Improved recovery of the hemodynamic response in diffuse optical imaging using short optode separations and state-space modeling
Research Highlights
► Small optode separations measurements help remove systemic interference in NIRS data. ► Simultaneous filtering and estimation allows better recovery of the HRF. ► Dynamic filtering take into account the non-stationary behavior of the interference. ► Works well even if the baseline short-long correlation is as low as 0.1.
Introduction
Diffuse optical imaging (DOI) is an experimental technique that uses near-infrared spectroscopy (NIRS) to image biological tissue (Villringer et al., 1993, Obrig and Villringer, 2003, Gibson et al., 2005, Hillman, 2007, Hoshi, 2007). The dominant chromophores in this spectrum are the two forms of hemoglobin: oxygenated hemoglobin (HbO) and reduced hemoglobin (HbR). In the past 15 years, this technique has been used for the noninvasive measurement of the hemodynamic changes associated with evoked brain activity (Villringer et al., 1993, Hoshi, 2007).
Compared with other existing functional imaging methods e.g., functional Magnetic Resonance Imaging (fMRI), Positron Emission Tomography (PET), Electroencephalography (EEG), and Magnetoencephalography (MEG), the advantages of DOI for studying brain function include good temporal resolution of the hemodynamic response, measurement of both HbO and HbR, nonionizing radiation, portability, and low cost. Disadvantages include modest spatial resolution and limited penetration depth.
The sensitivity of NIRS to evoked brain activity is also reduced by systemic physiological interference arising from cardiac activity, respiration, and other homeostatic processes (Obrig et al., 2000, Tonorov et al., 2000, Payne et al., 2009, Diamond et al., 2009). These sources of interference are called global interference or systemic interference. Part of the interference occurs both in the superficial layers of the head (scalp and skull) and in the brain tissue itself. However, the back-reflection geometry of the measurement makes NIRS significantly more sensitive to the superficial layers. As such, the NIRS signal is often dominated by systemic interference occurring in the skin and the skull.
Different methods have been used in the literature to remove the systemic interference from DOI measurements. Low pass filtering is widely used in the literature, as it is highly effective at removing cardiac oscillations (Franceschini et al., 2003, Jasdzewski et al., 2003). However, there is a significant overlap between the frequency spectrum of the hemodynamic response to brain activity and the spectrum of other physiological variations such as respiration, spontaneous low frequency oscillations and very low frequency oscillations. Frequency-based removal of these sources of interference can therefore result in large distortion and inaccurate timing for the recovered brain activity signal. As such, more powerful methods for global noise reduction have been developed. These include adaptive average waveform subtraction (Gratton and Corballis, 1995), subtraction of another NIRS source-detector (SD) channel performed over a non-activated region of the brain (Franceschini et al., 2003), principal component analysis (Zhang et al., 2005, Franceschini et al., 2006) and finally wavelet filtering (Lina et al., 2008, Lina et al., 2010, Matteau-Pelletier et al., 2009, Jang et al., 2009).
A recent development for removing global interference from NIRS measurements is to use additional optodes in the activated region with small SD separations that are sensitive to superficial layers only (Saager and Berger, 2008, Zhang et al., 2007a, Zhang et al., 2007b, Zhang et al., 2009, Umeyama and Yamada, 2009, Yamada et al., 2009, Gregg et al., 2010). Making the assumption that the signal collected in the superficial layers is dominated by systemic physiology which is also dominant in the longer SD separation NIRS channel, those additional measurements can be used as regressors to filter systemic interference from the longer SD separations. Saager and Berger (2005) used additional optodes and a linear minimum mean square estimator (LMMSE) to partially remove the systemic interference in the signal. In a second step, the evoked hemodynamic response was estimated using a traditional block-average method over the different trials. The algorithm was further refined by Zhang et al., 2007a, Zhang et al., 2007b, Zhang et al., 2009 to consider the non-stationary behavior of the systemic interference. They used an adaptive filtering technique together with additional small separation measurements to filter the systemic interference from the raw signal and then performed the block-average technique to estimate the hemodynamic response in a second step.
Although these methods greatly reduced global interference in NIRS data, the filtering of the systemic interference and the estimation of the hemodynamic response were performed in two steps, which might not be optimal. Previous studies have shown that the simultaneous estimation of the hemodynamic response and removal of the systemic interference using temporal basis functions (Kolehmainen et al., 2003, Prince et al., 2003) or auxiliary systemic measurements (Diamond et al., 2006) was possible using state-space modeling. Moreover, Diamond et al. proposed a way to quantify the accuracy of such filtering methods. Real NIRS data collected over the head of human subjects at rest were used to generate realistic noise. A synthetic hemodynamic response was added over the real NIRS baseline time course and the response was then recovered from this noisy data set. The recovered response was then compared with the synthetic one used to generate the time course. This method for evaluating reconstruction algorithms has been reproduced by other groups (Lina et al., 2008, Lina et al., 2010, Matteau-Pelletier et al., 2009).
In the present study, we combined small separation measurements and state-space modeling for the estimation of the hemodynamic response and simultaneous global interference cancellation. We developed both a static and a dynamic estimator. We evaluated the performance of our algorithms using baseline data taken from 6 human subjects at rest and by adding a synthetic hemodynamic response over the baseline measurements. We finally compared our new methods with the adaptive filter (Zhang et al., 2007a) and the standard method using no small SD separation measurement.
Section snippets
Experimental data
For this study, 6 healthy adult subjects were recruited. The Massachusetts General Hospital Institutional Review Board approved the study and all subjects gave written informed consent. Subjects were instructed to rest while simultaneous BOLD-fMRI and NIRS data were collected. Three 6-min long runs were collected for each subject. Only the NIRS data were used in this study. The localization and the geometry of the NIRS probe used are shown in Fig. 1a and b respectively. Only the two 1 cm SD
Results
Typical time courses of the recovered hemodynamic response overlapped with the true simulated response are shown in Fig. 3a to d for the four algorithms tested. The SNR for this particular simulation was 0.33 for HbO and 0.81 for HbR. The R2's and the MSEs for HbO and HbR are shown in the legend of each individual panel. Those individual results were obtained from a single simulation with 10 trials. The time courses for this specific simulation are shown in panel e) for HbO and f) for HbR. Both
Simultaneous filtering and estimation
One of the salient features of our Kalman filter estimator is that it filters the global interference and simultaneously estimates the hemodynamic response. This feature resulted in a more accurate recovery of the hemodynamic response with our Kalman filter estimator compared to the adaptive filter, for which the filtering and the estimation were performed in two distinct steps. Independent regression of the small separation channel potentially removes contributions of the hemodynamic response
Conclusion
In summary, we filtered the global interference present in NIRS data by using additional small separation optodes and we simultaneously estimated the hemodynamic response using a dynamic algorithm. Our dynamic Kalman filter performed better than the traditional adaptive filter, the static estimator and the standard block average estimator for both HbO and HbR recovery. These results were consistent with the fact that dynamic estimation better captures the non-stationary behavior of the systemic
Acknowledgments
This work was supported by NIH grants P41-RR14075 and R01-EB006385. L. Gagnon was supported by the Fonds Quebecois sur la Nature et les Technologies and by the IDEA-squared program at MIT. We acknowledge fruitful discussions with Sol Diamond, Emery Brown, Patrick Purdon, Lino Becerra and Dana Brooks. We would also like to thank Michele Desjardins for critical reading of the manuscript.
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