Dynamic Effective Connectivity using Physiologically informed Dynamic Causal Model with Recurrent Units: A functional Magnetic Resonance Imaging simulation study

Functional MRI (fMRI) is an indirect reflection of neuronal activity. Using generative biophysical model of fMRI data such as Dynamic Causal Model (DCM), the underlying neuronal activities of different brain areas and their causal interactions (i.e., effective connectivity) can be calculated. Most DCM studies typically consider the effective connectivity to be static for a cognitive task within an experimental run. However, changes in experimental conditions during complex tasks such as movie-watching might result in temporal variations in the connectivity strengths. In this fMRI simulation study, we leverage state-of-the-art Physiologically informed DCM (P-DCM) along with a recurrent window approach and discretization of the equations to infer the underlying neuronal dynamics and concurrently the dynamic (time-varying) effective connectivities between various brain regions for task-based fMRI. Results from simulation studies on 3- and 10-region models showed that functional magnetic resonance imaging (fMRI) blood oxygenation level-dependent (BOLD) responses and effective connectivity time-courses can be accurately predicted and distinguished from faulty graphical connectivity models representing cognitive hypotheses. In summary, we propose and validate a novel approach to determine dynamic effective connectivity between brain areas during complex cognitive tasks by combining P-DCM with recurrent units.

Investigations of hypoxia-induced deoxyhemoglobin as a contrast agent for cerebral perfusion imaging

The assessment of resting perfusion measures (mean transit time, cerebral blood flow, and cerebral blood volume) with magnetic resonance imaging currently requires the presence of a susceptibility contrast agent such as gadolinium. Here, we present an initial comparison between perfusion measures obtained using hypoxia-induced deoxyhemoglobin and gadolinium in healthy study participants. We hypothesize that resting cerebral perfusion measures obtained using precise changes of deoxyhemoglobin concentration will generate images comparable to those obtained using a clinical standard, gadolinium. Eight healthy study participants were recruited (6F; age 23-60). The study was performed using a 3-Tesla scanner with an eight-channel head coil. The experimental protocol consisted of a high-resolution T1-weighted scan followed by two BOLD sequence scans in which each participant underwent a controlled bolus of transient pulmonary hypoxia, and subsequently received an intravenous bolus of gadolinium. The resting perfusion measures calculated using hypoxia-induced deoxyhemoglobin and gadolinium yielded maps that looked spatially comparable. There was no statistical difference between methods in the average voxel-wise measures of mean transit time, relative cerebral blood flow and relative cerebral blood volume, in the gray matter or white matter within each participant. We conclude that perfusion measures generated with hypoxia-induced deoxyhemoglobin are spatially and quantitatively comparable to those generated from a gadolinium injection in the same healthy participant.

Perfusion MRI using endogenous deoxyhemoglobin as a contrast agent: Preliminary data

PURPOSE

To demonstrate the feasibility of mapping cerebral perfusion metrics with BOLD MRI during modulation of pulmonary venous oxygen saturation.

METHODS

A gas blender with a sequential gas delivery breathing circuit was used to implement rapid isocapnic changes in the partial pressure of oxygen of the arterial blood. Partial pressure of oxygen was initially lowered to a baseline of 40 mmHg. It was then rapidly raised to 95 mmHg for 20 s before rapidly returning to baseline. The induced cerebral changes in deoxyhemoglobin concentration were tracked over time using BOLD MRI in 6 healthy subjects and 1 patient with cerebral steno-occlusive disease. BOLD signal change, contrast-to-noise ratio, and time delay metrics were calculated. Perfusion metrics such as mean transit time, relative cerebral blood volume, and relative cerebral blood flow were calculated using a parametrized method with a mono-exponential residue function. An arterial input function from within the middle cerebral artery was used to scale relative cerebral blood volume and calculate absolute cerebral blood volume and cerebral blood flow.

RESULTS

In normal subjects, average gray and white matter were: BOLD change = 6.3 ± 1.2% and 2.5 ± 0.6%, contrast-to-noise ratio = 4.3 ± 1.3 and 2.6 ± 0.7, time delay = 2.3 ± 0.6 s and 3.6 ± 0.7 s, mean transit time = 3.9 ± 0.6 s and 5.5 ± 0.6 s, relative cerebral blood volume = 3.7 ± 0.9 and 1.6 ± 0.4, relative cerebral blood flow = 70.1 ± 8.3 and 20.6 ± 4.0, cerebral blood flow volume = 4.1 ± 0.9 mL/100 g and 1.8 ± 0.5 mL/100 g, and cerebral blood flow = 97.2 ± 18.7 mL/100 g/min and 28.7 ± 5.9 mL/100 g/min.

