Calculations of BOLD signals by use of NIRS Photon Migration

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					                                                                                                                                Calculations of BOLD signals by use of NIRS Photon Migration Hitting Density Functions
                                                                                                                                                                                                         A. Sassaroli*, Y. Tong*, B. B. Frederick#, P. F. Renshaw#, and Sergio Fantini*

                                                                                                                                                                                            *Tufts University, Department of Biomedical Engineering, Medford, MA; #McLean Hospital, Belmont, MA;

                                                                                                                                                                                                                                                                     Photon migration probability distribution                                                                                                                      Photon migration occurs with a hitting density expressed by:
Motivation of the study
The main motivation of this study was to better understand the different comparison between BOLD signal and the changes in oxy and deoxy-                                                                                                                                                                                                                                                                                                             z 2 exp(− k{( x 2 + y 2 + z 2 )1 / 2 + [(d − x) 2 + y 2 + z 2 ]1 / 2 })
hemoglobin that had been presented in the literature. Usually the BOLD signal is obtained as a simple average from all the activated voxels. However if                                                                                                                                                                                                                                                                            P ( x, y , z ) =                                                                           ×
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( x 2 + y 2 + z 2 ) 3 / 2 [(d − x) 2 + y 2 + z 2 ]3 / 2
we take a closer look to the signals calculated by selecting different clusters of voxels, we found that usually they don’t match, the difference being
either in the amplitude or sometimes in the shape, or both. The main point that we are making is that there is not a unique BOLD signal, therefore we                                                                                                                                                                                                                                                                             [ k ( x 2 + y 2 + z 2 )1 / 2 + 1]{k[(d − x) 2 + y 2 + z 2 ]1 / 2 + 1}
should question about the correct way to compare fMRI and NIRS. For this reason we propose a new method for the calculation of blood oxygen level
dependent (BOLD) signal which is more meaningful for comparison with near infrared spectroscopy (NIRS) data. We presented a case study of                                                                                                                                                                                                                                                                                                                                                             source                       detector
functional activation during a finger tapping test where we used the new method for the calculation of BOLD signal. For every optical source-detector                                                                                                                                                                                                                                                                              k = 3μ a μ s
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           (0,0,0)                                 (d,0,0)
pair we calculated a weighted BOLD signal by using a photon hitting-density function, and by using a simple backprojection algorithm we were able to                                                                                                                                                                                                                                                                               μ a absorption coefficient
generate BOLD 2D maps. We found that the weighted BOLD signals calculated from different source-detector pairs, scale in a similar way to the
                                                                                                                                                                                                                                                                                                                                                                                                                                   μ 's reduced scattering coefficient
corresponding oxy and deoxy-hemeoglobin concentration changes calculated from NIRS data, for most of the time range of the task. Therefore the
BOLD 2D maps were quantitatively similar to the optical maps calculated at different times during the protocol.

                                                                                                                                                                                                                                                                      k = 2 cm-1                                                                  k = 3 cm-1
                          BOLD front                                                                                                Difference in BOLD activation                                                                                                                                                                                                                                                          Standard BOLD activation map and localization of optical fibers
                                                                                                                                                                                                                                                           Definition of BOLD Photon Migration Averaged

                                                                                                                           4                                                                                                                                     BOLD (PMA)                                                                                                                                                                                        15
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             4       3
                                                                                                                                                                BOLD_back                                                                                                                                                                                                                                                                                                                                                      2
                                                                                                                                                                                                                                                                                                                                                                                                                                detector                                                                         B        A
                                                                                                           % BOLD change

                                                                                                                           3                                                                                                                                                                                                                                                                                                                                                 C
                                                                                                                                                                BOLD_front                                                                                                                                                                                                                                                                                                                                                     1
                                                                                                                                                                                                                                                                   x,                                                                                                                                                                                                                                   5

