Reduced-order modeling of light transport in tissue for real-time monitoring of brain hemodynamics using diffuse optical tomography.

This paper proposes a new reconstruction method for diffuse optical tomography using reduced-order models of light transport in tissue. The models, which directly map optical tissue parameters to optical flux measurements at the detector locations, are derived based on data generated by numerical simulation of a reference model. The reconstruction algorithm based on the reduced-order models is a few orders of magnitude faster than the one based on a finite element approximation on a fine mesh incorporating a priori anatomical information acquired by magnetic resonance imaging. We demonstrate the accuracy and speed of the approach using a phantom experiment and through numerical simulation of brain activation in a rat's head. The applicability of the approach for real-time monitoring of brain hemodynamics is demonstrated through a hypercapnic experiment. We show that our results agree with the expected physiological changes and with results of a similar experimental study. However, by using our approach, a three-dimensional tomographic reconstruction can be performed in ∼3 s per time point instead of the 1 to 2 h it takes when using the conventional finite element modeling approach.

Functional MRI in conscious rats using a chronically implanted surface coil.

PURPOSE: To establish procedures for functional MRI (fMRI) in rats without the need for anesthetic agents. MATERIALS AND METHODS: Rats were trained to habituate to restraint in a harness and scanner noise. Under anesthesia, rats were then prepared with a cranial implant that permitted stabilization of the head during subsequent imaging experiments. The cranial implant included an radiofrequency (RF) coil that was used to transmit and receive radiofrequency signals during imaging. Further training was then conducted to habituate the animals to head fixation whilst in the MR scanner. RESULTS: Using this method, we were able to successfully and repeatedly record BOLD fMRI responses to hypercapnia and whisker stimulation in awake rats. Electrical stimulation of the whisker pad produced a ∼7% increase in BOLD signal in the corresponding barrel cortex as well as adjacent negative BOLD responses, whilst hypercapnia produced larger increases in BOLD signal amplitude. CONCLUSION: This methodology leaves the face and limbs free from obstruction, making possible a range of behavioral or sensory stimulation protocols. Further development of this animal model could enable traditional behavioral neuroscience techniques to be combined with modern functional neuroimaging.

Complex spatiotemporal haemodynamic response following sensory stimulation in the awake rat.

Detailed understanding of the haemodynamic changes that underlie non-invasive neuroimaging techniques such as blood oxygen level dependent functional magnetic resonance imaging is essential if we are to continue to extend the use of these methods for understanding brain function and dysfunction. The use of animal and in particular rodent research models has been central to these endeavours as they allow in-vivo experimental techniques that provide measurements of the haemodynamic response function at high temporal and spatial resolution. A limitation of most of this research is the use of anaesthetic agents which may disrupt or mask important features of neurovascular coupling or the haemodynamic response function. In this study we therefore measured spatiotemporal cortical haemodynamic responses to somatosensory stimulation in awake rats using optical imaging spectroscopy. Trained, restrained animals received non-noxious stimulation of the whisker pad via chronically implanted stimulating microwires whilst optical recordings were made from the contralateral somatosensory cortex through a thin cranial window. The responses we measure from un-anaesthetised animals are substantially different from those reported in previous studies which have used anaesthetised animals. These differences include biphasic response regions (initial increases in blood volume and oxygenation followed by subsequent decreases) as well as oscillations in the response time series of awake animals. These haemodynamic response features do not reflect concomitant changes in the underlying neuronal activity and therefore reflect neurovascular or cerebrovascular processes. These hitherto unreported hyperemic response dynamics may have important implications for the use of anaesthetised animal models for research into the haemodynamic response function.

Balanced excitation and inhibition: model based analysis of local field potentials.

We have developed a model of the local field potential (LFP) based on the conservation of charge, the independence principle of ionic flows and the classical Hodgkin-Huxley (HH) type intracellular model of synaptic activity. Insights were gained through the simulation of the HH intracellular model on the nonlinear relationship between the balance of synaptic conductances and that of post-synaptic currents. The latter is dependent not only on the former, but also on the temporal lag between the excitatory and inhibitory conductances, as well as the strength of the afferent signal. The proposed LFP model provides a method for decomposing the LFP recordings near the soma of layer IV pyramidal neurons in the barrel cortex of anaesthetised rats into two highly correlated components with opposite polarity. The temporal dynamics and the proportional balance of the two components are comparable to the excitatory and inhibitory post-synaptic currents computed from the HH model. This suggests that the two components of the LFP reflect the underlying excitatory and inhibitory post-synaptic currents of the local neural population. We further used the model to decompose a sequence of evoked LFP responses under repetitive electrical stimulation (5Hz) of the whisker pad. We found that as neural responses adapted, the excitatory and inhibitory components also adapted proportionately, while the temporal lag between the onsets of the two components increased during frequency adaptation. Our results demonstrated that the balance between neural excitation and inhibition can be investigated using extracellular recordings. Extension of the model to incorporate multiple compartments should allow more quantitative interpretations of surface Electroencephalography (EEG) recordings into components reflecting the excitatory, inhibitory and passive ionic current flows generated by local neural populations.

