Near infrared spectroscopy (NIRS): a new tool to study hemodynamic changes during activation of brain function in human adults

Decrease in cortical activation during learning of a multi-joint discrete motor task

Understanding how the brain learns motor skills remains a very challenging task. To elucidate the neural mechanism underlying motor learning, we assessed brain activation changes on a trial-by-trial basis during learning of a multi-joint discrete motor task (kendama task). We used multi-channel near-infrared spectroscopy (NIRS) while simultaneously measuring upper limb movement changes by using a 3D motion capture system. Fourteen right-handed participants performed the task using their right upper limb while sitting a chair. The task involved tossing a ball connected by a string to the kendama stick (picking up movement) and catching the ball in the cup attached to the stick (catching movement). Participants performed a trial every 20 s for 90 trials. We measured the hemodynamic responses [oxygenated hemoglobin (oxy-Hb) and deoxygenated hemoglobin (deoxy-Hb) signals] around the predicted location of the sensorimotor cortices on both hemispheres. Analysis of the NIRS data revealed that the magnitudes of the event-related oxy-Hb responses to each trial decreased significantly as learning progressed. Analysis of movement data revealed that integrated upper limb muscle torques decreased significantly only for the picking up movements as learning progressed, irrespective of the outcome of the trials. In contrast, dispersion of the movement patterns decreased significantly only for the catching movements in the unsuccessful trials. Furthermore, we found significant positive correlations between the changes in the magnitudes of the oxy-Hb responses and those of the integrated upper limb muscle torques during learning. Our results suggest that the decrease in cortical activation in the sensorimotor cortex reflects changes in motor commands during learning of a multi-joint discrete movement.

Monitoring of pre-frontal oxygen status in helicopter pilots using near-infrared spectrophotometers

Background

There are few in-flight studies of cognition-related cerebral oxygen status in helicopter pilots.

Methods

Four male helicopter pilots volunteered for nine sorties during visual flight in a BK117 and UH-60J. The pilots' pre-frontal oxy-hemoglobin (O₂Hb) and deoxy-hemoglobin (HHb) concentration were continuously monitored from the right/left sections of the forehead using near-infrared spectrophotometers with a consideration of motion artifacts.

Results

The concentration of O₂Hb progressively increased (13.98 μmol•L^-1 as a maximum increased concentration) in both the right/left sections of the forehead from the basal level during the heightened cognitive demand of helicopter flight. There was comparatively little change (4.32 μmol•L^-1 as a maximum increased concentration) in HHb concentration during measurement of helicopter flight. HHb changes were apparently not affected by a heightened cognitive demand of helicopter pilots.

Conclusion

These results demonstrate that near-infrared spectroscopy, especially O₂Hb measurements, provides a sensitive method for the monitoring of cognitive demand (maneuvers) in helicopter pilots.

Effects of Milk Casein-derived Peptides on Absolute Oxyhaemoglobin Concentrations in the Prefrontal Area and on Work Efficiency after Mental Stress Loading in Male Students

This study examined the influence of milk casein-derived peptides on cerebral activity after mental stress loading. In a crossover study, 16 male students were given a drink containing peptides (peptide group), or water (control group) before stress loading. The oxyhaemoglobin (HbO2) concentration in the prefrontal area of the brain and work efficiency were measured as indicators of cerebral activity and differences in these parameters were examined according to type A or type B personality. Type A behaviour was defined as: aggression–hostility, hard-driving—time-urgency and speed–power, whereas type B behaviour did not have these characteristics. Peptide intake resulted in a significant increase in both HbO2 concentration and work efficiency, whilst a similar increase was not seen in the control group. When divided into type A or type B personality, the changes in HbO2 concentration for the control group differed significantly in the right prefrontal area. Moreover, in type A subjects the HbO2 concentration in the right prefrontal area following intake was significantly different between the peptide and control groups.

Measurement of layer-like hemodynamic trends in scalp and cortex: implications for physiological baseline suppression in functional near-infrared spectroscopy

A multidetector, continuous wave, near-infrared spectroscopy (NIRS) system is developed to examine whether the hemodynamics of the scalp and brain in adults contain significant layer-like hemodynamic trends. NIRS measurements are made using contrasting geometries, one with four detectors equidistant from a source 33 mm away, and one with detectors collinear with the source (5 to 33 mm away). When NIRS time series are acquired over the prefrontal cortex from resting adults using both geometries, variations among the time series are consistent with a substantially homogeneous two-layer model (p<0.001) and inconsistent with one dominated by heterogeneities. Additionally, when time series measured 5 mm from the source are subtracted from corresponding 33-mm signals via a least-squares algorithm, 60% of the hemoglobin changes are on average removed. These results suggest that hemodynamic trends present in the scalp can contribute significantly to NIRS measurements, and that attempts to reduce this noise by subtracting a simultaneous near-channel measurement using a two-layer model are justified. Such subtractions are then performed on NIRS measurements from two stimulus protocols. For systemic stimulations (Valsalva maneuver), the subtraction cancels the hemodynamic response, as desired. For localized stimulation of the occipital lobe (viewing a flickering pattern), the subtraction isolated a stimulus-correlated hemodynamic feature from background noise.

Intrinsic correlations of electroencephalography rhythms with cerebral hemodynamics during sleep transitions

To examine the correlation between electroencephalography fluctuations (EEGF) and cerebral hemodynamics during sleep after eliminating influences from cardiovascular activity, we simultaneously measured EEGF, the cerebral hemoglobin concentration change, and mean arterial blood pressure (MAP) during the sleep of healthy human adults. The cerebral hemoglobin concentration change was measured at 88 positions covering the whole head, by optical topography. We extracted the intrinsic correlation between EEGF and the cerebral hemoglobin concentration change without MAP contributions through cross-correlation and partial correlation analyses considering time lags. We found that increases in the power of the alpha rhythm in EEGF were correlated with increases in oxygenated hemoglobin (oxy-Hb) and decreases in deoxygenated hemoglobin (deoxy-Hb) and that increases in the power of the sigma rhythm in EEGF were correlated with decreases in oxy-Hb and increases in deoxy-Hb. The former correlations tended to appear in the transition from sleep stage 2 to sleep stage 1, and the latter correlations tended to appear in the transition from sleep stage 1 to sleep stage 2. The former correlations were found in the inferior frontal and middle temporal gyri and the latter correlations were found in the superior frontal, middle frontal, and angular gyri.