                                                                                                                                                                                                                                                           ∫ BOLD (x,y,z) Pn (x,y,z)dxdydz
                                                                                                                           2                                    all_activated                                                                                                                                                                                                                                                                                                                                       7
                                                                                                                                                                                                                                                                                                                                                                                                                                                              11                                           6            8
                                                                                                                                                                                                                                                                                                                                                                                                                                source                                                                              15
                                                                                                                           1                                                                                                                               V     bas                                                                                                                  Folding Average                                                                                                    14       D    C 16
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        13                         9
                                                                                                                           0                                                                                                                               ΔBOLD(y,z,t) = BOLD (x,y,z,t) - BOLD (x,y,z)
                                                                                                                                                                                                                                                                x,           act              bas                                                                                                                                                                                                                    11
                                                                                                                                0   10    20      30       40      50           60                                                                                                                                                                                                                                                                                                                           12           10


                                                                                                                                                                                                                                       Comparison NIRS data and BOLD PMA; t = 6 s after Onset of                                                                                                                                    Comparison NIRS data and BOLD PMA; t = 10 s after Onset
                                                                                                           The two cluster of voxels are shifted about 7 mm                                                                            activation (k = 2 cm-1)                                                                                                                                                                      of activation (k = 2 cm-1)
                          BOLD back
                                                                                                                                                                                                                                                             Δ[Hb] (μM)                                                             −Δ[HbO] (μM)                                                                                                  Δ[Hb] (μM)                                         −Δ[HbO] (μM)

Experimental protocol & data analysis for concerrent fMRI-NIRS
Functional magnetic resonance imaging (fMRI) is performed on a 3 Tesla Siemens Trio whole body magnetic resonance scanner (Siemens Medical
Systems, Erlangen, Germany). A quadrature birdcage probe, open at both ends and with a removable top section, is used to allow the optical fibers to be
placed on the subject’s head without significant bending. After localization and shimming, a series of fMRI images are acquired. Image parameters are as                                                                          -0.12 μM                                                                                                                                                                                      -0.19 μM                                0.002 μM    -0.42 μM
                                                                                                                                                                                                                                                                                  -0.0046 μM -0.29 μM                                                                    -0.005 μM                                                                                                                                            -0.016 μM
follows: gradient echo EPI, TE/TR=30/2020ms, 64x64 image matrix, full k-space acquisition, FOV 220x220, 30 interleaved coronal slices (R/L readout),
3mm thick, 0mm gap, with the slice stack centered on the motor strip. 120 time points are acquired after 12 dummy shots. Images are saved in DICOM                                                                                                           -BOLD PMA                                                                                                                                                                                                                             -BOLD PMA
                                                                                                                                                                                                                                                                                                                                                                         Ratio of signals C15/C11 at t = 6, 10, 20, 28 sec
format and processed using Brain Voyager QX (Brain Innovations B.V., Maastricht, The Netherlands). The update rate of fMRI data is 0.5 Hz.
The optical experimental setup is a frequency-domain tissue imager (Imagent, ISS, Inc.,Champaigne, IL) comprising sixteen laser sources at 690 nm and                                                                                                                                                                                                                                2
sixteen laser sources at 830 nm (average power about 1 mW) and four optical detectors (photomultipliers tubes, Hamamatsu Photonics R928). The laser                                                                                                                                                                                                                                 1.6

diodes are modulated at a frequency f =110 MHz, and are coupled to optical fibers 400 μm in core diameter and 10 m long. The subject (30 years old                                                                                                                                                                                                                                  1.4
healthy male) lies motionless inside the magnet. One minute of baseline optical and fMRI data are acquired. Afterwards six cycles of 20 sec right hand

