Improved recovery of the hemodynamic response in diffuse optical imaging using short optode separations and state-space modeling

Abstract

Diffuse optical imaging (DOI) allows the recovery of the hemodynamic response associated with evoked brain activity. The signal is contaminated with systemic physiological interference which occurs in the superficial layers of the head as well as in the brain tissue. The back-reflection geometry of the measurement makes the DOI signal strongly contaminated by systemic interference occurring in the superficial layers. A recent development has been the use of signals from small source-detector separation (1cm) optodes as regressors. Since those additional measurements are mainly sensitive to superficial layers in adult humans, they help in removing the systemic interference present in longer separation measurements (3 cm). Encouraged by those findings, we developed a dynamic estimation procedure to remove global interference using small optode separations and to estimate simultaneously the hemodynamic response. The algorithm was tested by recovering a simulated synthetic hemodynamic response added over baseline DOI data acquired from 6 human subjects at rest. The performance of the algorithm was quantified by the Pearson R(2) coefficient and the mean square error (MSE) between the recovered and the simulated hemodynamic responses. Our dynamic estimator was also compared with a static estimator and the traditional adaptive filtering method. We observed a significant improvement (two-tailed paired t-test, p<0.05) in both HbO and HbR recovery using our Kalman filter dynamic estimator compared to the traditional adaptive filter, the static estimator and the standard GLM technique.

Figure 1

a) Position of the probe over the head of the subjects b) Geometry of the optical probe. Two different SD separations were used: 1 cm and 3 cm. The NIRS channels used for the analysis are shown in red.

Figure 2

a) Temporal basis set used in the analysis. The finite impulse response (FIR) of the temporal basis functions ranged from 0 to 8 s after the onset of the simulated response. b) Noise-free simulated responses (dotted lines) overlapped with the responses recovered with a least-square fit (continuous lines) using the temporal basis set. The R² and the MSE of the fit are indicated for both HbO and HbR.

Figure 3

a) to d) Typical time courses of the recovered hemodynamic responses overlapped with the simulated hemodynamic response. For these specific traces, the SNR was 0.33 for HbO and 0.81 for HbR. R² coefficients and MSEs between the recovered (circles) and the simulated (dashed) response are shown in the legends. a) Kalman filter estimator b) Static estimator c) Adaptive filter d) Standard GLM with 3^rd order drift. e) HbO and f) HbR time courses of the 3 cm channel (with synthetic responses added) overlapped with the 1 cm channel. The positions of the onset time are also shown and the correlation coefficients between the 1 cm and the 3 cm channels (before adding synthetic responses) are indicated in parenthesis.

Figure 4

Pearson R² coefficients between simulated and recovered hemodynamic responses. The bars represent the means and the error bars represent standard deviations computed accross all subjects, all channels and all intances. The means and the standard deviation were computed in the Fisher space and then inverse transformed. Two-tailed paired t-tests were performed on the Fisher transformed R²’s. Statistical differences (p < 0.05) between the four algorithms are indicated by black horizontal lines over the corresponding bars.

Figure 5

Mean squared errors (MSE) between simulated and recovered hemodynamic responses. The bars represent the means and the error bars represent the standard deviations computed accross all subjects, all channels and all instances. Two-tailed paired t-tests were performed between the four estimators and statistical differences at the level p < 0.05 are indicated by black horizontal lines over the corresponding bars.