Alterations in prefrontal cortical activity in the course of treatment for late-life depression as assessed on near-infrared spectroscopy

AIM

To evaluate the severity of depression by measuring alterations in prefrontal cortical activity associated with mood disorders, as assessed on near-infrared spectroscopy.

METHODS

Ten of 27 subjects hospitalized for late-life depression from May 2006 to June 2007, were examined. In these 10 subjects changes in hemoglobin concentration were measured on near-infrared spectroscopy during two types of the rock, paper, scissors game as the cognitive tasks affecting prefrontal cortical activity on 2 days, including 1 day on which depressive symptoms had slightly improved due to treatment, and then on another day >4 weeks later. Severity of depression and cognitive impairment were also simultaneously assessed.

RESULTS

The change in oxygenated hemoglobin concentration during a difficult task (intentional loss task) was significantly larger than that during an easy task (try to win task) on the left side (left, P = 0.010; right, P = 0.059). On the left side there was a significant negative correlation between the ratio of oxygenated hemoglobin measurements on the second day to those on the first day, and the severity of depression on the second day (left, P = 0.012; right, P = 0.090). Thus, the more left prefrontal cortical activity tended to increase, the fewer depressive symptoms tended to be present on the second day of testing.

CONCLUSIONS

Measuring of alterations in prefrontal cortical activity associated with mood disorders, as assessed on near-infrared spectroscopy, is feasible in subjects with depression.

Hemodynamic response to visual stimulation in newborn infants using functional near-infrared spectroscopy

Brain activity is associated with physiological changes, which alter the optical properties of tissue. These changes can be detected by near-infrared spectroscopy (NIRS). Aim of the study was to determine changes in cerebral oxygenation in response to stimulation in the visual cortex in newborn infants during spontaneous sleep in the first days of life. We used an in-house developed multichannel NIRS imaging instrument, the MCP-II, to measure changes in concentration of oxyhemoglobin (O(2)Hb) and deoxyhemoglobin (HHb) in specific brain areas. In 10 out of 15 subjects, a significant increase in O(2)Hb and/or a significant decrease in HHb were found in one or more channels over the occipital cortex. During stimulation, O(2)Hb increased by a mean of 0.98 mumol/l, HHb decreased by a mean 0.17 mumol/l, and total-Hb increased by a mean of 0.81 mumol/l. The hemodynamic response to visual stimulation in the occipital cortex in newborn infants is similar to adults. The increase in O(2)Hb and the simultaneous decrease in HHb during stimulation suggest an increase in cerebral blood flow (CBF) that overcompensates for the increased oxygen consumption (CMRO(2)) in the activated cortical area.

A noninvasive, presurgical expressive and receptive language investigation in a 9-year-old epileptic boy using near-infrared spectroscopy

The intracarotid amobarbital test (IAT) is used for presurgical evaluation of language lateralization. However, this procedure has many limitations, especially in children. As an alternative to IAT, in the case described here, near-infrared spectroscopy (NIRS) was used to investigate expressive and receptive language lateralization as part of the presurgical evaluation of a 9-year-old Yiddish-speaking boy with a probable left temporal epileptic focus. This child could not tolerate IAT or functional MRI. He underwent two NIRS recording sessions while performing expressive and receptive language tasks. Results indicated predominantly left-sided expressive language in Broca's area with ipsilateral cortical recruitment of more posterior regions. Receptive language showed a bilateral cerebral pattern, perhaps as an expression of cerebral plasticity or compensation in this young patient. This case report illustrates that NIRS may contribute to presurgical investigation and could become a noninvasive alternative to IAT and functional MRI in determining speech lateralization in children.

Study on mental stress using near-infrared spectroscopy, electroencephalography, and peripheral arterial tonometry

In this research, we used near-infrared spectroscopy (NIRS) as an alternative technique for mental state analysis, and compared its performance with other conventional techniques such as electroencephalography (EEG) and peripheral arterial tonometry (PAT) during stress and healing tasks. We measured biological signals simultaneously in our experiments using these techniques for comparison. NIRS results showed that the level of total hemoglobin in the frontal cortex increased during a stress task and decreased during a healing task for all subjects whose blood volume change was properly recorded. EEG, however, showed inconsistent results due to task variation. Only PAT gave consistent results in many of the subjects. Taken together, the results suggest that NIRS might be suitable for mental state evaluation, with PAT as an alternative.

Altered frontal brain oxygenation in detoxified alcohol dependent patients with unaffected verbal fluency performance

Despite prominent prefrontal deficits and alterations in anatomy, neurophysiology, and neuropsychology after long-term alcohol consumption in alcohol dependent patients, only a few investigations of functional brain activity have been published. Using functional near-infrared spectroscopy (fNIRS), we examined the concentration changes in oxygenated (O(2)Hb) and deoxygenated (HHb) haemoglobin in 17 right-handed alcohol dependent patients after detoxification and 17 matched healthy controls during a verbal fluency task. Alcohol dependent patients were characterized by normal behavioural performance (number of words produced) and physiological activation patterns (increase of O(2)Hb and decrease of HHb) over frontotemporal regions during phonological and semantical verbal fluency. However, the degree of activation was diminished (lower magnitude of oxygenation) and the localization of the activation was more restricted to inferior frontal areas as compared with the healthy participants. fNIRS is a sensitive and valid method, to detect alterations in brain functioning in clinical groups like alcohol dependent patients. Altered prefrontal functional brain activation during verbal fluency in alcohol dependent patients in a detoxified state may precede behavioural or cognitive alterations with a later onset.

Comparison of light intensity on the brain surface due to laser exposure during optical topography and solar irradiation

Optical topography (OT), which is based on the near-infrared spectroscopy, is a powerful tool for observing brain activity noninvasively. To estimate the effect of laser exposure on the brain, photon-distribution profiles in bald heads of adults and neonates during the OT were calculated using the photon-diffusion equation. These calculations showed that although the absolute values of the intensity depend on details of the head model, the relative values of OT exposure to sunlight exposure were less sensitive to the model details. As an example, the light intensities on the brain surface during OT obtained by using a commercially available system were about 2% for adults and 3% for neonates of those values obtained under midday sunlight on a sunny day in midsummer. These values were obtained under the reasonable assumptions with a large safety factor.