tapping and 20 sec of rest are carried out by the subject while simultaneous NIRS and fMRI data are acquired The optical data are filtered to cut off the                                                                                                                                                                                                                           0.8
                                                                                                                                                                                                                                     -0.0155                                              -0.0004                                                                                                                                                                                  -0.03                                       -0.0013
lower (< .0125 Hz) and higher frequencies (>.1 Hz) , averaged over the six cycles (folding average) and then analyzed by using modified Lambert-Beer law                                                                                                                                                                                                                            0.6
for the change of oxy and deoxy hemoglobin. Temporal trends and spatial mapping are obtained for both NIRS and fMRI.                                                                                                                                                                                                                                                                0.2
                                                                                                                                                                                                                                                                                                                                                                                                     1                2     3               4            t (sec)
                                                                                                                                                                                                                                                                                                                                                                                                     6                10   20              28
                          NIRS                                                                                                                                                                                                              Comparison of BOLD (PMA) and NIRS temporal trends
    Optical/NIRS helmet              Block diagram of experiment setup
                                                                                                                                                                                                                                                                                       BOLD C_11
                                                                                                                                                                           Birdcage probe                                                   0.4
                                                                                                                                                                                                                                                                                       HbO C-11
                                                                                                                                                                                                                                                                                       Hb C-11               0.5
                                                                                                                                                                                                                                                                                                                                                                          BOLD C_15
                                                                                                                                                                                                                                                                                                                                                                          HbO C-15
                                                                                                                                                                                                                                            0.3                                                              0.4                                                          Hb C-15

                                                                                                                                                                                                                                            0.2                                                              0.3

                                             Pmt A
                                                                                                                                                                                                                                            0.1                                                              0.2
                                             Pmt B
                                                            RF electronics
                                                                                                                                                                                                                                              0                                                              0.1
                                             Pmt C                                                                                                                                                                                          -0.1
                                                                                                                                                                                                                                                   0        10         20         30               40

                                                                                                                                                                                                                                                                                                                                                                                                                                           1) Different BOLD signals are calculated in different voxels;
                                             Pmt D                                                                                                                                                                                                                 time (se c)

                                                                                                                                                                                                                                                                                                                    0               10           20
                                                                                                                                                                                                                                                                                                                                              time (sec)
                                                                                                                                                                                                                                                                                                                                                                    30                    40
                                                                                                                                                                                                                                                                                                                                                                                                                                               this reflects at least different intensities of the activation
                                              Laser driver 1,   λ
                                                                    =830                                                                                                                                                                                                                                                                                                                                                                       with respect to the rest condition
                                                                              Multiplexer circuit

                                              Laser driver 2,       =830
                                                                                                                                                                                                                                                                                 15                                                                                                                                                        2) Since in NIRS the changes that are measured on the surface
                                                                                                                                                                                                                                                       source                                    16
                                              Laser driver 3,       =690

                                                                                                                                                                                                                                                                            11                                                                                                                                                                are the results of the sensitivity of photon migration to the
                                                                                                                                                                                                                                                                                       C 9
                                              Laser driver 4,   λ
                                                                    =690                                                                                                                                                                                                                                                 0.6                                                                                                                  activated area, it is meaningful to define a BOLD signal which
                                                                                                                                                                                                                                                                                                                                                                                    HbO C-10
                                                                                                                                                                                                                                                                                 10                                      0.5
                                                                                                                                                                                                                                                                                                                                                                                    Hb C-10                                                   has the same sensitivity
                                                                                                                                                                                                                                                                                                                         0.4                                                        BOLD C_10


                                                                                                                                                                                                                                                                                                                         0.1                                                                                                               3) Comparison of the BOLD PMA with NIRS data shows that
                                                                                                                                               fMRI machine and view of the quadrature birdcage probe                                                                                                                      0
                                                                                                                                                                                                                                                                                                                                                                                                                                              the two methodologies are sensitive to the same physical changes
                                                                                                                                                                                                                                                                                                                                0        10               20                   30               40
                                                                                                                                                                                                                                                                                                                                                      time (se c)

                                                                                                                                                                     This work was supported by the National Science Foundation, Award No. BES-93840, and by the National Institutes of Health, Grant No. DA14178.
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