On a minimal model for hemodynamics and metabolism of lactate: application to low grade glioma and therapeutic strategies.

WHO II low grade glioma evolves inevitably to anaplastic transformation. Magnetic resonance imaging is a good non-invasive way to watch it, by hemodynamic and metabolic modifications, thanks to multinuclear spectroscopy (1)H/(31)P. In this work we study a multi-scale minimal model of hemodynamics and metabolism applied to the study of gliomas. This mathematical analysis leads us to a fast-slow system. The control of the position of the stationary point brings to the concept of domain of viability. Starting from this system, the equations bring to light the parameters that push glioma cells out of their domain of viability. Four fundamental factors are highlighted. The first two are cerebral blood flow and the rate of lactate transport through monocarboxylate transporters, which must be reduced in order to push glioma out of its domain of viability. Another factor is the intra arterial lactate, which must be increased. The last factor is pH, indeed a decrease of intra cellular pH could interfere with glioma growth. These reflections suggest that these four parameters could lead to new therapeutic strategies for the management of low grade gliomas.

Determinants of brain cell metabolic phenotypes and energy substrate utilization unraveled with a modeling approach.

Although all brain cells bear in principle a comparable potential in terms of energetics, in reality they exhibit different metabolic profiles. The specific biochemical characteristics explaining such disparities and their relative importance are largely unknown. Using a modeling approach, we show that modifying the kinetic parameters of pyruvate dehydrogenase and mitochondrial NADH shuttling within a realistic interval can yield a striking switch in lactate flux direction. In this context, cells having essentially an oxidative profile exhibit pronounced extracellular lactate uptake and consumption. However, they can be turned into cells with prominent aerobic glycolysis by selectively reducing the aforementioned parameters. In the case of primarily oxidative cells, we also examined the role of glycolysis and lactate transport in providing pyruvate to mitochondria in order to sustain oxidative phosphorylation. The results show that changes in lactate transport capacity and extracellular lactate concentration within the range described experimentally can sustain enhanced oxidative metabolism upon activation. Such a demonstration provides key elements to understand why certain brain cell types constitutively adopt a particular metabolic profile and how specific features can be altered under different physiological and pathological conditions in order to face evolving energy demands.

Proton MR spectroscopy in predicting the increase of perfusion MR imaging for WHO grade II gliomas.

PURPOSE: To investigate the correlation between the metabolite ratios obtained from proton magnetic resonance (MR) spectroscopy and those obtained from MR perfusion parameters (relative cerebral blood volume [rCBV]) in a cohort of low-grade glioma (LGG). MATERIALS AND METHODS: Patients underwent prospectively conventional MR, proton magnetic resonance spectroscopy ((1) HMRS), and perfusion-weighted images (PWI). Statistical analyses were performed to determine the correlative and independent predictive factors of rCBVmax and the metabolite ratio thresholds with optimum sensitivity and specificity. RESULTS: Thirty-one patients were included in this study. Linear correlations were observed between the metabolic ratios (lactate [Lac]/creatine [Cr], choline [Cho]/N-acetyl-aspartate [NAA], free-lipids/Cr) and rCBVmax (P < 0.05). These metabolic ratios were determined to be independent predictive factors of rCBVmax (P = 0.027, 0.011 and 0.032, respectively). According to the receiver operating characteristic curves, the cutoff values of the metabolic ratios to discriminate between the two populations of rCBVmax (<1.7 versus = 1.7) were 1.72, 1.54, and 1.40, respectively, with a sensitivity = 75% and a specificity >95% for Lac/Cr. CONCLUSION: This study demonstrated consistent correlations between the data from (1) HMRS and PWI. The Lac/Cr ratio predicts regional hemodynamic changes, which are themselves a useful biomarker of clinical prognosis in patients with LGG. As such, this ratio may provide a new parameter for making improved clinical decisions.

Mathematical modeling of energy metabolism and hemodynamics of WHO grade II gliomas using in vivo MR data.