Removal of the skin blood flow artifact in functional near-infrared spectroscopic imaging data through independent component analysis

We investigate whether the functional near-infrared spectroscopic (fNIRS) signal includes a signal from the changing skin blood flow. During a locomotor task on a treadmill, changes in the hemodynamic response in the front-parietal area of healthy human subjects are simultaneously recorded using an fNIRS imaging system and a laser Doppler tissue blood flow meter. Independent component analysis (ICA) for fNIRS signals is performed. The skin blood flow changes during locomotor tasks on a treadmill. The activated spatial distribution of one of the components separated by ICA reveals an overall increase in fNIRS channels. To evaluate the uniformity of the activated spatial distribution, we define a new statistical value-the coefficient of spatial uniformity (CSU). The CSU value is a highly discriminating value (e.g., 2.82) compared with values of other components (e.g., 1.41, 1.10, 0.96, 0.61, and 0.58). In addition, the independent component signal corresponding to the activated spatial distribution is similar to changes in skin blood flow measured with the laser Doppler tissue blood flow meter. The coefficient of correlation indicates strong correlation. Localized activation areas around the premotor and medial somatosensory cortices are shown more clearly by eliminating the extracted component.

Comparison of blood-oxygen-level-dependent functional magnetic resonance imaging and near-infrared spectroscopy recording during functional brain activation in patients with stroke and brain tumors

Blood-oxygen-level-dependent contrast functional magnetic resonance imaging (BOLD-fMRI) has been used to perform functional imaging in brain disorders such as stroke and brain tumors. However, recent studies have revealed that BOLD-fMRI does not image activation areas correctly in such patients. To clarify the characteristics of the evoked cerebral blood oxygenation (CBO) changes occurring in stroke and brain tumors, we have been comparing near-infrared spectroscopy (NIRS) and BOLD-fMRI recording during functional brain activation in these patients. We review our recent studies and related functional imaging studies on the brain disorders. In the primary sensorimotor cortex (PSMC) on the nonlesion side, the motor task consistently caused a decrease of deoxyhemoglobin (deoxy-Hb) with increases of oxyhemoglobin (oxy-Hb) and total hemoglobin (t-Hb), which is consistent with the evoked CBO response observed in normal adults. BOLD-fMRI demonstrated robust activation areas on the nonlesion side. In stroke patients, severe cerebral ischemia (i.e., misery perfusion) caused an increase of deoxy-Hb during the task, associated with increases of oxy-Hb and t-Hb, in the PSMC on the lesion side. In addition, the activation volume of BOLD-fMRI was significantly reduced on the lesion side. The BOLD signal did not change in some areas of the PSMC on the lesion side, but it tended to decrease in other areas during the tasks. In brain tumors, BOLD-fMRI clearly demonstrated activation areas in the PSMC on the lesion side in patients who displayed a normal evoked CBO response. However, the activation volume on the lesion side was significantly reduced in patients who exhibited an increase of deoxy-Hb during the task. In both stroke and brain tumors, false-negative activations (i.e., marked reductions of activation volumes) in BOLD imaging were associated with increases of deoxy-Hb, which could cause a reduction in BOLD signal. BOLD-fMRI investigations of patients with brain disorders should be performed while giving consideration to atypical evoked CBO changes.

Functional near-infrared spectroscopy: current status and future prospects

Near-infrared spectroscopy (NIRS), which was originally designed for clinical monitoring of tissue oxygenation, has been developing into a useful tool for neuroimaging studies (functional near-infrared spectroscopy). This technique, which is completely noninvasive, does not require strict motion restriction and can be used in a daily life environment. It is expected that NIRS will provide a new direction for cognitive neuroscience research, more so than other neuroimaging techniques, although several problems with NIRS remain to be explored. This review demonstrates the strengths and the advantages of NIRS, clarifies the problems, and identifies the limitations of NIRS measurements. Finally, its future prospects are described.

Functional optical signal analysis: a software tool for near-infrared spectroscopy data processing incorporating statistical parametric mapping

Optical topography (OT) relies on the near infrared spectroscopy (NIRS) technique to provide noninvasively a spatial map of functional brain activity. OT has advantages over conventional fMRI in terms of its simple approach to measuring the hemodynamic response, its ability to distinguish between changes in oxy- and deoxy-hemoglobin and the range of human participants that can be readily investigated. We offer a new software tool, functional optical signal analysis (fOSA), for analyzing the spatially resolved optical signals that provides statistical inference capabilities about the distribution of brain activity in space and time and by experimental condition. It does this by mapping the signal into a standard functional neuroimaging analysis software, statistical parametric mapping (SPM), and forms, in effect, a new SPM toolbox specifically designed for NIRS in an OT configuration. The validity of the program has been tested using synthetic data, and its applicability is demonstrated with experimental data.

Changes in hemoglobin concentration in the lateral occipital regions during shape recognition: a near-infrared spectroscopy study

By using near-infrared spectroscopy (NIRS), we measured the changes in the oxygenated and deoxygenated hemoglobin (oxy-Hb and deoxy-Hb, respectively) concentrations while performing visual tasks. We conducted experiments using two tasks: a shape recognition task and a position recognition task. It was found that the oxy-Hb concentration was substantially higher in the lateral occipital regions during shape recognition than during position recognition. The changes in the oxy-Hb concentration were considered to reflect the activation difference between the two tasks. No difference was observed in the oxy-Hb concentration during the memorization of shape and memorization of position. The deoxy-Hb concentration was different between the two tasks only when different stimuli were used but not when identical stimuli were used. In addition, it was suggested that the deoxy-Hb concentration is more sensitive to activation difference between the hemispheres and the activation at some regions. Measurements of the oxy-Hb and deoxy-Hb concentrations would reflect different aspects of cortical activations. The present results showed that measuring the oxy-Hb and deoxy-Hb concentrations separately can differentiate the activation of the regional cortical functions.

Progress of near-infrared spectroscopy and topography for brain and muscle clinical applications

This review celebrates the 30th anniversary of the first in vivo near-infrared (NIR) spectroscopy (NIRS) publication, which was authored by Professor Frans Jobsis. At first, NIRS was utilized to experimentally and clinically investigate cerebral oxygenation. Later it was applied to study muscle oxidative metabolism. Since 1993, the discovery that the functional activation of the human cerebral cortex can be explored by NIRS has added a new dimension to the research. To obtain simultaneous multiple and localized information, a further major step forward was achieved by introducing NIR imaging (NIRI) and tomography. This review reports on the progress of the NIRS and NIRI instrumentation for brain and muscle clinical applications 30 years after the discovery of in vivo NIRS. The review summarizes the measurable parameters in relation to the different techniques, the main characteristics of the prototypes under development, and the present commercially available NIRS and NIRI instrumentation. Moreover, it discusses strengths and limitations and gives an outlook into the "bright" future.

