Mathematical analysis of the influence of brain metabolism on the BOLD signal in Alzheimer's disease

Lactate's behavioral switch in the brain: An in-silico model

Emerging evidence emphasizes lactate's involvement in both physiological processes (energy metabolism, memory, etc.) and disease (traumatic brain injury, epilepsy, etc.). Furthermore, the usefulness of mathematical modeling in deciphering underlying dynamics of the brain to investigate lactate roles and mechanisms of action has been well established. Here, we analyze a novel mathematical model of brain lactate exchanges between four compartments: neurons, astrocytes, capillaries, and extracellular space. A system of four ordinary differential equations is proposed to explain interactions between these compartments. We first optimize and analyze the model's parameters under normal, resting state conditions, and then use it to simulate changes linked to elevated arterial lactate. Our results show that even though increased arterial lactate results in increased uptake by astrocytes and release to the extracellular space, it cannot strongly recover the initial drop in neuronal lactate concentration. Also, we show that the direction of lactate transport between the compartments is influenced by the maximum astrocyte production rate and the transport rate between astrocytes and extracellular space.

Mechanistic model for human brain metabolism and its connection to the neurovascular coupling

The neurovascular and neurometabolic couplings (NVC and NMC) connect cerebral activity, blood flow, and metabolism. This interconnection is used in for instance functional imaging, which analyses the blood-oxygen-dependent (BOLD) signal. The mechanisms underlying the NVC are complex, which warrants a model-based analysis of data. We have previously developed a mechanistically detailed model for the NVC, and others have proposed detailed models for cerebral metabolism. However, existing metabolic models are still not fully utilizing available magnetic resonance spectroscopy (MRS) data and are not connected to detailed models for NVC. Therefore, we herein present a new model that integrates mechanistic modelling of both MRS and BOLD data. The metabolic model covers central metabolism, using a minimal set of interactions, and can describe time-series data for glucose, lactate, aspartate, and glutamate, measured after visual stimuli. Statistical tests confirm that the model can describe both estimation data and predict independent validation data, not used for model training. The interconnected NVC model can simultaneously describe BOLD data and can be used to predict expected metabolic responses in experiments where metabolism has not been measured. This model is a step towards a useful and mechanistically detailed model for cerebral blood flow and metabolism, with potential applications in both basic research and clinical applications.

Exploring the relation between BOLD fMRI and cognitive performance using a computer-based quantitative systems pharmacology model: Applications to the COMTVAL158MET genotype and ketamine

BOLD fMRI is increasingly used mostly in an observational way to probe the effect of genotypes or therapeutic intervention in normal and diseased subjects. We use a mechanism-based quantitative systems pharmacology computer model of a human cortical microcircuit, previously calibrated for the 2-back working memory paradigm, adding established biophysical principles, of glucose metabolism, oxygen consumption, neurovascular effects and the paramagnetic impact on blood oxygen levels to calculate a readout for the voxel-based BOLD fMRI signal. The objective was to study the effect of the Catechol-O-methyl Transferase Val158Met (COMT) genotype on performance and BOLD fMRI. While the simulation suggests that on average virtual COMTVV genotype subjects perform worse, subjects with lower GABA, lower 5-HT₃ and higher 5-HT_1A activation can improve cognitive performance to the level of COMTMM subjects but at the expense of higher BOLD fMRI signal. In a schizophrenia condition, increased NMDA, GABA tone and noise levels, and lower D₁R activity can improve cognitive outcome with greater BOLD fMRI signal in COMT Val-carriers. We further generate hypotheses about why ketamine in healthy controls increases the BOLD fMRI signal but reduces cognitive performance. These simulations suggest a strong non-linear relationship between BOLD fMRI signal and cognitive performance. When validated, this mechanistic approach can be useful for moving beyond the descriptive nature of BOLD fMRI imaging and supporting the proper interpretation of imaging biomarkers in CNS disorders.

Impact of physiological noise in characterizing the functional MRI default-mode network in Alzheimer's disease

The functional connectivity of the default-mode network (DMN) monitored by functional magnetic resonance imaging (fMRI) in Alzheimer's disease (AD) patients has been found weaker than that in healthy participants. Since breathing and heart beating can cause fluctuations in the fMRI signal, these physiological activities may affect the fMRI data differently between AD patients and healthy participants. We collected resting-state fMRI data from AD patients and age-matched healthy participants. With concurrent cardiac and respiratory recordings, we estimated both physiological responses phase-locked and non-phase-locked to heart beating and breathing. We found that the cardiac and respiratory physiological responses in AD patients were 3.00 ± 0.51 s and 3.96 ± 0.52 s later (both p < 0.0001) than those in healthy participants, respectively. After correcting the physiological noise in the resting-state fMRI data by population-specific physiological response functions, the DMN estimated by seed-correlation was more localized to the seed region. The DMN difference between AD patients and healthy controls became insignificant after suppressing physiological noise. Our results indicate the importance of controlling physiological noise in the resting-state fMRI analysis to obtain clinically related characterizations in AD.

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.

Combined Use of MRI, fMRIand Cognitive Data for Alzheimer’s Disease: Preliminary Results

MRI can favor clinical diagnosis providing morphological and functional information of several neurological disorders. This paper deals with the problem of exploiting both data, in a combined way, to develop a tool able to support clinicians in the study and diagnosis of Alzheimer’s Disease (AD). In this work, 69 subjects from the ADNI open database, 33 AD patients and 36 healthy controls, were analyzed. The possible existence of a relationship between brain structure modifications and altered functions between patients and healthy controls was investigated performing a correlation analysis on brain volume, calculated from the MRI image, the clustering coefficient, derived from fRMI acquisitions, and the Mini Mental Score Examination (MMSE). A statistically-significant correlation was found only in four ROIs after Bonferroni’s correction. The correlation analysis alone was still not sufficient to provide a reliable and powerful clinical tool in AD diagnosis however. Therefore, a machine learning strategy was studied by training a set of support vector machine classifiers comparing different features. The use of a unimodal approach led to unsatisfactory results, whereas the multimodal approach, i.e., the synergistic combination of MRI, fMRI, and MMSE features, resulted in an accuracy of 95.65%, a specificity of 97.22%, and a sensibility of 93.93%.