# Estimating Functional Connectivity Symmetry between Oxy- and Deoxy-Haemoglobin: Implications for fNIRS Connectivity Analysis

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## Abstract

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_{2}) signal, while the deoxy-haemoglobin (HHb) is largely ignored. The in-common information of the connectivity networks of both HbO

_{2}and HHb is not regularly reported, or worse, assumed to be similar. Here we describe a methodology that allows the estimation of the symmetry between the functional connectivity (FC) networks of HbO

_{2}and HHb and propose a differential symmetry index (DSI) indicative of the in-common physiological information. Our hypothesis is that the symmetry between FC networks associated with HbO

_{2}and HHb is above what should be expected from random networks. FC analysis was done in fNIRS data collected from six freely-moving healthy volunteers over 16 locations on the prefrontal cortex during a real-world task in an out-of-the-lab environment. In addition, systemic data including breathing rate (BR) and heart rate (HR) were also synchronously collected and used within the FC analysis. FC networks for HbO

_{2}and HHb were established independently using a Bayesian networks analysis. The DSI between both haemoglobin (Hb) networks with and without systemic influence was calculated. The relationship between the symmetry of HbO

_{2}and HHb networks, including the segregational and integrational characteristics of the networks (modularity and global efficiency respectively) were further described. Consideration of systemic information increases the path lengths of the connectivity networks by 3%. Sparse networks exhibited higher asymmetry than dense networks. Importantly, our experimental connectivity networks symmetry between HbO

_{2}and HHb departs from random (t-test: t(509) = 26.39, p < 0.0001). The DSI distribution suggests a threshold of 0.2 to decide whether both HbO

_{2}and HHb FC networks ought to be studied. For sparse FC networks, analysis of both haemoglobin species is strongly recommended. Our DSI can provide a quantifiable guideline for deciding whether to proceed with single or both Hb networks in FC analysis.

## 1. Introduction

_{2}]) and deoxygenated (Δ[HHb]) haemoglobin in response to neuronal activation in the cerebral cortex. The bivariate nature of the paired haemoglobin reconstruction conveys rich information about the brain haemodynamics and oxygenation but increases the complexity of the analysis.

_{2}and decrease in HHb [1,5], consistent with our current understanding of the neurovascular coupling [6,7]. Most approaches for the analysis of connectivity yield a graph’s binary adjacency matrix characterizing the connectivity network. These approaches have two inherent shortcomings: (i) the binarization depends on a threshold that severely affects the graph density with important implications for interpretation [8]; (ii) a step to decide which haemoglobin (Hb) signal is to be used for subsequent analysis or whether analysing both Hb species is needed. Many researchers have studied different aspects of FC with fNIRS [9,10,11,12,13,14,15]; however, the analysis of connectivity maps is often done only using the fNIRS HbO

_{2}time courses. It is important to understand whether during the analysis both Hb species time courses are relevant, or if either provide analogous information and hence univariate analysis of connectivity may sufficient. In fNIRS connectivity analysis, an important decision is to opt for one of the haemoglobin species to generate the connectivity network of interest, whether the HbO

_{2}or HHb. A part of the scientific community favours the connectivity networks derived from the HbO

_{2}signal due to its higher signal-to-noise (SNR) ratio. Another part favours an analysis based on the HHb signal arguing its higher specificity to activity and higher robustness to physiological contaminations [16]. The rest of the community opts either for considering two univariate analysis or a true bivariate analysis [17].