Adaptive filtering to reduce global interference in evoked brain activity detection: a human subject case study

Following previous Monte Carlo simulations, we describe in detail an example of detecting evoked visual hemodynamic responses in a human subject as a preliminary demonstration of the novel global interference cancellation technology. The raw time series of oxyhemoglobin (O(2)Hb) and deoxyhemoglobin (HHb) changes, their block averaged results before and after adaptive filtering, together with the power spectral density analysis are presented. Simultaneous respiration and EKG recordings suggested that spontaneous low-frequency oscillation and cardiac activity were the major sources of global interference in our test. When global interference dominates (e.g., for O(2)Hb in our data, judged by power spectral density analysis), adaptive filtering effectively reduced this interference, doubling the contrast-to-noise ratio (CNR) for evoked visual response detection. When global interference is not obvious (e.g., in our HHb data), adaptive filtering provided no CNR improvement. The results also showed that the hemodynamic changes in the superficial layers and the estimated total global interference in the target measurement were highly correlated (r=0.96), which explains why this global interference cancellation method should work well when global interference is dominating. In addition, the results suggested that association between the superficial layer hemodynamics and the total global interference is time-varying.

D4 receptor gene variation modulates activation of prefrontal cortex during working memory

It has been shown that dopamine (DA) influences performance on neurocognitive tests, which are thought to rely on prefrontal activity. The purpose of this study was to explore the effects of gene polymorphisms related to DA activity, namely the D4 DA receptor (DRD4) gene exon III polymorphisms, on prefrontal cortex (PFC) activation. In this study we measured the brain oxygenation of the PFC during an n-back task with near-infrared spectroscopy (NIRS). We investigated 40 young healthy subjects, 12 of which carried the DRD4 exon III 7-repeat allele (group 7). These were compared with subjects without a 7-repeat allele (n=28, group 4). Additionally, we compared good and bad performers with respect to brain activation. As expected, we found significant increases in the concentration of oxygenated haemoglobin [O2Hb] during the 1-back and 2-back condition compared with baseline, and a corresponding significant decrease of deoxyhaemoglobin concentration. As a main result of this study we also found an interaction effect between task condition and DRD4 genotype with higher increases of [O2Hb] during the 2-back version compared with the 1-back version for the subjects of the 7-repeat allele group only. The same effect was seen as a statistical trend, when we compared bad performers with good performers. Therefore, we interpret the effects of the 7-repeat allele group of DRD4 as a sign of ineffective brain activity, perhaps even as a sign of prefrontal noise.

Cortical activation during two verbal fluency tasks in schizophrenic patients and healthy controls as assessed by multi-channel near-infrared spectroscopy

Near-infrared spectroscopy (NIRS) is an optical imaging method that allows non-invasive in-vivo measurements of changes in the concentration of oxygenated (O(2)Hb) and deoxygenated (HHb) hemoglobin in brain tissue. For the present study, we examined 12 schizophrenic patients and 12 age- and gender-matched healthy controls by means of multi-channel NIRS (Optical Topography; ETG-100, Hitachi Medical Co., Japan) during performance of two versions of the Verbal Fluency Test (VFT; letter and category version). The results indicate that the verbal fluency tasks generally led to clear frontal activation in healthy controls, which was significantly reduced in schizophrenic patients. The letter version of the VFT induced overall stronger activation than the category version, the group difference being particularly pronounced for phonological fluency. Moreover, significant positive correlations between task-related activation effects in prefrontal and temporal NIRS channels were found in both schizophrenic patients and healthy controls. The results confirm functional deficits within the frontal lobe in patients suffering from schizophrenic illnesses, but do not confirm previous findings on abnormal fronto-temporal correlations or increased temporal activation in this group of patients. The data furthermore underline the usefulness of functional NIRS in monitoring hemodynamic responses associated with cognitive processes in healthy controls and patients with neuro-psychiatric disorders.

Source of nonlinearity of the BOLD response revealed by simultaneous fMRI and NIRS

The nonlinearity of the blood oxygenation level-dependent (BOLD) response to stimuli of different duration, particularly those of short duration, has been well studied by functional magnetic resonance imaging (fMRI). This nonlinearity is assumed to be due to neural adaptation and the nonlinearity of the response in the oxygen extraction fraction (OEF); the latter has not been examined quantitatively in humans. To evaluate how the OEF response contributes to the nonlinearity of the BOLD response to neural activity, we used simultaneous fMRI and near-infrared spectroscopy (NIRS). The responses to visual stimuli of four different durations were measured as changes in the BOLD signal and the NIRS-derived hemoglobin concentrations. The hemodynamic response nonlinearity was quantified using an impulse response function model with saturation nonlinearity scaling in the response amplitude, assuming that the unknown neural adaptation parameters varied within a physiologically feasible range. Independent of the degree of neural adaptation, the BOLD response consistently showed saturation nonlinearity similar to that of the OEF response estimated from the NIRS measures, the nonlinearity of which was greater than that of the response in the total hemoglobin concentration representing the cerebral blood volume (CBV). We also found that the contribution of the OEF response to the BOLD response was four to seven times greater than the contribution of the CBV response. Thus, we conclude that the nonlinearity of the BOLD response to neural activity originates mainly from that of the OEF response.

Physiological noise in near-infrared spectroscopy: implications for optical brain computer interfacing

Near-infrared spectroscopy is a non-invasive optical method used to detect functional activation of the cerebral cortex. Cognitive, visual, auditory and motor tasks are among the functions that have been investigated by this technique in the context of optical brain computer interfacing. In order to determine whether the optical response is due to a stimulus, it is essential to identify and reduce the effects of physiological noise. This paper characterizes noise typically present in optical responses and reports signal processing approaches used to overcome such noise.

Effects of sedative and non-sedative H1 antagonists on cognitive tasks: behavioral and near-infrared spectroscopy (NIRS) examinations

RATIONALE

It is well known that the newer H1-receptor antagonists elicit better performance of working memory and selective attention relative to the first generation drugs in this class. However, the neural correlates of the poorer performance associated with first-generation H1-receptor antagonists remain unknown.