Therapeutic management of low-grade gliomas (LGG) is a challenge because they have undergone anaplastic transformation with variable delay. Today, only progressive volume growth on successive MRI allows an in vivo monitoring of this evolution. On the other hand, multinuclear spectroscopy and perfusion available during MRI may also provide assessment of metabolic changes underlying morphological modifications. To overcome this drawback, we developed a mathematical model of the metabolism and the hemodynamic of gliomas, based on a physiological model previously published, and including the MR parameters. This allows us to suggest that some specific profiles of metabolic and hemodynamic changes would be good indicators of potential anaplastic transformation.

Basic properties of electrical field coupling between neurons: an analytical approach.

The basic properties of the electrical field coupling between two parallel neurons, with linear electrical properties of the membranes, are investigated using a mathematical model-based on Laplace transform and matrix algebra, assuming that the system is unidimensional. This approach is extended to a ramified dendritic tree, and to a set of parallel neurons a subset of which is synaptically activated. We show that the electrical field effect is governed by certain geometrical and electrophysiological parameters, the most important being a coupling coefficient k, which depends on the extra- and intracellular resistivity, as well as the extracellular volume fraction. These results support the hypothesis that electrical field effects play an important role in the regions of the brain where neurons are densely packed, even in the absence of, or before, cell firing.

Proton magnetic resonance spectroscopy predicts proliferative activity in diffuse low-grade gliomas.

The aim of the study was to investigate the ability of (1)HMRS to reflect proliferative activity of diffuse low-grade gliomas (WHO grade II). Between November 2002 and March 2007, a prospective study was performed on consecutive patients with suspected supratentorial hemispheric diffuse low-grade tumors. All the patients underwent MR examination using uniform procedures, and then surgical resection or biopsy within 2 weeks of the MR examination. Proliferative activity of the tumors was assessed by Ki-67 immunochemistry (Mb-1) on paraffin embedded tumor sections. Spectroscopic data was compared with Ki-67 labeling index and other histologic data such as histological subtype, cellular atypia, cellular density using univariate and multivariate analysis. 82 of 97 consecutive patients had histologically confirmed WHO grade 2 gliomas. Ki-67 proliferation index (PI) was correlated with specific spectral patterns: (1) low PI (<4%) was associated with increased Cho/Cr and absence of both free lipids or lactates; (2) intermediate PI (4-8%) was associated with resonance of lactates; and (3) high PI (>8%) was characterized by a resonance of free lipids. On multivariate analysis, resonance of lactates and resonance of free lipids appeared as independent predictors of intermediate PI (P < 0.001) and high PI (P < 0.001), respectively; moreover, free lipids resonance was correlated with cellular atypia (P < 0.05). This study suggests that (1)HMRS is a reliable tool to evaluate the proliferation activity of WHO grade 2 glioma and to identify potentially more aggressive clinical behavior.

Activity-dependent regulation of energy metabolism by astrocytes: an update.

Astrocytes play a critical role in the regulation of brain metabolic responses to activity. One detailed mechanism proposed to describe the role of astrocytes in some of these responses has come to be known as the astrocyte-neuron lactate shuttle hypothesis (ANLSH). Although controversial, the original concept of a coupling mechanism between neuronal activity and glucose utilization that involves an activation of aerobic glycolysis in astrocytes and lactate consumption by neurons provides a heuristically valid framework for experimental studies. In this context, it is necessary to provide a survey of recent developments and data pertaining to this model. Thus, here, we review very recent experimental evidence as well as theoretical arguments strongly supporting the original model and in some cases extending it. Aspects revisited include the existence of glutamate-induced glycolysis in astrocytes in vitro, ex vivo, and in vivo, lactate as a preferential oxidative substrate for neurons, and the notion of net lactate transfer between astrocytes and neurons in vivo. Inclusion of a role for glycogen in the ANLSH is discussed in the light of a possible extension of the astrocyte-neuron lactate shuttle (ANLS) concept rather than as a competing hypothesis. New perspectives offered by the application of this concept include a better understanding of the basis of signals used in functional brain imaging, a role for neuron-glia metabolic interactions in glucose sensing and diabetes, as well as novel strategies to develop therapies against neurodegenerative diseases based upon improving astrocyte-neuron coupled energetics.

Compartmentalization of brain energy metabolism between glia and neurons: insights from mathematical modeling.