_{2}and HHb often exhibit highly anticorrelated patterns during brain activation, one might expect a strong match between the connectivity graphs generated from either signal. However, this is not always the case. For instance, classical reconstruction methods based on inverting the modified Beer-Lambert law introduce cross-talk between the two signals species [6], further artifactually supporting the univariate argument of equivalent results. In addition, these fNIRS haemodynamic signals have notable differences in their contribution from factors such as systemic physiology [18,19,20]. When two brain regions are co-active, this may conceal any substantial differences in the HbO

_{2}and HHb network structures. Differences in structural connections of FC networks can be described quantitatively by simple enough methods such as the Jaccard index (Ji). Nevertheless, the Ji is sensitive to the density of links in each network, which can lead to suggest two networks to be symmetric only because the number of connections is high. The FC analysis with fNIRS has mostly focused on describing and understanding the cortical connections within the normal healthy brain. However, when the connectivity analysis is expanded to the diseased brain, there can be various pathological conditions that involve the alteration of neurovascular coupling mechanisms (e.g., Alzheimer’s disease or stroke) and thus differences in the dynamics and in the connectivity networks of HbO

_{2}and HHb might occur. In addition, having now the capacity to monitor functional brain activity on freely moving people in the real-world through wearable fNIRS systems, bigger changes in systemic physiology might occur. Current investigations have expanded the research on more complex realistic settings which consider, for example, inter-personal interactions [21,22]. Therefore, the analysis of data recorded in such ecologically-valid settings might require further consideration of which haemoglobin signal is the best indicator of FC due to differences in systemic interferences between the signals.

_{2}and HHb species has been estimated mainly as a complementary instead of a guiding task for the connectivity analysis. Correlations between the BOLD signal and the haemoglobin species hinted a latent incongruence between HbO

_{2}and HHb responses [23] with Strangman et al. [24] suggesting to address the issue prior the analysis. Wolf et al. [25] found different symmetric patterns across brain areas; for instance, while in the visual cortex the HbO

_{2}and HHb exhibited symmetry, in the motor cortex such symmetry was not found. These asymmetries may also occur across frequency bands [26]. More importantly, such asymmetry may substantially alter the FC analysis itself, for instance using during a independent component analysis (ICA) when analysing resting state connectivity [12] as ICA-based analysis is capable of removing certain types of noise and artefacts [27]. Despite these early studies, more studies are needed regarding the understanding of the asymmetry/symmetry between Hb species. There are very few studies that investigated the symmetry of Hb species prior to the FC analysis and none has studied the symmetry directly from the Hb connectivity networks. However, in the context of FC networks, we emphasise that any symmetry analysis metric should take into account the structural features of these networks. In this paper, our goal is to quantify differences (if any) between the FC networks retrieved from the analysis based on each Hb species, both at baseline and during task-evoked responses, in order to understand how these two Hb derived networks are related. To achieve this, we describe a new metric for the quantification of the symmetry between the FC networks of HbO

_{2}versus the HHb. In addition, we introduce FC analysis between fNIRS signals and systemic variables, allowing for the first time an analysis approach that takes into consideration systemic driven fNIRS changes. We derived a set of connectivity networks for both haemoglobin species complicated functional study in freely moving participants in an ecological situation. We select an out-of-lab situation due to the induced walk-related systemic changes whereby the observed response would be affected and therefore also the expected symmetry values. In this sense, we hypothesize that in healthy subjects during certain brain functional experiments these non-neuronal confounding factors disproportionately affect the structure of the connectivity networks causing a decrease in their symmetry. Finally, we propose a novel index to quantify the extent of symmetry between Hb-derived connectivity networks; and further suggest a threshold which can aid in the decision of opting for one Hb signal over the other or either keeping both. The decision of opting for one signal over the other or either keeping both has important implications for interpretation. The analysis based on incomplete brain networks information could lead to deceptive inference. For instance, as the different Hb species FC networks depart from symmetry, their associated connectivity graph will consequently be dissimilar. Reducing connectivity analysis to a single Hb species under disparate responses will pose a greater risk for misinterpretation. Also, it can be argued that upon showing symmetry or asymmetry, this may justify univariate analysis saving otherwise mandatory bivariate FC connectivity analysis and to draw wrong conclusions when e.g., predicting whether a person is a healthy control or a patient [28,29].

