Demián A. Vera,*
Héctor A. García,
M. Victoria Waks-Serra,
Nicolás A. Carbone,
Daniela I. Iriarte,
and Juan A. Pomarico
Centro de Investigaciones en Física e Ingeniería del Centro de la Provincia de Buenos Aires (CIFICEN, UNCPBA—CICPBA—CONICET), Pinto 399, B7000GHG—Tandil, Buenos Aires, Argentina
Demián A. Vera, Héctor A. García, M. Victoria Waks-Serra, Nicolás A. Carbone, Daniela I. Iriarte, and Juan A. Pomarico, "Reconstruction of light absorption changes in the human head using analytically computed photon partial pathlengths in layered media," J. Opt. Soc. Am. A 40, C126-C137 (2023)
Functional near infrared spectroscopy has been used in recent decades to sense and quantify changes in hemoglobin concentrations in the human brain. This noninvasive technique can deliver useful information concerning brain cortex activation associated with different motor/cognitive tasks or external stimuli. This is usually accomplished by considering the human head as a homogeneous medium; however, this approach does not explicitly take into account the detailed layered structure of the head, and thus, extracerebral signals can mask those arising at the cortex level. This work improves this situation by considering layered models of the human head during reconstruction of the absorption changes in layered media. To this end, analytically calculated mean partial pathlengths of photons are used, which guarantees fast and simple implementation in real-time applications. Results obtained from synthetic data generated by Monte Carlo simulations in two- and four-layered turbid media suggest that a layered description of the human head greatly outperforms typical homogeneous reconstructions, with errors, in the first case, bounded up to ${\sim}20\%$ maximum, while in the second case, the error is usually larger than 75%. Experimental measurements on dynamic phantoms support this conclusion.
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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Background Absorption Coefficients for the Upper Layer () and Lower Layer () and Their Corresponding Variations ( and , Respectively) for All Three Experimental Cases Considered (All Units in )a
Case 1
0
1.02
1.05
15
Case 2
0
1.02
1.05
15
Case 3
1.02
0.94
10
The reduced scattering coefficients of both layers (in ${{\rm mm}^{- 1}}$) as well as the thickness of the upper layer (in mm) are given in the last three columns. In case 3, absorption changes were introduced simultaneously in both layers.
Table 2.
Retrieval of Absorption Changes in a Two-Layered Medium for Situations 1 and 2 (All Units in ) for Homogeneous and Two-Layered Reconstructions, Computed as the Mean of All Timepoints Corresponding to the Activation Perioda
Two-Layered
Homogeneous
Situation 1
—[15.0%]
—[16.0%]
—[92.4%]
Situation 2
—[5.0%]
—[20.0%]
—[82.2%]
In each case, the percentage relative error (compared to the true values $|\Delta {\mu _{a,u}}| = 2 \times {10^{- 3}} \;{{\rm mm}^{- 1}}$ and $\Delta {\mu _{a,l}} = 5 \times {10^{- 3}} \;{{\rm mm}^{- 1}}$) is shown between square brackets.
Table 3.
Retrieval of Absorption Changes in a Four-Layered Medium for Situations 1 and 2 (All Units in ) for Homogeneous, Two-Layered, and Four-Layered Reconstructions, Computed as the Mean of All Timepoints Corresponding to the Activation Perioda
Two-Layered
Four-Layered
Homogeneous
Situation 1
—[75.0%]
—[14.0%]
—[10.0%]
—[6.0%]
—[74.0%]
Situation 2
—[25.0%]
—[34.0%]
—[5.0%]
—[20.0%]
—[76.0%]
In each case, the percentage relative error (compared to the true values $|\Delta {\mu _{a,u}}| = 2 \times {10^{- 3}} \;{{\rm mm}^{- 1}}$ and $\Delta {\mu _{a,l}} = 5 \times {10^{- 3}} \;{{\rm mm}^{- 1}}$) is shown between square brackets. Please note that $\Delta {\mu _{a,l}}$ for the two-layered reconstruction does not correspond to the same layer as the $\Delta {\mu _{a,l}}$ for the four-layered reconstruction.
Table 4.
Retrieval of the Absorption Changes in Two-Layered Phantoms for Cases 1, 2, and 3 (All Units in ) for Two-Layered and Homogeneous Reconstructionsa
Two-Layered
Homogeneous
Case 1
—
—[0]
—[0]
Case 2
—[0]
—
—
Case 3
—
—
—
In each case, the objective absorption change is shown (for easy comparison purposes) between square brackets. Errors are calculated as the standard deviation of the retrieved signals.
Tables (4)
Table 1.
Background Absorption Coefficients for the Upper Layer () and Lower Layer () and Their Corresponding Variations ( and , Respectively) for All Three Experimental Cases Considered (All Units in )a
Case 1
0
1.02
1.05
15
Case 2
0
1.02
1.05
15
Case 3
1.02
0.94
10
The reduced scattering coefficients of both layers (in ${{\rm mm}^{- 1}}$) as well as the thickness of the upper layer (in mm) are given in the last three columns. In case 3, absorption changes were introduced simultaneously in both layers.
Table 2.
Retrieval of Absorption Changes in a Two-Layered Medium for Situations 1 and 2 (All Units in ) for Homogeneous and Two-Layered Reconstructions, Computed as the Mean of All Timepoints Corresponding to the Activation Perioda
Two-Layered
Homogeneous
Situation 1
—[15.0%]
—[16.0%]
—[92.4%]
Situation 2
—[5.0%]
—[20.0%]
—[82.2%]
In each case, the percentage relative error (compared to the true values $|\Delta {\mu _{a,u}}| = 2 \times {10^{- 3}} \;{{\rm mm}^{- 1}}$ and $\Delta {\mu _{a,l}} = 5 \times {10^{- 3}} \;{{\rm mm}^{- 1}}$) is shown between square brackets.
Table 3.
Retrieval of Absorption Changes in a Four-Layered Medium for Situations 1 and 2 (All Units in ) for Homogeneous, Two-Layered, and Four-Layered Reconstructions, Computed as the Mean of All Timepoints Corresponding to the Activation Perioda
Two-Layered
Four-Layered
Homogeneous
Situation 1
—[75.0%]
—[14.0%]
—[10.0%]
—[6.0%]
—[74.0%]
Situation 2
—[25.0%]
—[34.0%]
—[5.0%]
—[20.0%]
—[76.0%]
In each case, the percentage relative error (compared to the true values $|\Delta {\mu _{a,u}}| = 2 \times {10^{- 3}} \;{{\rm mm}^{- 1}}$ and $\Delta {\mu _{a,l}} = 5 \times {10^{- 3}} \;{{\rm mm}^{- 1}}$) is shown between square brackets. Please note that $\Delta {\mu _{a,l}}$ for the two-layered reconstruction does not correspond to the same layer as the $\Delta {\mu _{a,l}}$ for the four-layered reconstruction.
Table 4.
Retrieval of the Absorption Changes in Two-Layered Phantoms for Cases 1, 2, and 3 (All Units in ) for Two-Layered and Homogeneous Reconstructionsa
Two-Layered
Homogeneous
Case 1
—
—[0]
—[0]
Case 2
—[0]
—
—
Case 3
—
—
—
In each case, the objective absorption change is shown (for easy comparison purposes) between square brackets. Errors are calculated as the standard deviation of the retrieved signals.
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