We review the contribution of mathematical modeling of metabolic pathways to the study of the compartmentalization of brain energy metabolism between neurons and glia. We especially focus on the role of lactate in the relationship between glia and neurons and the possible presence of an astrocyte-neuron lactate shuttle (ANLS). We first discuss models of glucose, pyruvate, and lactate kinetics, which are relevant to neuron-glia interactions. We then review models of compartmentalized energy metabolism, which deal with the concepts of 'red' and 'white' stimulations, and the ANLS hypothesis. We next show the contribution of a study of model robustness to the debate about the potential role of lactate in metabolic interactions between glia and neurons. Finally, we discuss the possible implications of modeling for further experimental studies.

A coherent neurobiological framework for functional neuroimaging provided by a model integrating compartmentalized energy metabolism.

Functional neuroimaging has undergone spectacular developments in recent years. Paradoxically, its neurobiological bases have remained elusive, resulting in an intense debate around the cellular mechanisms taking place upon activation that could contribute to the signals measured. Taking advantage of a modeling approach, we propose here a coherent neurobiological framework that not only explains several in vitro and in vivo observations but also provides a physiological basis to interpret imaging signals. First, based on a model of compartmentalized energy metabolism, we show that complex kinetics of NADH changes observed in vitro can be accounted for by distinct metabolic responses in two cell populations reminiscent of neurons and astrocytes. Second, extended application of the model to an in vivo situation allowed us to reproduce the evolution of intraparenchymal oxygen levels upon activation as measured experimentally without substantially altering the initial parameter values. Finally, applying the same model to functional neuroimaging in humans, we were able to determine that the early negative component of the blood oxygenation level-dependent response recorded with functional MRI, known as the initial dip, critically depends on the oxidative response of neurons, whereas the late aspects of the signal correspond to a combination of responses from cell types with two distinct metabolic profiles that could be neurons and astrocytes. In summary, our results, obtained with such a modeling approach, support the concept that both neuronal and glial metabolic responses form essential components of neuroimaging signals.

Brain lactate kinetics: Modeling evidence for neuronal lactate uptake upon activation.

A critical issue in brain energy metabolism is whether lactate produced within the brain by astrocytes is taken up and metabolized by neurons upon activation. Although there is ample evidence that neurons can efficiently use lactate as an energy substrate, at least in vitro, few experimental data exist to indicate that it is indeed the case in vivo. To address this question, we used a modeling approach to determine which mechanisms are necessary to explain typical brain lactate kinetics observed upon activation. On the basis of a previously validated model that takes into account the compartmentalization of energy metabolism, we developed a mathematical model of brain lactate kinetics, which was applied to published data describing the changes in extracellular lactate levels upon activation. Results show that the initial dip in the extracellular lactate concentration observed at the onset of stimulation can only be satisfactorily explained by a rapid uptake within an intraparenchymal cellular compartment. In contrast, neither blood flow increase, nor extracellular pH variation can be major causes of the lactate initial dip, whereas tissue lactate diffusion only tends to reduce its amplitude. The kinetic properties of monocarboxylate transporter isoforms strongly suggest that neurons represent the most likely compartment for activation-induced lactate uptake and that neuronal lactate utilization occurring early after activation onset is responsible for the initial dip in brain lactate levels observed in both animals and humans.

Interaction between astrocytes and neurons studied using a mathematical model of compartmentalized energy metabolism.

Understanding cerebral energy metabolism in neurons and astrocytes is necessary for the interpretation of functional brain imaging data. It has been suggested that astrocytes can provide lactate as an energy fuel to neurons, a process referred to as astrocyte-neuron lactate shuttle (ANLS). Some authors challenged this hypothesis, defending the classical view that glucose is the major energy substrate of neurons, at rest as well as in response to a stimulation. To test the ANLS hypothesis from a theoretical point of view, we developed a mathematical model of compartmentalized energy metabolism between neurons and astrocytes, adopting hypotheses highly unfavorable to ANLS. Simulation results can be divided between two groups, depending on the relative neuron versus astrocyte stimulation. If this ratio is low, ANLS is observed during all the stimulus and poststimulus periods (continuous ANLS), but a high ratio induces ANLS only at the beginning of the stimulus and during the poststimulus period (triphasic behavior). Finally, our results show that current experimental data on lactate kinetics are compatible with the ANLS hypothesis, and that it is essential to assess the neuronal and astrocytic NADH/NAD+ ratio changes to test the ANLS hypothesis.