CONCLUSION

This study demonstrates that induced abrupt changes in deoxyhemoglobin can function as a noninvasive vascular contrast agent that may be used for cerebral perfusion imaging.

Determining laminar neuronal activity from BOLD fMRI using a generative model

Laminar fMRI using the BOLD contrast enables the non-invasive investigation of mesoscopic functional circuits in the human brain. However, the laminar neuronal activity is spatiotemporally biased in the observed cortical depth profiles of the BOLD signal. In this study, we propose a generative fMRI signal model, comprehensively covering the relationship between cortical depth-dependent changes in excitatory and inhibitory neuronal activity with the sampling of the BOLD signal with finite voxels. The generative model allowed us to investigate pertinent questions regarding the accuracy of the laminar BOLD signal relative to the neuronal activity, and we found that: a) condition differences in laminar BOLD signals may be more reflective of neuronal activity than single condition BOLD signal depth profiles; b) angular dependence of the BOLD signal induces significant signal variability, which can mask underlying activity profiles; c) even if only three neuronal depths are of interest, more BOLD signal depths should be considered in the analysis. In addition, we recommend that the laminar BOLD data should be displayed using the centroid method to appreciate its spatial distribution in the original resolution. Finally, we showed that Bayesian model inversion of the generative model can improve sensitivity and specificity of assessing depth-dependent neuronal changes both for steady-state and dynamically.

Unraveling the contributions to the neuromelanin-MRI contrast

The Locus Coeruleus (LC) and the Substantia Nigra (SN) are small brainstem nuclei that change with aging and may be involved in the development of various neurodegenerative and psychiatric diseases. Magnetization Transfer (MT) MRI has been shown to facilitate LC and the SN visualization, and the observed contrast is assumed to be related to neuromelanin accumulation. Imaging these nuclei may have predictive value for the progression of various diseases, but interpretation of previous studies is hindered by the fact that the precise biological source of the contrast remains unclear, though several hypotheses have been put forward. To inform clinical studies on the possible biological interpretation of the LC- and SN contrast, we examined an agar-based phantom containing samples of natural Sepia melanin and synthetic Cys-Dopa-Melanin and compared this to the in vivo human LC and SN. T₁ and T₂* maps, MT spectra and relaxation times of the phantom, the LC and the SN were measured, and a two-pool MT model was fitted. Additionally, Bloch simulations and a transient MT experiment were conducted to confirm the findings. Overall, our results indicate that Neuromelanin-MRI contrast in the LC likely results from a lower macromolecular fraction, thus facilitating interpretation of results in clinical populations. We further demonstrate that in older individuals T₁ lengthening occurs in the LC.

Locus coeruleus imaging as a biomarker for noradrenergic dysfunction in neurodegenerative diseases

Pathological alterations to the locus coeruleus, the major source of noradrenaline in the brain, are histologically evident in early stages of neurodegenerative diseases. Novel MRI approaches now provide an opportunity to quantify structural features of the locus coeruleus in vivo during disease progression. In combination with neuropathological biomarkers, in vivo locus coeruleus imaging could help to understand the contribution of locus coeruleus neurodegeneration to clinical and pathological manifestations in Alzheimer's disease, atypical neurodegenerative dementias and Parkinson's disease. Moreover, as the functional sensitivity of the noradrenergic system is likely to change with disease progression, in vivo measures of locus coeruleus integrity could provide new pathophysiological insights into cognitive and behavioural symptoms. Locus coeruleus imaging also holds the promise to stratify patients into clinical trials according to noradrenergic dysfunction. In this article, we present a consensus on how non-invasive in vivo assessment of locus coeruleus integrity can be used for clinical research in neurodegenerative diseases. We outline the next steps for in vivo, post-mortem and clinical studies that can lay the groundwork to evaluate the potential of locus coeruleus imaging as a biomarker for neurodegenerative diseases.