Is optical imaging spectroscopy a viable measurement technique for the investigation of the negative BOLD phenomenon? A concurrent optical imaging spectroscopy and fMRI study at high field (7 T).

Traditionally functional magnetic resonance imaging (fMRI) has been used to map activity in the human brain by measuring increases in the Blood Oxygenation Level Dependent (BOLD) signal. Often accompanying positive BOLD fMRI signal changes are sustained negative signal changes. Previous studies investigating the neurovascular coupling mechanisms of the negative BOLD phenomenon have used concurrent 2D-optical imaging spectroscopy (2D-OIS) and electrophysiology (Boorman et al., 2010). These experiments suggested that the negative BOLD signal in response to whisker stimulation was a result of an increase in deoxy-haemoglobin and reduced multi-unit activity in the deep cortical layers. However, Boorman et al. (2010) did not measure the BOLD and haemodynamic response concurrently and so could not quantitatively compare either the spatial maps or the 2D-OIS and fMRI time series directly. Furthermore their study utilised a homogeneous tissue model in which is predominantly sensitive to haemodynamic changes in more superficial layers. Here we test whether the 2D-OIS technique is appropriate for studies of negative BOLD. We used concurrent fMRI with 2D-OIS techniques for the investigation of the haemodynamics underlying the negative BOLD at 7 Tesla. We investigated whether optical methods could be used to accurately map and measure the negative BOLD phenomenon by using 2D-OIS haemodynamic data to derive predictions from a biophysical model of BOLD signal changes. We showed that despite the deep cortical origin of the negative BOLD response, if an appropriate heterogeneous tissue model is used in the spectroscopic analysis then 2D-OIS can be used to investigate the negative BOLD phenomenon.

Neurovascular coupling is brain region-dependent.

Despite recent advances in alternative brain imaging technologies, functional magnetic resonance imaging (fMRI) remains the workhorse for both medical diagnosis and primary research. Indeed, the number of research articles that utilise fMRI have continued to rise unabated since its conception in 1991, despite the limitation that recorded signals originate from the cerebral vasculature rather than neural tissue. Consequently, understanding the relationship between brain activity and the resultant changes in metabolism and blood flow (neurovascular coupling) remains a vital area of research. In the past, technical constraints have restricted investigations of neurovascular coupling to cortical sites and have led to the assumption that coupling in non-cortical structures is the same as in the cortex, despite the lack of any evidence. The current study investigated neurovascular coupling in the rat using whole-brain blood oxygenation level-dependent (BOLD) fMRI and multi-channel electrophysiological recordings and measured the response to a sensory stimulus as it proceeded through brainstem, thalamic and cortical processing sites - the so-called whisker-to-barrel pathway. We found marked regional differences in the amplitude of BOLD activation in the pathway and non-linear neurovascular coupling relationships in non-cortical sites. The findings have important implications for studies that use functional brain imaging to investigate sub-cortical function and caution against the use of simple, linear mapping of imaging signals onto neural activity.

Vascular Origins of BOLD and CBV fMRI Signals: Statistical Mapping and Histological Sections Compared.

Comparison of 3T blood oxygenation level dependent (BOLD) and cerebral blood volume (CBV) activation maps to histological sections enables the spatial discrimination of functional magnetic resonance imaging (fMRI) signal changes into different vascular compartments. We use a standard gradient echo-echo planar imaging technique to measure BOLD signal changes in the somatosensory cortex in response to whisker stimulation. Corresponding changes in CBV were estimated following the infusion of a super-paramagnetic contrast agent. We imaged in a tangential imaging plane that covered the cortical surface. Images were associated with post mortem histological sections showing both the surface vasculature and cytochrome oxidase stained whisker barrel cortex. We found a significant BOLD signal change in the large draining veins which occurred in the absence of a corresponding CBV change. Results suggest that in the venous drainage system, ~3mm distant from the area of activity, there is a robust change in blood oxygen saturation with little or no volume change. CBV changes are localised over the somatosensory barrel cortex and overlying arterial supply, supporting the theory that CBV changes are greater in the arterial than in the venous vasculature. This work investigating BOLD signal and underlying hemodynamics provides more information on the vascular origins of these important neuroimaging signals.

