A model of brain circulation and metabolism: NIRS signal changes during physiological challenges

We construct a model of brain circulation and energy metabolism. The model is designed to explain experimental data and predict the response of the circulation and metabolism to a variety of stimuli, in particular, changes in arterial blood pressure, CO(2) levels, O(2) levels, and functional activation. Significant model outputs are predictions about blood flow, metabolic rate, and quantities measurable noninvasively using near-infrared spectroscopy (NIRS), including cerebral blood volume and oxygenation and the redox state of the Cu(A) centre in cytochrome c oxidase. These quantities are now frequently measured in clinical settings; however the relationship between the measurements and the underlying physiological events is in general complex. We anticipate that the model will play an important role in helping to understand the NIRS signals, in particular, the cytochrome signal, which has been hard to interpret. A range of model simulations are presented, and model outputs are compared to published data obtained from both in vivo and in vitro settings. The comparisons are encouraging, showing that the model is able to reproduce observed behaviour in response to various stimuli.     

A cerebrovascular response model for functional neuroimaging including dynamic cerebral autoregulation

Functional neuroimaging techniques such as functional magnetic resonance imaging (fMRI) and near-infrared spectroscopy (NIRS) can be used to isolate an evoked response to a stimulus from significant background physiological fluctuations. Data analysis approaches typically use averaging or linear regression to remove this physiological baseline with varying degrees of success. Biophysical model-based analysis of the functional hemodynamic response has also been advanced previously with the Balloon and Windkessel models. In the present work, a biophysical model of systemic and cerebral circulation and gas exchange is applied to resting state NIRS neuroimaging data from 10 human subjects. The model further includes dynamic cerebral autoregulation, which modulates the cerebral arteriole compliance to control cerebral blood flow. This biophysical model allows for prediction, from noninvasive blood pressure measurements, of the background hemodynamic fluctuations in the systemic and cerebral circulations. Significantly higher correlations with the NIRS data were found using the biophysical model predictions compared to blood pressure regression and compared to transfer function analysis (multifactor ANOVA, p < 0.0001). This finding supports the further development and use of biophysical models for removing baseline activity in functional neuroimaging analysis. Future extensions of this work could model changes in cerebrovascular physiology that occur during development, aging, and disease.     

BrainSignals Revisited: Simplifying a Computational Model of Cerebral Physiology

Multimodal monitoring of brain state is important both for the investigation of healthy cerebral physiology and to inform clinical decision making in conditions of injury and disease. Near-infrared spectroscopy is an instrument modality that allows non-invasive measurement of several physiological variables of clinical interest, notably haemoglobin oxygenation and the redox state of the metabolic enzyme cytochrome c oxidase. Interpreting such measurements requires the integration of multiple signals from different sources to try to understand the physiological states giving rise to them. We have previously published several computational models to assist with such interpretation. Like many models in the realm of Systems Biology, these are complex and dependent on many parameters that can be difficult or impossible to measure precisely. Taking one such model, BrainSignals, as a starting point, we have developed several variant models in which specific regions of complexity are substituted with much simpler linear approximations. We demonstrate that model behaviour can be maintained whilst achieving a significant reduction in complexity, provided that the linearity assumptions hold. The simplified models have been tested for applicability with simulated data and experimental data from healthy adults undergoing a hypercapnia challenge, but relevance to different physiological and pathophysiological conditions will require specific testing. In conditions where the simplified models are applicable, their greater efficiency has potential to allow their use at the bedside to help interpret clinical data in near real-time.     