OBJECTIVES

This study examined the effects of first- and second-generation H1-receptor antagonists on neural correlates of cognitive tasks using near-infrared spectroscopy (NIRS), a novel method of brain imaging suitable for psychological experiments.

MATERIALS AND METHODS

We measured the NIRS responses of 12 healthy volunteer subjects during the performance of working memory, selective attention, and visual perception tasks, 3 h after taking a first-generation antagonist (ketotifen), second-generation antagonist (epinastine), or placebo. We also measured subjective sleepiness by visual analogue scale (VAS) test.

RESULTS

Cortical activation at the lateral prefrontal region increased during the performance of working memory and selective attention tasks in subjects receiving epinastine and placebo but not in those who took ketotifen. No significant difference was observed at the occipital region in the visual perception task among the three drug groups. VAS score and the behavioral performance during working memory and visual perception tasks indicated sedative effects of ketotifen consistent with the findings of previous studies.

CONCLUSIONS

Our results suggest that the neural response for working memory and selective attention task was impaired by the administration of ketotifen in comparison with that of epinastine and placebo. The sedative effect in the neural response was not observed after epinastine administration.

Brain tissue oxygen concentration measurements

Brain function depends exquisitely on oxygen for energy metabolism. Measurements of brain tissue oxygen tension, by a variety of quantitative and qualitative techniques, going back for >50 years, have led to a number of significant conclusions. These conclusions have important consequences for understanding brain physiology as it is now being explored by techniques such as blood-oxygen-level-dependent functional magnetic resonance imaging (BOLD fMRI) and near-infrared spectroscopy (NIRS). It has been known for some time that most of the measured oxygen tensions are less than venous pO2 and are distributed in a spatially and temporally heterogeneous manner on a microregional scale. Although certain large-scale methods can provide reproducible average brain pO2 measurements, no useful concept of a characteristic oxygen tension or meaningful average value for brain tissue oxygen can be known on a microregional level. Only an oxygen field exists with large local gradients due to local tissue respiration, and the most useful way to express this is with a pO2 distribution curve or histogram. The neurons of the brain cortex normally exist in a low-oxygen environment and on activation are oxygenated by increases in local capillary blood flow that lead to increases in hemoglobin saturation and tissue oxygen.

Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography

Functional neuroimaging is a vital element of neuroscience and cognitive research and, increasingly, is an important clinical tool. Diffuse optical imaging is an emerging, noninvasive technique with unique portability and hemodynamic contrast capabilities for mapping brain function in young subjects and subjects in enriched or clinical environments. We have developed a high-performance, high-density diffuse optical tomography (DOT) system that overcomes previous limitations and enables superior image quality. We show herein the utility of the DOT system by presenting functional hemodynamic maps of the adult human visual cortex. The functional brain images have a high contrast-to-noise ratio, allowing visualization of individual activations and highly repeatable mapping within and across subjects. With the improved spatial resolution and localization, we were able to image functional responses of 1.7 cm in extent and shifts of <1 cm. Cortical maps of angle and eccentricity in the visual field are consistent with retinotopic studies using functional MRI and positron-emission tomography. These results demonstrate that high-density DOT is a practical and powerful tool for mapping function in the human cortex.

Adaptive filtering for global interference cancellation and real-time recovery of evoked brain activity: a Monte Carlo simulation study

The sensitivity of near-infrared spectroscopy (NIRS) to evoked brain activity is reduced by physiological interference in at least two locations: 1. the superficial scalp and skull layers, and 2. in brain tissue itself. These interferences are generally termed as "global interferences" or "systemic interferences," and arise from cardiac activity, respiration, and other homeostatic processes. We present a novel method for global interference reduction and real-time recovery of evoked brain activity, based on the combination of a multiseparation probe configuration and adaptive filtering. Monte Carlo simulations demonstrate that this method can be effective in reducing the global interference and recovering otherwise obscured evoked brain activity. We also demonstrate that the physiological interference in the superficial layers is the major component of global interference. Thus, a measurement of superficial layer hemodynamics (e.g., using a short source-detector separation) makes a good reference in adaptive interference cancellation. The adaptive-filtering-based algorithm is shown to be resistant to errors in source-detector position information as well as to errors in the differential pathlength factor (DPF). The technique can be performed in real time, an important feature required for applications such as brain activity localization, biofeedback, and potential neuroprosthetic devices.

Applications of functional near-infrared spectroscopy (fNIRS) to Neurorehabilitation of cognitive disabilities

Functional Near-Infrared Spectroscopy (fNIRS) is a neuroimaging technique that utilizes light in the near-infrared spectrum (between 700 and 1000 nm) to detect hemodynamic changes within the cortex when sensory, motor, or cognitive activation occurs. FNIRS principles have been used to study brain oxygenation for several decades, but have more recently been applied to study cognitive processes. This paper provides a description of basic fNIRS techniques, and provides a review of the rehabilitation-related literature. The authors discuss strengths and weaknesses of this technique, assert that fNIRS may be particularly beneficial to neurorehabilitation of cognitive disabilities, and suggest future applications.

Brain activation in elderly people with and without dementia: Influences of gender and medication

Patients suffering from dementia show altered functional brain activation patterns especially in prefrontal brain regions, as research suggests. The present study follows three aims: to replicate these findings, to investigate treatment effects when administering galantamine, and to put gender differences in focus. We compared 12 patients with dementia to 12 age- and gender-matched healthy subjects regarding changes in haemoglobin concentration in brain tissue while performing a verbal fluency task (VFT). Concentration changes of oxygenated (O(2)Hb) and deoxygenated (HHb) haemoglobin were measured by multi-channel near-infrared spectroscopy (NIRS), an easily applicable and non-invasive method of optical topography. In the patient group, measurement was repeated 4 and 8 weeks after starting treatment with galantamine. The results showed a reduced increase in O(2)Hb during task performance for patients compared to healthy controls. Furthermore, female subjects showed more pronounced activation in O(2)Hb as well as HHb compared to male subjects. Regarding treatment effects, no clear results could be obtained. In HHb, evidence for an entrainment effect was found. In the light of existing literature, the present study suggests an interaction of gender and age regarding brain activation patterns which should be aimed at in future investigations.