## 2. Materials and Methods

#### 2.1. Experimental Protocol

#### 2.2. Data Acquisition and Processing

_{2}and HHb from an arbitrary zero baseline at the beginning of the measurement period were calculated by the fNIRS system processing unit [32]. Using the modified Beer-Lambert law the concentration values were calculated and expressed in molar concentrations (mmol/L) multiplied by the path length (mm) as they are not corrected for the optical path length. The processing included down-sampling to 1 Hz, and motion artifacts identification and correction was performed through a wavelet-based method [33]. Physiological noise reduction was achieved by using a band-pass filter (3rd order Butterworth band-pass filter, 0.008–0.2 Hz) to remove slow trends and physiological noise (e.g., respiration). The general pipeline is shown in Figure 2.

#### 2.3. Functional Connectivity Analysis

_{2}and HHb connectivity networks. In order to articulate our results (see Section 3), we opt for a group-level analysis by using a VTS representation.

_{2}, HHb) and the inclusion or not of systemic information—heart rate (HR) and breathing rate (BR)—as nodes in the network.

#### 2.4. Quantification of Network Symmetry

_{2}and HHb networks respectively. A graph density is calculated according to Equation (2):

_{2}) and deoxy-haemoglobin (HHb), respectively. Note that the DSI represents the residuals of a symmetry model for random networks discounting the mathematical baseline and leaving what is assumed to be the physiological contribution. The DSI has been implemented in Matlab 2017b and can be downloaded at https://github.com/multimodalspectroscopy/DSI.git.

## 3. Results

#### 3.1. Network Symmetry Analysis

_{1}= ℓ

_{2}= 1) each one. Because our experimental dataset has 16 channels we fixed the random networks size to sixteen nodes (n = 16). Henceforth, we continue increasing their density by randomly adding one link at time until both networks are fully connected (ℓ

_{1}= ℓ

_{2}= L with L = (n × (n − 1))/2). For each pair of edges cardinality <ℓ

_{1}, ℓ

_{2}> we repeated the process 50 times. Then, the connection densities and their associated Ji were calculated for every scenario. Finally, the mean Ji across the 50 repetitions was calculated.

_{2}and HHb experimental networks retrieved from the six participants with systemic information is projected over the expected symmetry space in Figure 3. The experimental functional connectivity (FC) networks exhibit low densities but with comparatively higher symmetry than would be expected from random behaviour. Then, we can expect small absolute changes in both symmetry and density values when systemic variables are added. The symmetry of experimental FC networks (M = 0.2, SD = 0.07) significantly differ from the symmetry of the random networks pairs (M = 0.09, SD = 0.02) (t-test: t(509) = 26.39, p < 0.0001 assuming equal variances; C.I. 95% for the Difference (0.11,0.13)) (see Figure 3 blue rectangle).

**a**coefficients of the bilinear interpolation in Equation (4) to approximate $\widehat{f}(\cdot )$ were computed (

**a**= (0.0768, −0.0484, −0.0485, 1.0512)). The mean Ji based symmetry from pairs of random networks and the approximated bilinear model are presented in Figure 4.