A New Functional MRI Approach for Investigating Modulations of Brain Oxygen Metabolism

Functional MRI (fMRI) using the blood oxygenation level dependent (BOLD) signal is a common technique in the study of brain function. The BOLD signal is sensitive to the complex interaction of physiological changes including cerebral blood flow (CBF), cerebral blood volume (CBV), and cerebral oxygen metabolism (CMRO₂). A primary goal of quantitative fMRI methods is to combine BOLD imaging with other measurements (such as CBF measured with arterial spin labeling) to derive information about CMRO₂. This requires an accurate mathematical model to relate the BOLD signal to the physiological and hemodynamic changes; the most commonly used of these is the Davis model. Here, we propose a new nonlinear model that is straightforward and shows heuristic value in clearly relating the BOLD signal to blood flow, blood volume and the blood flow-oxygen metabolism coupling ratio. The model was tested for accuracy against a more detailed model adapted for magnetic fields of 1.5, 3 and 7T. The mathematical form of the heuristic model suggests a new ratio method for comparing combined BOLD and CBF data from two different stimulus responses to determine whether CBF and CMRO₂ coupling differs. The method does not require a calibration experiment or knowledge of parameter values as long as the exponential parameter describing the CBF-CBV relationship remains constant between stimuli. The method was found to work well for 1.5 and 3T but is prone to systematic error at 7T. If more specific information regarding changes in CMRO₂ is required, then with accuracy similar to that of the Davis model, the heuristic model can be applied to calibrated BOLD data at 1.5T, 3T and 7T. Both models work well over a reasonable range of blood flow and oxygen metabolism changes but are less accurate when applied to a simulated caffeine experiment in which CBF decreases and CMRO₂ increases.     

Model analysis of steady-state ventilatory response to CO2 into component factors

A method is described to partition measured values of steady-state ventilatory response into an estimation of the blood flow in the respiratory controller and the sensitivity of the controller to CO2 assuming proportional control. The analysis is derived from the describing equations of a computer model and leads to the definition of a grid of lines emanating from a hypothetical reference point at negative ventilation and zero central nervous system metabolism. Data from the literature reporting differences in CO2 response among normal subjects and changes in resting ventilation and cerebral blood flow with age are reinterpreted from this perspective. Use of a structural model to interpret physiological data is shown to give a different meaning to data reduction in contrast to interpretation using statistical models like regression.     

Modelling Blood Flow and Metabolism in the Preclinical Neonatal Brain during and Following Hypoxic-Ischaemia

Hypoxia-ischaemia (HI) is a major cause of neonatal brain injury, often leading to long-term damage or death. In order to improve understanding and test new treatments, piglets are used as preclinical models for human neonates. We have extended an earlier computational model of piglet cerebral physiology for application to multimodal experimental data recorded during episodes of induced HI. The data include monitoring with near-infrared spectroscopy (NIRS) and magnetic resonance spectroscopy (MRS), and the model simulates the circulatory and metabolic processes that give rise to the measured signals. Model extensions include simulation of the carotid arterial occlusion used to induce HI, inclusion of cytoplasmic pH, and loss of metabolic function due to cell death. Model behaviour is compared to data from two piglets, one of which recovered following HI while the other did not. Behaviourally-important model parameters are identified via sensitivity analysis, and these are optimised to simulate the experimental data. For the non-recovering piglet, we investigate several state changes that might explain why some MRS and NIRS signals do not return to their baseline values following the HI insult. We discover that the model can explain this failure better when we include, among other factors such as mitochondrial uncoupling and poor cerebral blood flow restoration, the death of around 40% of the brain tissue.     