European Ultrahigh-Field Imaging Network for Neurodegenerative Diseases (EUFIND)

Introduction

The goal of European Ultrahigh-Field Imaging Network in Neurodegenerative Diseases (EUFIND) is to identify opportunities and challenges of 7 Tesla (7T) MRI for clinical and research applications in neurodegeneration. EUFIND comprises 22 European and one US site, including over 50 MRI and dementia experts as well as neuroscientists.

Methods

EUFIND combined consensus workshops and data sharing for multisite analysis, focusing on 7 core topics: clinical applications/clinical research, highest resolution anatomy, functional imaging, vascular systems/vascular pathology, iron mapping and neuropathology detection, spectroscopy, and quality assurance. Across these topics, EUFIND considered standard operating procedures, safety, and multivendor harmonization.

Results

The clinical and research opportunities and challenges of 7T MRI in each subtopic are set out as a roadmap. Specific MRI sequences for each subtopic were implemented in a pilot study presented in this report. Results show that a large multisite 7T imaging network with highly advanced and harmonized imaging sequences is feasible and may enable future multicentre ultrahigh-field MRI studies and clinical trials.

Discussion

The EUFIND network can be a major driver for advancing clinical neuroimaging research using 7T and for identifying use-cases for clinical applications in neurodegeneration.

Pulsatility of Lenticulostriate Arteries Assessed by 7 Tesla Flow MRI-Measurement, Reproducibility, and Applicability to Aging Effect

Characterization of flow properties in cerebral arteries with 1.5 and 3 Tesla MRI is usually limited to large cerebral arteries and difficult to evaluate in the small perforating arteries due to insufficient spatial resolution. In this study, we assessed the feasibility to measure blood flow waveforms in the small lenticulostriate arteries with 7 Tesla velocity-sensitive MRI. The middle cerebral artery was included as reference. Imaging was performed in five young and five old healthy volunteers. Flow was calculated by integrating time-varying velocity values over the vascular cross-section. MRI acquisitions were performed twice in each subject to determine reproducibility. From the flow waveforms, the pulsatility index and damping factor were deduced. Reproducibility values, in terms of the intraclass correlation coefficients, were found to be good to excellent. Measured pulsatility index of the lenticulostriate arteries significantly increased and damping factor significantly decreased with age. In conclusion, we demonstrate that blood flow through the lenticostriate arteries can be precisely measured using 7 Tesla MRI and reveal effects of arterial stiffness due to aging. These findings hold promise to provide relevant insights into the pathologies involving perforating cerebral arteries.

Subthalamic Nucleus Deep Brain Stimulation: Basic Concepts and Novel Perspectives

Over the last decades, extensive basic and clinical knowledge has been acquired on the use of subthalamic nucleus (STN) deep brain stimulation (DBS) for Parkinson's disease (PD). It is now clear that mechanisms involved in the effects of this therapy are far more complex than previously anticipated. At frequencies commonly used in clinical practice, neural elements may be excited or inhibited and novel dynamic states of equilibrium are reached. Electrode contacts used for chronic DBS in PD are placed near the dorsal border of the nucleus, a highly cellular region. DBS may thus exert its effects by modulating these cells, hyperdirect projections from motor cortical areas, afferent and efferent fibers to the motor STN. Advancements in neuroimaging techniques may allow us to identify these structures optimizing surgical targeting. In this review, we provide an update on mechanisms and the neural elements modulated by STN DBS.

fMRI Adaptation between Action Observation and Action Execution Reveals Cortical Areas with Mirror Neuron Properties in Human BA 44/45

Mirror neurons (MNs) are considered to be the supporting neural mechanism for action understanding. MNs have been identified in monkey’s area F5. The identification of MNs in the human homolog of monkeys’ area F5 Broadmann Area 44/45 (BA 44/45) has been proven methodologically difficult. Cross-modal functional MRI (fMRI) adaptation studies supporting the existence of MNs restricted their analysis to a priori candidate regions, whereas studies that failed to find evidence used non-object-directed (NDA) actions. We tackled these limitations by using object-directed actions (ODAs) differing only in terms of their object directedness in combination with a cross-modal adaptation paradigm and a whole-brain analysis. Additionally, we tested voxels’ blood oxygenation level-dependent (BOLD) response patterns for several properties previously reported as typical MN response properties. Our results revealed 52 voxels in left inferior frontal gyrus (IFG; particularly BA 44/45), which respond to both motor and visual stimulation and exhibit cross-modal adaptation between the execution and observation of the same action. These results demonstrate that part of human IFG, specifically BA 44/45, has BOLD response characteristics very similar to monkey’s area F5.