A dynamic model of neurovascular coupling: implications for blood vessel dilation and constriction.

Neurovascular coupling in response to stimulation of the rat barrel cortex was investigated using concurrent multichannel electrophysiology and laser Doppler flowmetry. The data were used to build a linear dynamic model relating neural activity to blood flow. Local field potential time series were subject to current source density analysis, and the time series of a layer IV sink of the barrel cortex was used as the input to the model. The model output was the time series of the changes in regional cerebral blood flow (CBF). We show that this model can provide excellent fit of the CBF responses for stimulus durations of up to 16 s. The structure of the model consisted of two coupled components representing vascular dilation and constriction. The complex temporal characteristics of the CBF time series were reproduced by the relatively simple balance of these two components. We show that the impulse response obtained under the 16-s duration stimulation condition generalised to provide a good prediction to the data from the shorter duration stimulation conditions. Furthermore, by optimising three out of the total of nine model parameters, the variability in the data can be well accounted for over a wide range of stimulus conditions. By establishing linearity, classic system analysis methods can be used to generate and explore a range of equivalent model structures (e.g., feed-forward or feedback) to guide the experimental investigation of the control of vascular dilation and constriction following stimulation.

Optimisation on the least squares identification of dynamical systems with application to hemodynamic modelling.

Dynamic modelling using the traditional least squares method with noisy input/output data can yield biased and sometimes unstable model predictions. This is largely because the cost function employed by the traditional least squares method is based on the one-step-ahead prediction errors. In this paper, the model-predicted-output errors are used in estimating the model parameters. As the cost function is highly nonlinear in terms of the model parameters, the particle swarm optimisation method is used to search for the optimal parameters. We will show that compared with model predictions using the traditional least squares method, the model-predicted-output approach is more robust at dealing with noisy input/output data. The algorithm is applied to identify the dynamic relationship between changes in cerebral blood flow and volume due to evoked changes in neural activity and is shown to produce better predictions than that using the least squares method.

A dynamic causal model of the coupling between pulse stimulation and neural activity.

We present a dynamic causal model that can explain context-dependent changes in neural responses, in the rat barrel cortex, to an electrical whisker stimulation at different frequencies. Neural responses were measured in terms of local field potentials. These were converted into current source density (CSD) data, and the time series of the CSD sink was extracted to provide a time series response train. The model structure consists of three layers (approximating the responses from the brain stem to the thalamus and then the barrel cortex), and the latter two layers contain nonlinearly coupled modules of linear second-order dynamic systems. The interaction of these modules forms a nonlinear regulatory system that determines the temporal structure of the neural response amplitude for the thalamic and cortical layers. The model is based on the measured population dynamics of neurons rather than the dynamics of a single neuron and was evaluated against CSD data from experiments with varying stimulation frequency (1-40 Hz), random pulse trains, and awake and anesthetized animals. The model parameters obtained by optimization for different physiological conditions (anesthetized or awake) were significantly different. Following Friston, Mechelli, Turner, and Price (2000), this work is part of a formal mathematical system currently being developed (Zheng et al., 2005) that links stimulation to the blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal through neural activity and hemodynamic variables. The importance of the model described here is that it can be used to invert the hemodynamic measurements of changes in blood flow to estimate the underlying neural activity.

Refinement of optical imaging spectroscopy algorithms using concurrent BOLD and CBV fMRI.

We describe the use of the three dimensional characteristics of the functional magnetic resonance imaging (fMRI) blood oxygenation level dependent (BOLD) and cerebral blood volume (CBV) MRI signal changes to refine a two dimensional optical imaging spectroscopy (OIS) algorithm. The cortical depth profiles of the BOLD and CBV changes following neural activation were used to parameterise a 5-layer heterogeneous tissue model used in the Monte Carlo simulations (MCS) of light transport through tissue in the OIS analysis algorithm. To transform the fMRI BOLD and CBV measurements into deoxy-haemoglobin (Hbr) profiles we inverted an MCS of extra-vascular MR signal attenuation under the assumption that the extra-/intravascular ratio is 2:1 at a magnetic field strength of 3 T. The significant improvement in the quantitative accuracy of haemodynamic measurements using the new heterogeneous tissue model over the original homogeneous tissue model OIS algorithm was demonstrated on new concurrent OIS and fMRI data covering a range of stimulus durations.