Neurogenic Neuroprotection

1. Stimulation of the rostral-ventromedial pole of the cerebellar fastigial nucleus exerts powerful effects on systemic and cerebral circulation.2. Excitation of fibers passing through the fastigial nucleus evokes sympathoactivation and increases in arterial pressure.3. Increase in cerebral blood flow evoked by excitation of fibers passing through the FN is mediated by intrinsic brain mechanisms independently of metabolism.4. Excitation of the fastigial nucleus neurons in contrast decreases arterial pressure and cerebral blood flow. The latter probably is secondary to the suppression of brain metabolism.5. Excitation of the fastigial nucleus neurons significantly decreases damaging effects of focal and global ischemia on the brain.6. The fastigial nucleus-evoked neuroprotection can be conditioned: 1-h stimulation protects the brain for up to 3 weeks.7. Other brain structures such as subthalamic cerebrovasodilator area and dorsal periaqueductal gray matter also produce long-lasting brain salvage when stimulated.8. More than one mechanism may account for neurogenic neuroprotection.9. Early neuroprotection, which develops immediately after the stimulation, involves opening of potassium channels.10. Delayed long-lasting neuroprotection may involve changes in genes expression resulting in suppression of inflammatory reaction and apoptotic cascade.11. It is conceivable that intrinsic neuroprotective system exists within the brain, which renders the brain more tolerant to adverse stimuli when activated.12. Knowledge of the mechanisms of neurogenic neuroprotection will allow developing new neuroprotective approaches.     

Exploiting tumor metabolism for non-invasive imaging of the therapeutic activity of molecularly targeted anticancer agents

Rational drug discovery and development requires biomarkers to inform on target modulation and treatment efficacy. Many aspects of metabolism are altered in cancer, compared to normal tissues, and are often regulated by oncogene activation. Non-invasive imaging of spatio-temporal effects of molecularly targeted anticancer agents on tumor metabolism has considerable potential in the development and use of personalized molecular medicine approaches to cancer treatment. Here we describe how non-invasive monitoring of metabolism, using primarily magnetic resonance spectroscopy (MRS), can be used to follow treatment with novel molecularly targeted anticancer agents. We discuss how the regulation of metabolic pathways by oncogenic signaling can affect MRS-detectable metabolic signals together with the physiological factors that can influence the measured changes. Finally, the translation of these metabolic measurements from pre-clinical models to patients will be discussed.     

In vivo 13C NMR studies of compartmentalized cerebral carbohydrate metabolism

Localized 13C nuclear magnetic resonance (NMR) spectroscopy provides a unique window for studying cerebral carbohydrate metabolism through, e.g. the completely non-invasive measurement of cerebral glucose and glycogen metabolism. In addition, label incorporation into amino acid neurotransmitters such as glutamate (Glu), GABA and aspartate can be measured providing information on Krebs cycle flux and oxidative metabolism. Given the compartmentation of key enzymes such as pyruvate carboxylase and glutamine synthetase, the detection of label incorporation into glutamine indicated that neuronal and glial metabolism can be measured in vivo. The purpose of this paper is to provide a critical overview of these recent advances into measuring compartmentation of brain energy metabolism using localized in vivo 13C NMR spectroscopy. The studies reviewed herein showed that anaplerosis is significant in brain, as is oxidative ATP generation in glia and the rate of glial glutamine synthesis attributed to the replenishment of the neuronal Glu pool and that brain glycogen metabolism is slow under resting conditions. This new modality promises to provide a new investigative tool to study aspects of normal and diseased brain hitherto unaccessible, such as the interplay between glutamatergic action, glucose and glycogen metabolism during brain activation, and the derangements thereof in patients with hepatic encephalopathy, neurodegenerative diseases and diabetes.     

Mechanistic Mathematical Modeling Tests Hypotheses of the Neurovascular Coupling in fMRI