Brain–computer interface using a simplified functional near-infrared spectroscopy system

A brain-computer interface (BCI) is a device that allows a user to communicate with external devices through thought processes alone. A novel signal acquisition tool for BCIs is near-infrared spectroscopy (NIRS), an optical technique to measure localized cortical brain activity. The benefits of using this non-invasive modality are safety, portability and accessibility. A number of commercial multi-channel NIRS system are available; however we have developed a straightforward custom-built system to investigate the functionality of a fNIRS-BCI system. This work describes the construction of the device, the principles of operation and the implementation of a fNIRS-BCI application, 'Mindswitch' that harnesses motor imagery for control. Analysis is performed online and feedback of performance is presented to the user. Mindswitch presents a basic 'on/off' switching option to the user, where selection of either state takes 1 min. Initial results show that fNIRS can support simple BCI functionality and shows much potential. Although performance may be currently inferior to many EEG systems, there is much scope for development particularly with more sophisticated signal processing and classification techniques. We hope that by presenting fNIRS as an accessible and affordable option, a new avenue of exploration will open within the BCI research community and stimulate further research in fNIRS-BCIs.

Selectivity and localization of cortical response to auditory and visual stimulation in awake infants aged 2 to 4 months

To better understand the development of multimodal perception, we examined selectivity and localization of cortical responses to auditory and visual stimuli in young infants. Near-infrared optical topography with 24 channels was used to measure event-related cerebral oxygenation changes of the bilateral temporal cortex in 15 infants aged 2 to 4 months, when they were exposed to speech sounds lasting 3 s and checkerboard pattern reversals lasting 3 s, which were asynchronously presented with different alternating intervals. Group analysis revealed focal increases in oxy-hemoglobin and decreases in deoxy-hemoglobin in both hemispheres in response to auditory, but not to visual, stimulation. These results indicate that localized areas of the primary auditory cortex and the auditory association cortex are involved in auditory perception in infants as young as 2 months of age. In contrast to the hypothesis that perception of distinct sensory modalities may not be separated due to cross talk over the immature cortex in young infants, the present study suggests that unrelated visual events do not influence on the auditory perception of awake infants.

TMS orientation for NIRS-functional motor mapping

Functional near-infrared spectroscopic imaging (NIRS imaging) has the potential to elucidate the relationship between neuronal activity and oxygenation responses. However, its signal specificity to the functional cortex is sometimes spoiled by its rough spatial resolution. In this study we incorporated transcranial magnetic stimulation (TMS) motor mapping into an NIRS imaging study to enhance spatial specificity to the functional cortex. Distinctive biphasic responses in the cortical oxygenation status were observed in the center of the primary motor cortex during a motor task. The early response phase, occurring within 1 to 3 seconds after task initiation, represents a cortical deoxygenation which consists of a significant increase in deoxygenated hemoglobin concentration (HbR) and a nonsignificant decreasing tendency in oxygenated hemoglobin concentration (HbO(2)). The delayed response phase represents an excess of incoming blood flow, which appears as an increase in HbO(2)/total Hb (tHb) and a decrease in HbR following the early response. In the surrounding area, cortical oxygenation change showed a monophasic response consisting of an increase in HbO(2)/tHb and a decrease in HbR. Combining TMS mapping with NIRS imaging enabled us to specify the cortex with the strongest functional activity.

The oxygenation response to functional stimulation: is there a physiological meaning to the lag between parameters?

To investigate the regulation of the hemodynamic response to functional stimulation, functional near-infrared spectroscopy (fNIRS) has been used, due to its ability to assess the dynamics of oxygenated, deoxygenated and total hemoglobin concentration ([oxy-Hb], [deoxy-Hb] and [tot-Hb]). Concerning the latency of these parameters, recent studies have returned a consistent picture when comparing the oxygenation response in the sensorimotor to the visual system: changes in [oxy-Hb] lead those in [deoxy-Hb] by 1.6+/-0.2 s (mean+/-SD) for the sensorimotor system but not for the visual system (0.1+/-0.3 s). A number of physiological differences between these cortical areas may account for such a discrepancy, however, the methodological properties of transcranial NIRS also have a relevant influence. Here we show that for the motor system the latency between changes in oxy- compared to deoxy-Hb vanishes once efforts are made to reduce the effects of a systemic response accompanying sensorimotor activity. We apply two independent approaches to reduce the systemic response and find a simultaneous change in [oxy-Hb] and [deoxy-Hb] even in response to a motor paradigm. The two approaches are: (i) an experimental paradigm with alternating contralateral and ipsilateral motor performance without interspersed rest periods designed to minimize systemic changes and (ii) a global correction scheme in an experiment, comparing a unilateral motor performance to rest. These data shed some doubt on the alleged fundamental physiological difference between cortical hemodynamic regulation in motor and visual cortex and highlight the relevance to respect contributions of the systemic hemodynamics.

Hemoglobin concentration changes in the contralateral hemisphere during and after theta burst stimulation of the human sensorimotor cortices

Using near infrared spectroscopy and repetitive transcranial magnetic stimulation (rTMS), we studied interhemispheric interactions between bilateral motor and sensory cortices in humans. RTMS consisted of a triple-pulse burst (50 Hz) repeated every 200 m for 2 s (10 bursts, 30 pulses); one kind of theta burst TMS (TBS) (Huang et al. in Neuron 45:201-206, 2005). The hemoglobin concentration changes were recorded at the right prefrontal cortex, premotor area (PM), primary hand motor area (M1) and primary sensory area (S1) during and after TBS over the left PM, M1 and S1 or sham stimulation in eight normal volunteers. In addition, motor evoked potentials (MEPs) to TMS over the right M1 were recorded from the left first dorsal interosseous muscle after the conditioning TBS over left S1. TBS over PM induced a significant oxy-Hb decrease at the contralateral PM. TBS over M1 elicited a significant oxy-Hb decrease at the contralateral S1, and TBS over S1 significant oxy-Hb decreases at the contralateral M1 and S1. MEPs to TMS of the right M1 were significantly suppressed by the conditioning TBS over the left S1. These results suggest that there are mainly inhibitory interactions between bilateral PMs and bilateral sensorimotor cortices in humans. Those are partly compatible with the previous findings. In addition to between the primary motor cortices, bilateral connection is requisite for smooth bimanual coordination between the sensory cortices or premotor cortices.