Network-based statistics for a community driven transparent publication process

The current publishing system with its merits and pitfalls is a mending topic for debate among scientists of various disciplines. Editors and reviewers alike, both face difficult decisions about the judgment of new scientific findings. Increasing interdisciplinary themes and rapidly changing dynamics in method development of each field make it difficult to be an “expert” with regard to all issues of a certain paper. Although unintended, it is likely that misunderstandings, human biases, and even outright mistakes can play an unfortunate role in final verdicts. We propose a new community-driven publication process that is based on network statistics to make the review, publication, and scientific evaluation process more transparent.

Quantifying the link between anatomical connectivity, gray matter volume and regional cerebral blood flow: an integrative MRI study

Background

In the graph theoretical analysis of anatomical brain connectivity, the white matter connections between regions of the brain are identified and serve as basis for the assessment of regional connectivity profiles, for example, to locate the hubs of the brain. But regions of the brain can be characterised further with respect to their gray matter volume or resting state perfusion. Local anatomical connectivity, gray matter volume and perfusion are traits of each brain region that are likely to be interdependent, however, particular patterns of systematic covariation have not yet been identified.

Methodology/Principal Findings

We quantified the covariation of these traits by conducting an integrative MRI study on 23 subjects, utilising a combination of Diffusion Tensor Imaging, Arterial Spin Labeling and anatomical imaging. Based on our hypothesis that local connectivity, gray matter volume and perfusion are linked, we correlated these measures and particularly isolated the covariation of connectivity and perfusion by statistically controlling for gray matter volume. We found significant levels of covariation on the group- and regionwise level, particularly in regions of the Default Brain Mode Network.

Conclusions/Significance

Connectivity and perfusion are systematically linked throughout a number of brain regions, thus we discuss these results as a starting point for further research on the role of homology in the formation of functional connectivity networks and on how structure/function relationships can manifest in the form of such trait interdependency.

Predictors of response to treadmill exercise in stroke survivors

BACKGROUND

Aerobic treadmill exercise (T-EX) therapy has been shown to benefit walking and cardiorespiratory fitness in stroke survivors with chronic gait impairment even long after their stroke. The response, however, varies between individuals.

OBJECTIVE

The purpose of this post hoc analysis of 2 randomized controlled T-EX trials was to identify predictors for therapy response.

METHODS

In all, 52 participants received T-EX for 3 (Germany) or 6 (United States) months. Improvements in overground walking velocity (10 m/6-min walk) and fitness (peak VO(2)) were indicators of therapy response. Lesion location and volume were measured on T1-weighted magnetic resonance scans.

RESULTS

T-EX significantly improved gait and fitness, with gains in 10-m walk tests ranging between +113% and -25% and peak VO(2) between -12% and 88%. Baseline walking impairments or fitness deficits were not predictive of therapy response; 10-m walk velocity improved more in those with subcortical rather than cortical lesions and in patients with smaller lesions. Improvements in 6-minute walk velocity were greater in those with more recent strokes and left-sided lesions. No variable other than training intensity, which was different between trials, predicted fitness gains.

CONCLUSIONS

Despite proving overall effectiveness, the response to T-EX varies markedly between individuals. Whereas intensity of aerobic training seems to be an important predictor of gains in cardiovascular fitness, lesion size and location as well as interval between stroke onset and therapy delivery likely affect therapy response. These findings may be used to guide the timing of training and identify subgroups of patients for whom training modalities could be optimized.

Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass

OBJECTIVE

Noninvasive near-infrared spectroscopy (NIRS) is increasingly used to monitor cerebral oxygenation and blood flow status, which is also of high relevance during cardiovascular surgical interventions with cardiopulmonary bypass. Contamination of the cerebral signal by contamination from overlaying extracerebral tissue, however, has been proposed to reduce sensitivity and cerebral selectivity of this promising technique.