Functional magnetic resonance imaging (fMRI) measures brain activity by detecting the blood-oxygen-level dependent (BOLD) response to neural activity. The BOLD response depends on the neurovascular coupling, which connects cerebral blood flow, cerebral blood volume, and deoxyhemoglobin level to neuronal activity. The exact mechanisms behind this neurovascular coupling are not yet fully investigated. There are at least three different ways in which these mechanisms are being discussed. Firstly, mathematical models involving the so-called Balloon model describes the relation between oxygen metabolism, cerebral blood volume, and cerebral blood flow. However, the Balloon model does not describe cellular and biochemical mechanisms. Secondly, the metabolic feedback hypothesis, which is based on experimental findings on metabolism associated with brain activation, and thirdly, the neurotransmitter feed-forward hypothesis which describes intracellular pathways leading to vasoactive substance release. Both the metabolic feedback and the neurotransmitter feed-forward hypotheses have been extensively studied, but only experimentally. These two hypotheses have never been implemented as mathematical models. Here we investigate these two hypotheses by mechanistic mathematical modeling using a systems biology approach; these methods have been used in biological research for many years but never been applied to the BOLD response in fMRI. In the current work, model structures describing the metabolic feedback and the neurotransmitter feed-forward hypotheses were applied to measured BOLD responses in the visual cortex of 12 healthy volunteers. Evaluating each hypothesis separately shows that neither hypothesis alone can describe the data in a biologically plausible way. However, by adding metabolism to the neurotransmitter feed-forward model structure, we obtained a new model structure which is able to fit the estimation data and successfully predict new, independent validation data. These results open the door to a new type of fMRI analysis that more accurately reflects the true neuronal activity.     

Fusing EEG and fMRI based on a bottom-up model: inferring activation and effective connectivity in neural masses

The elucidation of the complex machinery used by the human brain to segregate and integrate information while performing high cognitive functions is a subject of imminent future consequences. The most significant contributions to date in this field, known as cognitive neuroscience, have been achieved by using innovative neuroimaging techniques, such as electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI), which measure variations in both the time and the space of some interpretable physical magnitudes. Extraordinary maps of cerebral activation involving function-restricted brain areas, as well as graphs of the functional connectivity between them, have been obtained from EEG and fMRI data by solving some spatio-temporal inverse problems, which constitutes a top-down approach. However, in many cases, a natural bridge between these maps/graphs and the causal physiological processes is lacking, leading to some misunderstandings in their interpretation. Recent advances in the comprehension of the underlying physiological mechanisms associated with different cerebral scales have provided researchers with an excellent scenario to develop sophisticated biophysical models that permit an integration of these neuroimage modalities, which must share a common aetiology. This paper proposes a bottom-up approach, involving physiological parameters in a specific mesoscopic dynamic equations system. Further observation equations encapsulating the relationship between the mesostates and the EEG/fMRI data are obtained on the basis of the physical foundations of these techniques. A methodology for the estimation of parameters from fused EEG/fMRI data is also presented. In this context, the concepts of activation and effective connectivity are carefully revised. This new approach permits us to examine and discuss some future prospects for the integration of multimodal neuroimages.     

Decreased cerebral blood flow and hemodynamic parameters during acute hyperglycemia in mice model observed by dual‐wavelength speckle imaging

In this study, we use dual‐wavelength optical imaging‐based laser speckle technique to assess cerebral blood flow and metabolic parameters in a mouse model of acute hyperglycemia (high blood glucose). The effect of acute glucose levels on physiological processes has been extensively described in multiple organ systems such as retina, kidney, and others. We postulated that hyperglycemia also alters brain function, which in turn can be monitored optically using dual‐wavelength laser speckle imaging (DW‐LSI) platform. DW‐LSI is a wide‐field, noncontact optical imaging modality that integrates the principles of laser flowmetry and oximetry to obtain macroscopic information such as hemoglobin concentration and blood flow. A total of eight mice (C57/BL6) were used, randomized into two groups of normoglycemia (control, n = 3) and hyperglycemia (n = 5). Hyperglycemia was induced by intraperitoneal injection of a commonly used anesthetic drug combining ketamine and xylazine (KX combo). We found that this KX combo increases blood glucose (BG) levels from 150 to 350 mg/dL, approximately, when measured 18 minutes post‐administration. BG continues to increase throughout the test period, with BG reaching an average of 463 ± 20.34 mg/dL within 60 minutes. BG levels were measured every 10 minutes from tail blood using commercially available glucometer. Experimental results demonstrated reductions in cerebral blood flow (CBF) by 55%, tissue oxygen saturation (SO₂) by 15%, and cerebral metabolic rate of oxygen (CMRO₂) by 75% following acute hyperglycemia. The observed decrease in these parameters was consistent with results reported in the literature, measured by a variety of experimental techniques. Measurements with laser Doppler flowmetry (LDF) were also performed which confirmed a reduction in CBF following acute hyperglycemia. In summary, our findings indicate that acute hyperglycemia modified brain hemodynamic response and induced significant changes in blood flow and metabolism. As far as we are aware, the implementation of the DW‐LSI to monitor brain hemodynamic and metabolic response to acute hyperglycemia in intact mouse brain has not been previously reported.      