#### 3.2. Integrational Analysis of Connectivity

_{2}and HHb networks for each condition. Also, Figure 6 depicts the FC networks obtained with and without the systemic factors (heart rate and breathing rate). Regarding in-common links, the inclusion of systemic variables increases the number of such relations during BL, OG, and NonSocPM conditions by 4, 8, and 2 increments respectively. The OGc condition remains unchanged and SocPM condition diminished in 2 links. More connections were found in the PM blocks (Figure 6c,d,h,i) in respect to the OG blocks (Figure 6b,g,e,j). These connections are more observed between the two hemispheres and, some of them, at the left and right lateral prefrontal cortex (PFC). Also, Figure 6b,g shows a set of connections between the close channels 13–14, 15–16, 2–5, 7–8, 9–12 within the same region. On the other hand, connections between corresponding channels (Ch. 2–14, 4–16, 3–10, 7–13) in the two lateral PFC were also found (Figure 6d,i). This could be caused by a higher involvement of lateral PFC, which has been observed in prospective memory tasks and a major involvement of medial PFC is related to OG activities [31]. Table 1 summarises the changes in density and symmetry values from the combined networks presented in Figure 6. The five FC networks exhibits an increase in density of 2%, 3%, 2%, 2% and 5% for BL, OG, SocPM, NonSocPM, and OGc conditions respectively. In terms of Jaccard symmetry, BL, OG, and NonSocPM conditions showed increasing values of 4%, 8%, and 1% respectively while the SocPM and OGc conditions decreased by 4% and 3% respectively. Unlike random networks, fNIRS FC networks tends to have absolute low values of symmetry. Thus, the addition of the systemic information produced small changes in both symmetry and density.

_{2}networks were found to be over the mean MOD value.

## 4. Discussion

_{2}and HHb. This novel approach is based on the DSI and the Jaccard index; and can help in improving the interpretation of functional connectivity (FC) analyses with fNIRS. In addition, we have demonstrated for the first time how systemic data can be integrated within the HbO

_{2}and HHb FC networks to disentangle spurious relation between brain regions. Considering that the brain networks are dynamically produced, we can expect some variations in their structures across subjects, or even longitudinally within the same person [10,15]. The DSI is able to separate the symmetric response of the FC networks between HbO

_{2}and HHb derived from physiology by removing the mathematical contribution of the Jaccard index. This provides us with a new tool to decide whether HbO

_{2}or HHb networks individually would lead to a better representation of the functional paths, or if both signals must be used to assess FC.

#### 4.1. Symmetry between HbO_{2} and HHb Connectivity Networks

_{2}and HHb above its random counterpart. In synthetic random networks, the symmetry value is higher when the connectivity density in both networks increases. This is consistent with the experimental observation that, for highly dense diffuse optical tomography spatial configurations, both HbO

_{2}and HHb networks include a high number of functional links [11]. Such higher channels density is often associated with a higher number of links i.e., denser networks (ℓ ≈ L). In this case, the decision of choosing one of the two Hb species is not crucial, as we expect high symmetries between them. In case of low channel density data sets, we cannot ignore the differences in the symmetry between HbO

_{2}and HHb FC networks. Most of the current fNIRS technologies are still spatially low channel density devices [2], hence likely to be accompanied with a less dense-connectivity graph. Therefore, the symmetry between HbO

_{2}and HHb FC networks must be investigated and taken into consideration to draw more correct neuroscientific conclusions based on fNIRS-derived FC measures. Regarding the fNIRS networks presented here, the social and non-social prospective memory (SocPM and NonSocPM) conditions achieved more symmetric responses (Figure 6 bigger markers) between the HbO

_{2}and HHb FC networks. In this sense, this could be related the prospective memory task itself. In fact, prospective memory involves the integration of several executive functions (e.g., planning, retrospective/working memory, cognitive flexibility and inhibitory control, attentional monitoring, etc. [50]) and requires the conscious interruption of the OG task to fulfill the delayed intention, thus being more complex than only the OG task or the rest conditions. Our data suggests that the memory-related tasks within our current functional protocol produced higher symmetric FC networks between the Hb species compared to the other tasks. In addition, the walking-related tasks were found to produce more asymmetrical FC networks between the Hb species. These results refer to the particular prospective memory protocol described here. Additional work is needed to further expand and investigate the proposed DSI method with additional functional paradigms, different experimental designs and brain regions.

_{2}and HHb activation maps, or on a different example, the DSI could evaluate the (dis-)similarity among HbO

_{2}or HHb activation maps longitudinally acquired for a subject. However, different comparison functions and different features would combine to generate different bias, which is what our second term of the DSI removes. Further work is necessary to allow the development of a more generally applied second term.