METHODS

We evaluated a novel depth-resolved approach for the determination of cerebral hemodynamics by near-infrared spectroscopic tracking of intravenously administered indocyanine green boluses. A frequency domain technique was applied, allowing simultaneous determination of light absorption changes and time of flight of single photons and enabling the differentiation between extracerebral and intracerebral tracer kinetics. Depth-resolved near-infrared spectroscopy was tested in 4 patients undergoing cardiopulmonary bypass and compared with data derived by conventional continuous-wave near-infrared spectroscopy.

RESULTS

Depth resolution extracted the differential responses of extracerebral and intracerebral blood vessels from near-infrared bolus tracking signals. Postoperative blood flow indices derived from the intracerebral time course exceeded preoperative values by 1.5 +/- 0.2 times, indicating a significant increase of cerebral blood flow not detectable by conventional near-infrared spectroscopy.

CONCLUSION

The depth-resolved approach provides additional and relevant data for the interpretation of intraoperative cerebral perfusion during cardiothoracic surgery. The validity of this approach for patients with preexisting risk factors for cerebral hypoperfusion remains to be determined in larger clinical trials.

Caffeine alters the temporal dynamics of the visual BOLD response

The blood oxygenation level-dependent (BOLD) responses to visual stimuli, using both a 1-s long single trial stimulus and a 20-s long block stimulus, were measured in a 4-T magnetic field both before and immediately after a 200-mg caffeine dose. In addition, resting levels of cerebral blood flow (CBF) were measured using arterial spin labeling. For the single trial stimulus, the caffeine dose significantly (p<0.05) reduced the time to peak (TTP), the time after the peak at which the response returned to 50% of the peak amplitude (TA50), and the amplitude of the poststimulus undershoot in all subjects (N=5). Other parameters, such as the full-width half-maximum (FWHM) and the peak amplitude, also showed significant changes in the majority of subjects. For the block stimulus, the TTP, TA50, and the time for the response to reach 50% of the peak amplitude (T50) were significantly reduced. In some subjects, oscillations were observed in the poststimulus portion of the response with median peak periods of 9.1 and 9.5 s for the single trial and block responses, respectively. Resting CBF was reduced by an average of 24%. The reproducibility of the results was verified in one subject who was scanned on 3 different days. The dynamic changes are similar to those previously reported for baseline CBF reductions induced by hypocapnia and hyperoxia.

Neurovascular coupling analyzed non-invasively in the human brain

Most functional brain imaging methods detect neuronal activations indirectly through the accompanying neurovascular response. Here, we demonstrate that a novel methodological approach, the combination of DC-magnetoencephalography (DC-MEG) and near-infrared spectroscopy (NIRS), allows non-invasive assessment of the dynamics of neurovascular coupling in the human brain: detecting directly slow neuronal processes (with time constants of 30s), DC-MEG revealed, even in unaveraged recordings, sustained neuronal activations at pericentral hand cortices contralateral to repetitive finger movements; these were accompanied by the ensuing local vascular response showing similar dynamical features as quantified by simultaneously recorded NIRS. This non-invasive approach opens a new avenue for the understanding of neurovascular coupling during physiological tasks as well as in diseases involving slow neuronal depolarization shifts and alterations of blood flow, such as stroke or migraine.

Habituation of the visually evoked potential and its vascular response: implications for neurovascular coupling in the healthy adult

In the human, visually evoked potentials (VEP) and cerebral oxygenation changes, as measured by near-infrared spectroscopy (NIRS), are assessed to elucidate the relation between electrophysiological and vascular responses to a checkerboard stimulus reversing at 3 Hz. Habituation of either response is analysed on two time scales. Within the 1-min stimulation period we find a decrease in P100N135-component amplitude, closely coupled to a decrease in the amplitude of the oxygenation parameters (concentration changes in oxygenated and deoxygenated haemoglobin, [oxy-Hb] and [deoxy-Hb]). The N75P100-component amplitude exhibits a different behaviour along the 1-min stimulation period. An initial increase is overridden by an overall decrease, the latter not reaching statistical significance. The analysis across the 13 successive stimulation blocks separated by resting periods of equal duration yields a trend for an decrease in the VEP-components' amplitude, not reflected in the vascular response. When calculating a ratio between the amplitude of the P100N135-component and the concentration changes in the haemoglobins a "coupling index" of a 0.2 microM decrease in [deoxy-Hb] and an increase of 0.6 microM in [oxy-Hb] is found per 1 microV increase in VEP-component amplitude. The ratio is the same irrespective of its assessment from the difference stimulation/ rest or from the habituation effect, i.e., the difference between the amplitudes at the beginning and towards the end of the stimulation period. Although supporting the notion that the coupling between neuronal activation and the vascular response exhibits linear aspects, our findings cannot be taken as a proof of such a linearity across all brain regions and activation types. On the contrary, tentatively calculating a coupling index for the data assessed in the visual system, we intend to stress the necessity to assess both neuronal and vascular response to allow for a comparison between different systems and conditions in whom neurovascular coupling is expected to be altered (Miller et al, 2001; Mechelli et al, 2001).