A time-invariant visco-elastic windkessel model relating blood flow and blood volume.

The difference between the rate of change of cerebral blood volume (CBV) and cerebral blood flow (CBF) following stimulation is thought to be due to circumferential stress relaxation in veins (Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679-689). In this paper we explore the visco-elastic properties of blood vessels, and present a dynamic model relating changes in CBF to changes in CBV. We refer to this model as the visco-elastic windkessel (VW) model. A novel feature of this model is that the parameter characterising the pressure-volume relationship of blood vessels is treated as a state variable dependent on the rate of change of CBV, producing hysteresis in the pressure-volume space during vessel dilation and contraction. The VW model is nonlinear time-invariant, and is able to predict the observed differences between the time series of CBV and that of CBF measurements following changes in neural activity. Like the windkessel model derived by Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., Weisskoff, R.M., 1999. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679-689, the VW model is primarily a model of haemodynamic changes in the venous compartment. The VW model is demonstrated to have the following characteristics typical of visco-elastic materials: (1) hysteresis, (2) creep, and (3) stress relaxation, hence it provides a unified model of the visco-elastic properties of the vasculature. The model will not only contribute to the interpretation of the Blood Oxygen Level Dependent (BOLD) signals from functional Magnetic Resonance Imaging (fMRI) experiments, but also find applications in the study and modelling of the brain vasculature and the haemodynamics of circulatory and cardiovascular systems.

Altered neurovascular coupling during information-processing states.

Brain imaging techniques rely on changes in blood flow, volume and oxygenation to infer the loci and magnitude of changes in activity. Although progress has been made in understanding the link between stimulus-evoked neural activity and haemodynamics, the extent to which neurovascular-coupling relationships remain constant during different states of baseline cortical activity is poorly understood. Optical imaging spectroscopy, laser Doppler flowmetry and electrophysiology were used to measure haemodynamics and neural activity in the barrel cortex of anaesthetized rats. The responses to stimulation of the whisker pad were recorded during quiescence and cortical desynchronization produced by stimulation of the brainstem. Cortical desynchronization was accompanied by increases in baseline blood flow, volume and oxygenation. Haemodynamic responses to low-frequency whisker stimuli (1 Hz) were attenuated during arousal compared with that observed during quiescence. During arousal it was possible to increase stimulus-evoked haemodynamics by increasing the frequency of the stimulus. Neural responses to low-frequency stimuli were also attenuated but to a far lesser extent than the reduction in the accompanying haemodynamics. In contrast, neuronal activity evoked by high-frequency stimuli (40 Hz) was enhanced during arousal, but induced haemodynamic responses of a similar magnitude compared with that observed for the same high-frequency stimulus presented during quiescence. These data suggest that there may be differences in stimulus-evoked neural activity and accompanying haemodynamics during different information-processing states.

Theory and generalization of Monte Carlo models of the BOLD signal source.

The dependency of the blood oxygenation level dependent (BOLD) signal on underlying hemodynamics is not well understood. Building a forward biophysical model of this relationship is important for the quantitative estimation of the hemodynamic changes and neural activity underlying functional magnetic resonance imaging (fMRI) signals. We have developed a general model of the BOLD signal which can model both intra- and extravascular signals for an arbitrary tissue model across a wide range of imaging parameters. The model of the BOLD signal was instantiated as a look-up-table (LuT), and was verified against concurrent fMRI and optical imaging measurements of activation induced hemodynamics.

Investigating the coupling between stimulation and neural activity: a dynamic modeling approach.

The objective of the present study was to build a dynamic model relating changes in neural responses in rat barrel cortex to an electrical whisker stimulation pulse train of varying frequencies. This work is part of a formal mathematical system currently being developed, which links stimulation to the Blood Oxygen Level Dependent (BOLD) functional Magnetic Resonance Imaging (fMRI) signal. Neural responses were measured in terms of local field potentials, which were then converted into current source density (CSD) data. Responses were found to be strongly suppressed immediately following the first stimulus pulse, before recovering to a steady state, which was maintained throughout the rest of the stimulation. The amplitude of this steady state decreases as the stimulation frequency increases. The model structure is based on the physiological pathway from the rat sensory organ to the cortex. Dynamic linear second order systems are used to model the excitatory as well as the suppressive components of the neural response. The interactions between components contain nonlinear modulations. The model was evaluated against CSD data from experiments with varying stimulation frequency (1-40 Hz), and shows a plausible fit. The model parameters obtained by optimization for different physiological conditions (anaesthetized or awake) were significantly different. Although this is a descriptive model, it may well have some physiological implications.

