of Curran et al. [H.J. Curran, P. Gaffuri, W.J. Pitz, and C.K. Westbrook, A comprehensive modeling study of iso-octane oxidation, Combust. Flame 129 (2002), pp. 253–280], which involves 561/2538 species/reactions. From these two skeletal mechanisms, a number of reduced mechanisms of various sizes are produced and analysed. The validity of the reduced mechanism with the minimum size is demonstrated by considering its accuracy regarding the mass fractions of major and minor species, the temperature, and the flame speed, over a wide range of equivalence ratios and pressures