Noninvasive monitoring of cerebral blood flow by a dye bolus method: separation of brain from skin and skull signals

Tracking a bolus of contrast agent traveling through the cerebral vasculature provides a measure of the blood flow velocity in the respective cerebral tissue. This principle has been the basis for the first approaches in functional magnetic resonance (MR) imaging and is of great value for investigating patients with vascular disease, especially stroke. While bolus measurements are a standard procedure in MR imaging, optical bolus tracking is as yet not established. Here we study optical absorption changes induced by a bolus of the dye indocyanine-green with near infrared spectroscopy in healthy volunteers. The aim is to assess the latency and shape of the change in absorption. Since application in the adult human critically depends on differentiation between extra- and intracerebral vascular compartments we focus on an approach for such a separation. To do this frequency-domain and multidistance measurements are analyzed by a Monte Carlo based model for photon transport in tissue. Based on measurements of both the photon's mean time of flight (phase) and the intensity, our results allow differentiation between an upper (skin and skull) and a lower layer (brain). The bolus in the deeper tissue layers has a peak of about 10 s width, while the change in absorption in the upper layers shows a much longer recovery time. This is in qualitative agreement with MR imaging results using a gadolinium bolus. This result is promising with respect to the potential of bedside monitoring of mean transit time (MTT) changes in patients with stroke or related vascular disease.

Dopplersonographic measurement of global cerebral circulation time using echo contrast-enhanced ultrasound in normal individuals and patients with arteriovenous malformations

Echo-contrast "bolus tracking" by ultrasound (US) is an exciting new tool to study cerebral haemodynamics. In the present study, a global cerebral circulation time (CCT) was measured by extracranial Doppler as the time difference of contrast bolus arrival between the internal carotid artery and internal jugular vein. A total of 64 healthy volunteers and 9 patients with an angiographically diagnosed arteriovenous malformation (AVM) were studied. CCT in volunteers and patients was calculated as the time interval between the points of 10% rise (CCT(1)) and 90% rise (CCT(3)) of the total intensity increase and between the turning points (CCT(2)) of the resulting time-intensity curves. In the volunteer group, CCT(1) was 5.4 +/- 1.8 s, CCT(2) was 7 +/- 1.3 s and CCT(3) 7.5 +/- 1.8 s. CCT results in the AVM group were 2.8 +/- 2.5 s, 3.0 +/- 1.3 s and 4.5 +/- 2.1 s, respectively, and differed significantly from the controls. For the first time, we could confirm a significant shortening of CCT in patients with cerebral AVM by US. The presented test might become a new, additional tool for AVM evaluation and follow-up of treatment in these patients.

Cross talk in the Lambert-Beer calculation for near-infrared wavelengths estimated by Monte Carlo simulations

Using the modified Lambert-Beer law to analyze attenuation changes measured noninvasively during functional activation of the brain might result in an insufficient separation of chromophore changes ("cross talk") due to the wavelength dependence of the partial path length of photons in the activated volume of the head. The partial path length was estimated by performing Monte Carlo simulations on layered head models. When assuming cortical activation (e.g., in the depth of 8-12 mm), we determine negligible cross talk when considering changes in oxygenated and deoxygenated hemoglobin. But additionally taking changes in the redox state of cytochrome-c-oxidase into account, this analysis results in significant artifacts. An analysis developed for changes in mean time of flight--instead of changes in attenuation--reduces the cross talk for the layers of cortical activation. These results were validated for different oxygen saturations, wavelength combinations and scattering coefficients. For the analysis of changes in oxygenated and deoxygenated hemoglobin only, low cross talk was also found when the activated volume was assumed to be a 4-mm-diam sphere.