Relation between cerebral blood flow and metabolism explained by a model of oxygen exchange.

The cerebral blood flow (CBF) and cerebral metabolic rate of oxygen (CMRo(2)) are major determinants of the contrast in functional magnetic resonance imaging and optical imaging. However, the coupling between CBF and CMRo(2) during cerebral activation remains controversial. Whereas most of the previous models tend to show a nonlinear coupling, experimental studies have led to conflicting conclusions. A physiologic model was developed of oxygen transport through the blood-brain barrier (BBB) for dynamic and stationary states. Common model simplifications are proposed and their implications for the CBF/CMRo(2) relation are studied. The tissue oxygen pool, the BBB permeability, and the hemoglobin dissociation curve are physiologic parameters directly involved in the CBF/CMRo(2) relation. We have been shown that the hypothesis of a negligible tissue oxygen pool, which was admitted by most of the previous models, implies a tight coupling between CBF and CMRo(2). By relaxing this hypothesis, a real uncoupling was allowed that gives a more coherent view of the CBF/CMRo(2) relation, in better agreement with the hypercapnia data and with the variability reported in experimental works for the relative changes of those two variables. This also allows a temporal mismatch between CBF and CMRo(2), which influences the temporal shape of oxygenation at the capillary end.

A model of the coupling between brain electrical activity, metabolism, and hemodynamics: application to the interpretation of functional neuroimaging.

In order to improve the interpretation of functional neuroimaging data, we implemented a mathematical model of the coupling between membrane ionic currents, energy metabolism (i.e., ATP regeneration via phosphocreatine buffer effect, glycolysis, and mitochondrial respiration), blood-brain barrier exchanges, and hemodynamics. Various hypotheses were tested for the variation of the cerebral metabolic rate of oxygen (CMRO(2)): (H1) the CMRO(2) remains at its baseline level; (H2) the CMRO(2) is enhanced as soon as the cerebral blood flow (CBF) increases; (H3) the CMRO(2) increase depends on intracellular oxygen and pyruvate concentrations, and intracellular ATP/ADP ratio; (H4) in addition to hypothesis H3, the CMRO(2) progressively increases, due to the action of a second messenger. A good agreement with experimental data from magnetic resonance imaging and spectroscopy (MRI and MRS) was obtained when we simulated sustained and repetitive activation protocols using hypotheses (H3) or (H4), rather than hypotheses (H1) or (H2). Furthermore, by studying the effect of the variation of some physiologically important parameters on the time course of the modeled blood-oxygenation-level-dependent (BOLD) signal, we were able to formulate hypotheses about the physiological or biochemical significance of functional magnetic resonance data, especially the poststimulus undershoot and the baseline drift.

Modeling of pathophysiological coupling between brain electrical activation, energy metabolism and hemodynamics: insights for the interpretation of intracerebral tumor imaging.

Gliomas can display marked changes in the concentrations of energy metabolism molecules such as creatine (Cr), phosphocreatine (PCr) and lactate, as measured using magnetic resonance spectroscopy (MRS). Moreover, the BOLD (blood oxygen level dependent) contrast enhancement in functional magnetic resonance imaging (fMRI) can be reduced or missing within or near gliomas, while neural activity is not significantly reduced (so-called neurovascular decoupling), so that the location of functionally eloquent areas using fMRI can be erroneous. In this paper, we adapt a previously developed model of the coupling between neural activation, energy metabolism and hemodynamics, by including the venous dilatation "Balloon model" of Buxton and Frank. We show that decreasing the cerebral blood flow (CBF) baseline value, or the CBF increase fraction, results in a decrease of the BOLD signal and an increase of the lactate peak during a sustained activation. Baseline lactate and PCr levels are not significantly affected by CBF baseline reduction, but are altered even by a moderate decrease of mitochondrial respiration. Decreasing the total Cr and PCr concentration reduces the BOLD signal after the initial overshoot. In conclusion, we suggest that the coupled use of BOLD fMRI and MRS could contribute to a better understanding of the neurovascular and metabolic decoupling in gliomas.