#### 4.2. Inclusion of Systemic Data in fNIRS Functional Connectivity Analysis

_{2}and HHb connectivity density and symmetry when systemic data were included. Based on our group-level results presented in Figure 7, we showed that the addition of systemic information tends to change both integrational and segregational characteristic measures of the networks.

_{2}network seems to increase the global efficiency. This could be caused by the inclusion of confounding variables that removes spurious relationships and generate a re-route of the functional paths between regions, resulting in a larger one. On the other hand, the segregational measure, the modularity, presents the opposite pattern in respect to the global efficiency. The modularity of both Hb networks increases when non-neuronal signals are taken into account. The inclusion of physiological variables is performed by considering them as nodes. These systemic nodes become mediators between channel nodes, creating new paths and producing a reorganization of groups of nodes (community structure). Here, we found that the 80% of the functional networks are above 0.3 modularity, a value from which a network is considered to have a significant community structure.

_{2}and HHb connectivity networks varies in case of different cognitive tasks and task designs (e.g., block, event-related, continuous), and across different brain regions, and with less/more dense channels configurations.

## 5. Conclusions

_{2}and HHb functional connectivity (FC) networks. This is achieved by our proposed Differential Symmetry Index or DSI.

_{2}and HHb FC networks can help in deciding if it is more appropriate to use one Hb signal (either HbO

_{2}or HHb) or both when computing FC. This becomes particularly relevant when we deal with fNIRS experiments with low-density FC networks or with naturally sparse functional networks—as in typical commercially-available fNIRS devices. Simultaneously, it is possible to infer that having high-density data makes such contrast likely redundant as a high symmetry between HbO

_{2}and HHb networks may be expected. From a data set including six healthy subjects performing a series of cognitive tasks in an ecological environment while walking, we recovered the task-related FC networks. We found that the FC networks of HbO

_{2}and HHb retrieved from the social and non-social prospective memory tasks are more symmetric than the networks from the other tasks. Furthermore, we investigated the segregational and integrational impact on the networks when including walk-related breathing rate and heart rate systemic factors. By including these non-neuronal factors, the information expressed by the functional networks was elucidated. A set of spurious associations vanished (conjectured from the increase in path length and a decrease in global efficiency), and the distribution of functional links changed (inferred from the change in modularity). In summary, the resulting symmetry values were significantly different from the expected ones as shown by the random networks analysis. Therefore, the FC analysis must include a subsequent integration-segregation measures analysis and the addition of a symmetry analysis between HbO

_{2}and HHb FC networks is highly recommended. The DSI distribution suggested that values over 0.2 indicate that Hb networks are symmetric.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Examples of the baseline, ongoing, social prospective memory, non-social prospective memory, and ongoing contaminated conditions during the experiment; (

**b**) functional near infrared spectroscopy (fNIRS) channels distribution.

**Figure 2.**Preprocessing flowchart. fNIRS measurements were acquired by using a wearable optical topography fNIRS system. Then, the haemoglobin (Hb) signals were reconstructed and preprocessed, and the systemic information was added. A set of connectivity networks were determined by the PC [34] algorithm by using the implementation in pcalg R package [35]. Finally, the symmetry between functional connectivity networks and global efficiency and modularity across networks were computed.

**Figure 3.**Jaccard symmetry response from experimental and random connectivity networks pairs varying density. The x-axis represents HbO

_{2}density and the y-axis represents HHb density. Color encodes the extent of symmetry. The background symmetry field corresponds to values expected for random synthetic networks from disconnected to complete connected ([0−1]) in both networks. Triangles correspond to experimental functional connectivity (FC) networks pairs from the six-subjects across conditions. High-density networks are those with a large number of connections (ℓ ≈ L). The results for high symmetry values are observed only for high-density random networks pairs but not for our experimental fNIRS FC networks pairs.