Preservation of visual cortical function following retinal pigment epithelium transplantation in the RCS rat using optical imaging techniques.

The aim of this study was to determine the extent of cortical functional preservation following retinal pigment epithelium (RPE) transplantation in the Royal College of Surgeons (RCS) rat using single-wavelength optical imaging and spectroscopy. The cortical responses to visual stimulation in transplanted rats at 6 months post-transplantation were compared with those from age-matched untreated dystrophic and non-dystrophic rats. Our results show that cortical responses were evoked in non-dystrophic rats to both luminance changes and pattern stimulation, whereas no response was found in untreated dystrophic animals to any of the visual stimuli tested. In contrast, a cortical response was elicited in most of the transplanted rats to luminance changes and in many of those a response was also evoked to pattern stimulation. Although the transplanted rats did not respond to high spatial frequency information we found evidence of preservation in the cortical processing of luminance changes and low spatial frequency stimulation. Anatomical sections of transplanted rat retinas confirmed the capacity of RPE transplantation to rescue photoreceptors. Good correlation was found between photoreceptor survival and the extent of cortical function preservation determined with optical imaging techniques. This study determined the efficacy of RPE transplantation to preserve visual cortical processing and established optical imaging as a powerful technique for its assessment.

Simultaneous laser Doppler flowmetry and arterial spin labeling MRI for measurement of functional perfusion changes in the cortex.

This study compares laser Doppler flowmetry (LDF) and arterial spin labeling (ASL) for the measurement of functional changes in cerebral blood flow (CBF). The two methods were applied concurrently in a paradigm of electrical whisker stimulation in the anaesthetised rat. Multi-channel LDF was used, with each channel corresponding to different fiber separation (and thus measurement depth). Continuous ASL was applied using separate imaging and labeling coils at 3 T. Careful experimental set up ensured that both techniques recorded from spatially concordant regions of the barrel cortex, where functional responses were maximal. Strong correlations were demonstrated between CBF changes measured by each LDF channel and ASL in terms of maximum response magnitude and response time-course within a 6-s-long temporal resolution imposed by ASL. Quantitatively, the measurements of the most superficial LDF channels agreed strongly with those of ASL, whereas the deeper LDF channels underestimated consistently the ASL measurement. It was thus confirmed that LDF quantifies CBF changes consistently at a superficial level, and for this case the two methods provided concordant measures of functional CBF changes, despite their essentially different physical principles and spatiotemporal characteristics.

Haemodynamic and neural responses to hypercapnia in the awake rat.

The relationship between localized changes in brain activity and metabolism, and the blood oxygenation level-dependent (BOLD) signal used in functional magnetic resonance imaging studies is not fully understood. One source of complexity is that stimulus-elicited changes in the BOLD signal arise both from changes in oxygen consumption due to increases in activity and purely 'haemodynamic' changes such as increases in cerebral blood flow. It is well established that robust cortical haemodynamic changes can be elicited by increasing the concentration of inspired CO(2) (inducing hypercapnia) and it is widely believed that these haemodynamic changes occur without significant effects upon neural activity or cortical metabolism. Hypercapnia is therefore commonly used as a calibration condition in functional magnetic resonance imaging studies to enable estimation of oxidative metabolism from subsequent stimulus-evoked functional magnetic resonance imaging BOLD signal changes. However, there is little research that has investigated in detail the effects of hypercapnia upon all components of the haemodynamic response (changes in cerebral blood flow, volume and oxygenation) in addition to recording neural activity. In awake animals, we used optical and electrophysiological techniques to measure cortical haemodynamic and field potential responses to hypercapnia (60 s, 5% CO(2)). The main findings are that firstly, in the awake rat, the temporal structure of the haemodynamic response to hypercapnia differs from that reported previously in anaesthetized preparations in that the response is more rapid. Secondly, there is evidence that hypercapnia alters ongoing neural activity in awake rats by inducing periods of cortical desynchronization and this may be associated with changes in oxidative metabolism.