Neural attunement processes in infants during the acquisition of a language-specific phonemic contrast

To elucidate the developmental neural attunement process in the language-specific phonemic repertoire, cerebral hemodynamic responses to a Japanese durational vowel contrast were measured in Japanese infants using near-infrared spectroscopy. Because only relative durational information distinguishes this particular vowel contrast, both first and second language learners have difficulties in acquiring this phonemically crucial durational difference. Previous cross-linguistic studies conducted on adults showed that phoneme-specific, left-dominant neural responses were observed only for native Japanese listeners. Using the same stimuli, we show that a larger response to the across-category changes than to the within-category changes occurred transiently in the 6- to 7-month-old group before stabilizing in the groups older than 12 months. However, the left dominance of the phoneme-specific response in the auditory area was observed only in the groups of 13 months and above. Thus, the durational phonemic contrast is most likely processed first by a generic auditory circuit at 6-7 months as a result of early auditory experience. The neural processing of the contrast is then switched over to a more linguistic circuit after 12 months, this time with a left dominance similar to native adult listeners.

Activation of the prefrontal cortex during memory learning: near-infrared spectroscopy study

Near-infrared spectroscopy (NIRS) is an optical method to determine oxygenated and deoxygenated hemoglobin concentration changes in the human cerebral cortex. The purpose of this study was to examine the hemodynamic response of the prefrontal area during words memory learning using NIRS. A total of 23 healthy subjects participated in the present study. Hemodynamic response in the prefrontal cortex was measured using a NIRS system. The number of words recalled and stimulus category repetition (SCR) were analyzed by the words memory learning task. During the words memory learning task, oxygenated hemoglobin concentrations increased and deoxygenated hemoglobin concentrations decreased. This typical pattern was maintained during each memory stage, but the degree of change of [oxyHb] during encoding from the first condition to the second condition was significantly larger than that during retrieval. This suggests that memory organization is facilitated during encoding of the first condition, and that the retrieval period through two conditions still involves more activation in the prefrontal area than the encoding period. An increase of [oxyHb] was not recognized and activation was inhibited when the strategy was applied. Subjects produced more SCR in the second condition than in the first condition in spite of strategy instruction. This result suggests healthy people can find out implicit category by themselves following learning even without instruction. There were no significant relationships between the behavior indices and the changes in hemoglobin. Further studies are needed to clarify usefulness of NIRS in patients with psychiatric disorder.

Functional Near Infrared Spectroscopy (fNIRS): An Emerging Neuroimaging Technology with Important Applications for the Study of Brain Disorders

Functional near-infrared spectroscopy (fNIRS) is an emerging functional neuroimaging technology offering a relatively non-invasive, safe, portable, and low-cost method of indirect and direct monitoring of brain activity. Most exciting is its potential to allow more ecologically valid investigations that can translate laboratory work into more realistic everyday settings and clinical environments. Our aim is to acquaint clinicians and researchers with the unique and beneficial characteristics of fNIRS by reviewing its relative merits and limitations vis-à-vis other brain-imaging technologies such as functional magnetic resonance imaging (fMRI). We review cross-validation work between fMRI and fNIRS, and discuss possible reservations about its deployment in clinical research and practice. Finally, because there is no comprehensive review of applications of fNIRS to brain disorders, we also review findings from the few studies utilizing fNIRS to investigate neurocognitive processes associated with neurological (Alzheimer's disease, Parkinson's disease, epilepsy, traumatic brain injury) and psychiatric disorders (schizophrenia, mood disorders, anxiety disorders).

Functional near infrared spectroscopy in novice and expert surgeons--a manifold embedding approach

Monitoring expertise development in surgery is likely to benefit from evaluations of cortical brain function. Brain behaviour is dynamic and nonlinear. The aim of this paper is to evaluate the application of a nonlinear dimensionality reduction technique to enhance visualisation of multidimensional functional Near Infrared Spectroscopy (fNIRS) data. Manifold embedding is applied to prefrontal haemodynamic signals obtained during a surgical knot tying task from a group of 62 healthy subjects with varying surgical expertise. The proposed method makes no assumption about the functionality of the data set and is shown to be capable of recovering the intrinsic low dimensional structure of in vivo brain data. After manifold embedding, Earth Mover's Distance (EMD) is used to quantify different patterns of cortical behaviour associated with surgical expertise and analyse the degree of inter-hemispheric channel pair symmetry.

Multiple-time replicability of near-infrared spectroscopy recording during prefrontal activation task in healthy men

Near-infrared spectroscopy (NIRS) has the potential for clinical application in neuropsychiatry because it enables non-invasive and convenient measurement of hemodynamic response to cognitive activation. Using 24-channel NIRS in 12 healthy men, we examined the replicability of oxy- and deoxy-hemoglobin concentration ([oxyHb], [deoxyHb]) changes in the prefrontal cortex during the category fluency task over four repeated sessions (each 1-week apart). Multiple methods were employed to evaluate the replicability of magnitude, location, and time course of the NIRS signals ([oxyHb], [deoxyHb]). Task performances did not differ significantly across sessions, nor were they significantly correlated with NIRS signals. Repeated measures ANOVA and variance component analysis indicated high replicability of magnitude for both NIRS measures, whereas the effect sizes of between-session differences in [oxyHb] were not negligible. The number and spatial location of significantly activated channels were sufficiently replicable for both measures, except that the across-session overlap of significantly activated channels was weak in [deoxyHb]. The time course of the activation was acceptably replicable in both measures. Taken together, these findings suggest there is considerable replicability of multiple-time measurements of prefrontal hemodynamics during cognitive activation in men. Further studies using different conditions or assessing sensitivity to longitudinal changes following interventions are necessary.

Quantitative spatial comparison of diffuse optical imaging with blood oxygen level-dependent and arterial spin labeling-based functional magnetic resonance imaging

Akin to functional magnetic resonance imaging (fMRI), diffuse optical imaging (DOI) is a noninvasive method for measuring localized changes in hemoglobin levels within the brain. When combined with fMRI methods, multimodality approaches could offer an integrated perspective on the biophysics, anatomy, and physiology underlying each of the imaging modalities. Vital to the correct interpretation of such studies, control experiments to test the consistency of both modalities must be performed. Here, we compare DOI with blood oxygen level-dependent (BOLD) and arterial spin labeling fMRI-based methods in order to explore the spatial agreement of the response amplitudes recorded by these two methods. Rather than creating optical images by regularized, tomographic reconstructions, we project the fMRI image into optical measurement space using the optical forward problem. We report statistically better spatial correlation between the fMRI-BOLD response and the optically measured deoxyhemoglobin (R=0.71, p=1x10(-7)) than between the BOLD and oxyhemoglobin or total hemoglobin measures (R=0.38, p=0.04|0.37, p=0.05, respectively). Similarly, we find that the correlation between the ASL measured blood flow and optically measured total and oxyhemoglobin is stronger (R=0.73, p=5x10(-6) and R=0.71, p=9x10(-6), respectively) than the flow to deoxyhemoglobin spatial correlation (R=0.26, p=0.10).