An integrative dynamic model of brain energy metabolism using <Emphasis Type="Italic">in vivo</Emphasis> neurochemical measurements

An integrative, systems approach to the modelling of brain energy metabolism is presented. Mechanisms such as glutamate cycling between neurons and astrocytes and glycogen storage in astrocytes have been implemented. A unique feature of the model is its calibration using in vivo data of brain glucose and lactate from freely moving rats under various stimuli. The model has been used to perform simulated perturbation experiments that show that glycogen breakdown in astrocytes is significantly activated during sensory (tail pinch) stimulation. This mechanism provides an additional input of energy substrate during high consumption phases. By way of validation, data from the perfusion of 50 μM propranolol in the rat brain was compared with the model outputs. Propranolol affects the glucose dynamics during stimulation, and this was accurately reproduced in the model by a reduction in the glycogen breakdown in astrocytes. The model’s predictive capacity was verified by using data from a sensory stimulation (restraint) that was not used for model calibration. Finally, a sensitivity analysis was conducted on the model parameters, this showed that the control of energy metabolism and transport processes are critical in the metabolic behaviour of cerebral tissue.     

Neurovascular coupling and oximetry during epileptic events

Epilepsy is an abnormal brain state in which a large population of neurons is synchronously active, causing an enormous increase in metabolic demand. Recent investigations using high-resolution imaging techniques, such as optical recording of intrinsic signals and voltagesensitive dyes, as well as measurements with oxygen-sensitive electrodes have elucidated the spatiotemporal relationship between neuronal activity, cerebral blood volume, and oximetry in vivo. A focal decrease in tissue oxygenation and a focal increase in deoxygenated hemoglobin occurs following both interictal and ictal events. This “epileptic dip” in oxygenation can persist for the duration of an ictal event, suggesting that cerebral blood flow is inadequate to meet metabolic demand. A rapid focal increase in cerebral blood flow and cerebral blood volume also accompanies epileptic events; however, this increase in perfusion soon (>2 s) spreads to a larger area of the cortex than the excitatory change in membrane potential. Investigations in humans during neurosurgical operations have confirmed the laboratory data derived from animal studies. These data not only have clinical implications for the interpretation of noninvasive imaging studies such as positron emission tomography, single-photon emission tomography, and functional magnetic resonance imaging but also provide a mechanism for the cognitive decline in patients with chronic epilepsy.     

Cerebral infarction--a general-medical problem]

A knowledge of events accompanying the acute coronary failure may help understanding the acute cerebral blood flow insufficiency leading to brain infarction. Cerebral blood flow should be treated as an integral part of the systemic blood circulation. It is of importance when the disease produces lesions to the vascular wall, and the brain looses its autoregulation functions. In such a situation every extracerebral disorders--even slight--may produce extensive lesions to nervous tissue. Therefore, the treatment of the acute cerebral circulation failure requires proper functioning of all factors which may affect hemodynamics and tissue metabolism. Duration of cerebral flow disorders plays an important role in the avoidance of unfavourable complications such as brain infarction. Therefore, every physician is obliged to undertake any possible actions preventing such complications.     