Diffuse optical tomography system to image brain activation with improved spatial resolution and validation with functional magnetic resonance imaging

Although most current diffuse optical brain imaging systems use only nearest- neighbor measurement geometry, the spatial resolution and quantitative accuracy of the imaging can be improved through the collection of overlapping sets of measurements. A continuous-wave diffuse optical imaging system that combines frequency encoding with time-division multiplexing to facilitate overlapping measurements of brain activation is described. Phantom measurements to confirm the expected improvement in spatial resolution and quantitative accuracy are presented. Experimental results showing the application of this instrument for imaging human brain activation are also presented. The observed improvement in spatial resolution is confirmed by functional magnetic resonance imaging.

Exploring the false discovery rate in multichannel NIRS

Near infrared spectroscopy (NIRS), an emerging non-invasive tool for functional neuroimaging, has evolved as a multichannel technique allowing simultaneous measurements through many channels ranging from below ten to above hundred. Simultaneous testing of such a large number of channels escalates the risk of Type I error, therefore multiplicity correction is unavoidable. To date, only a few studies have considered this issue using Bonferroni correction, which is an effective conservative solution, but may be too severe for neuroimaging. Its power varies in inverse proportion of the number of channels, which varies among NIRS studies depending on selected region of interest (ROI), thereby leading to a subjective inference. This problem may be well circumvented by a more contemporary approach, called false discovery rate (FDR) that is widely being adopted in functional neuroimaging. An FDR-based procedure controls the expected proportion of erroneously rejected hypotheses among the rejected hypotheses, which offers a more objective, powerful, and consistent measure of Type I error than Bonferroni correction and maintains a better balance between power and specificity. In this technical note, we examine FDR approach using examples from simulated and real NIRS data. The FDR-based procedure could yield 52% more power than Bonferroni correction in a 172-channel real NIRS study and proved to be more robust against the changing number of channels.

Wavelet analysis for detecting body-movement artifacts in optical topography signals

We have developed a wavelet-based method of detecting body-movement artifacts in optical topography (OT) signals. Although OT, which is a noninvasive imaging technique for measuring hemodynamic response related to brain activation, is particularly useful for studying infants, the signals occasionally contain undesirable artifacts caused by body movements, so data corrupted by body-movement artifacts must be eliminated to obtain reliable results. For this purpose, we applied a wavelet transform to automatically detect body-movement artifacts in OT signals. We measured OT signals from nine healthy infants in response to speech stimuli. After the continuous signals had been divided into blocks (a block is a time series of OT signal in a 30-s period including a 10-s stimulation period), they were classified into two groups (movement blocks and non-movement blocks) according to whether the participants moved or not by video judgment. Using those data, we developed a wavelet-based algorithm for detecting body-movement artifacts at a high discrimination rate being consistent with the actual body-movement state. The wavelet method has two parameters (scale and threshold), and a Monte Carlo analysis gave the mean optimal parameters as 9+/-1.9 (mean+/-standard deviation) for the scale and as 42.7+/-1.9 for the threshold. Our wavelet method with the mean optimal parameters (scale=9, threshold=43) achieved a higher discrimination rate (mean+/-standard deviation: 86.3+/-8.8%) for actual body movement than a previous method (mean+/-standard deviation: 80.6+/-8.7%) among different participants (paired t test: t(8)=2.92, p<0.05). These results demonstrate that our wavelet method is useful in practice for eliminating blocks containing body-movement artifacts in OT signals. It will contribute to obtaining reliable results from OT studies of infants.

Cerebrovascular reactivity to hypercapnia in migraine patients measured with near-infrared spectroscopy

Migraine pain is considered to manifest itself as a result of an impaired cerebrovascular reactivity. Hence, proper quantification and diagnosis of this problem without causing more disturbance has always been a challenge in investigating migraine pathogenesis. Functional near-infrared spectroscopy system (fNIRS) is being proposed as an inexpensive, rapid, safe and accurate technique to monitor cerebrovascular dynamics. We have developed NIROXCOPE 201, a novel multi source and detector device of fNIRS, and attempted to investigate the cerebrovascular reactivity of migraine patients to a breath hold task which produces a metabolic perturbation. Six normals and six migraine patients performed four consecutive breath holding task. A typical brain hemodynamic response (BHR) is observed both for controls and migraineurs with an initial phase, main response and a recovery phase. Hence, fitting to a sum of three sequentially arranged gaussian curves proved that amplitudes of [Hb] and [HbO2] signals acquired by fNIRS are approximately two to five times higher in controls than migraine patients (P<0.01) for all phases. Moreover, amplitude change between successive breath holds tends to converge to a steady value for controls whereas an uncontrolled percent change is observed for migraineurs. Our results confirm an impaired cerebrovascular reactivity in the frontal cortex of migraine patients interictally.

Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging

An efficient computation of the time-dependent forward solution for photon transport in a head model is a key capability for performing accurate inversion for functional diffuse optical imaging of the brain. The diffusion approximation to photon transport is much faster to simulate than the physically correct radiative transport equation (RTE); however, it is commonly assumed that scattering lengths must be much smaller than all system dimensions and all absorption lengths for the approximation to be accurate. Neither of these conditions is satisfied in the cerebrospinal fluid (CSF). Since line-of-sight distances in the CSF are small, of the order of a few millimeters, we explore the idea that the CSF scattering coefficient may be modeled by any value from zero up to the order of the typical inverse line-of-sight distance, or approximately 0.3 mm(-1), without significantly altering the calculated detector signals or the partial path lengths relevant for functional measurements. We demonstrate this in detail by using a Monte Carlo simulation of the RTE in a three-dimensional head model based on clinical magnetic resonance imaging data, with realistic optode geometries. Our findings lead us to expect that the diffusion approximation will be valid even in the presence of the CSF, with consequences for faster solution of the inverse problem.