Neurometabolic coupling between neural activity,glucose, and lactate in activated visual cortex

Neural activity is closely coupled with energy metabolism but details of the association remain to be identified. One basic area involves the relationships between neural activity and the main supportive substrates of glucose and lactate. This is of fundamental significance for the interpretation of non‐invasive neural imaging. Here, we use microelectrodes with high spatial and temporal resolution to determine simultaneous co‐localized changes in glucose, lactate, and neural activity during visual activation of the cerebral cortex in the cat. Tissue glucose and lactate concentration levels are measured with electrochemical microelectrodes while neural spiking activity and local field potentials are sampled by a microelectrode. These measurements are performed simultaneously while neurons are activated by visual stimuli of different contrast levels, orientations, and sizes. We find immediate decreases in tissue glucose concentration and simultaneous increases in lactate during neural activation. Both glucose and lactate signals return to their baseline levels instantly as neurons cease firing. No sustained changes or initial dips in glucose or lactate signals are elicited by visual stimulation. However, co‐localized measurements of cerebral blood flow and neural activity demonstrate a clear delay in the cerebral blood flow signal such that it does not correlate temporally with the neural response. These results provide direct real‐time evidence regarding the coupling between co‐localized energy metabolism and neural activity during physiological stimulation. They are also relevant to a current question regarding the role of lactate in energy metabolism in the brain during neural activation.

     

Differential cerebral hypothermia

Differential cerebral hypothermia was induced in these experiments by isolating the cerebral circulation in the halothane-anesthetized goat. The brain was perfused through isolated cerebral branches of the internal maxillary artery using a height-adjusted reservoir system which provided a constant inflow pressure. Cerebral blood flow (CBF) and cerebral O₂ metabolic rate (CMRO₂) were measured continuously as brain temperatures were decreased from 38 to 28, 18 and 8 °C and during rewarming. Arterial blood gases were maintained constant. During hypothermia CBF decreased at brain temperatures of 28 °C and did decrease further at 18 or 8 °C. CMRO₂ decreased linearly from 38 to 8 °C and was 7% control levels at 8 °C. CBF and CMRO₂ returned to control levels upon rewarming. Cerebral lactate metabolism did not change significantly during hypothermia or rewarming. Evoked cortical potentials were abolished at 8 °C but recovered upon rewarming. These results indicate that if adequate brain perfusion is maintained during hypothermia and rewarming, recovery of CBF, metabolism, and brain neural activity can be obtained.     

1H NMR detection of cerebral myo-inositol

A previously unassigned group of prominent multiplets of the 360 MHz 1H NMR spectrum of acid stable metabolite extracts from rat brain is shown to arise from free myo-inositol. This conclusion is derived from a systematic analysis of the high-resolution 1H NMR spectra of brain acid extracts, in which appropriate conditions and optimal proton signals have been selected for the quantitative analysis of up to 15 metabolites. Developmental variations in the cerebral content of myo-inositol could be readily detected using this approach, which provides a novel alternative to study myo-inositol metabolism under physiological or pathological conditions.     

Nonlinear modelling of renal vasoaction

The control of blood pressure is a complex mixture of neural, hormonal and intrinsic interactions at the level of the heart, kidney and blood vessels. While experimental approaches to understanding these interactions are useful, it remains difficult to conduct experiments to quantify these interactions as the number of parameters increases. Thus, modelling of such physiological systems can offer considerable assistance. Typical mathematical models which describe the ability of the blood vessels to change their diameter (vasoconstriction) assume linearity of operation. However, due to the interaction of multiple vasocontrictive and vasodilative effectors, there is a significant nonlinear response to the influence of neural factors, particularly at higher levels of nerve activity (often seen in subjects with high blood pressure) which leads to low blood flow rates. This paper proposes a number of nonlinear mathematical models for the relationship between neural influences (sympathetic nerve activity (SNA)) and renal blood flow, using a feedback path to model the predominantly nonlinear effect of local vasoactive modulators such as nitric oxide, which oppose the action of SNA. The model structures are motivated by basic physiological principles, while the model parameters are determined using numerical optimisation techniques using open-loop data collected from rabbits. The models were verified by demonstrating correlation between experimental results and model outputs.