**Figure 4.**Symmetry space from random networks. Surfaces obtained from the Ji values (

**a**) and the approximation from the bilinear model (

**b**). The graphical comparison and the differences between both surfaces (

**c**). Higher order interpolation models can yield a better approximation with increasing degree of complexity.

**Figure 5.**(

**a**) Projection of the symmetry values of fNIRS FC networks obtained by Jaccard index (blue dots) over the random baseline approximated by a bilinear model (green surface); (

**b**) differential symmetry index (DSI) values grouped by condition and its distribution (left margin histogram). A threshold (grey dashed line) derived from the distribution of DSI values is also shown.

**Figure 6.**Combined HbO

_{2}-HHb functional connectivity networks recovered from a virtual-typical-subject. Top (

**a**–

**e**) and bottom (

**f**–

**j**) rows show the networks without and with systemic variables information respectively. From left to right, columns representing the conditions: baseline (

**a**,

**f**), ongoing (

**b**,

**g**), social prospective memory (

**c**,

**h**), non-social prospective memory (

**d**,

**i**), and ongoing contaminated (

**e**,

**j**). Functional links determined from HbO

_{2}and HHb are shown in solid red and dashed blue respectively and in-common links in bold magenta.

**Figure 7.**Measures of integration (global efficiency) and segregation (modularity) in functional networks. The size, shape, colour and padding of markers encode the amount of symmetry, experimental condition, Hb signal and the inclusion or exclusion of systemic data, respectively.

**Table 1.**Density, Jaccard and DSI symmetry changes with/without systemic information from the virtual-typical-subject. Experimental connectivity networks from baseline, ongoing, social prospective memory, non-social prospective memory, and ongoing contaminated conditions.

FC Network | Density | Jaccard Symmetry | DSI Symmetry | |||
---|---|---|---|---|---|---|

Condition | With Systemic | Without Systemic | With Systemic | Without Systemic | With Systemic | Without Systemic |

Baseline (BL) | 0.22 ↑ | 0.20 | 0.24 ↑ | 0.20 | 0.15 ↑ | 0.11 |

Ongoing (OG) | 0.25 ↑ | 0.22 | 0.26 ↑ | 0.18 | 0.18 ↑ | 0.09 |

Social PM (SocPM) | 0.29 ↑ | 0.27 | 0.18 ↓ | 0.22 | 0.09 ↓ | 0.12 |

Non-Social PM (NonSocPM) | 0.27 ↑ | 0.25 | 0.14 ↑ | 0.13 | 0.06 ↑ | 0.04 |

Ongoing Condition (OGc) | 0.29 ↑ | 0.24 | 0.11 ↓ | 0.14 | 0.02 ↓ | 0.04 |

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**MDPI and ACS Style**

Montero-Hernandez, S.; Orihuela-Espina, F.; Sucar, L.E.; Pinti, P.; Hamilton, A.; Burgess, P.; Tachtsidis, I. Estimating Functional Connectivity Symmetry between Oxy- and Deoxy-Haemoglobin: Implications for fNIRS Connectivity Analysis. *Algorithms* **2018**, *11*, 70.
https://doi.org/10.3390/a11050070

**AMA Style**

Montero-Hernandez S, Orihuela-Espina F, Sucar LE, Pinti P, Hamilton A, Burgess P, Tachtsidis I. Estimating Functional Connectivity Symmetry between Oxy- and Deoxy-Haemoglobin: Implications for fNIRS Connectivity Analysis. *Algorithms*. 2018; 11(5):70.
https://doi.org/10.3390/a11050070

**Chicago/Turabian Style**

Montero-Hernandez, Samuel, Felipe Orihuela-Espina, Luis Enrique Sucar, Paola Pinti, Antonia Hamilton, Paul Burgess, and Ilias Tachtsidis. 2018. "Estimating Functional Connectivity Symmetry between Oxy- and Deoxy-Haemoglobin: Implications for fNIRS Connectivity Analysis" *Algorithms* 11, no. 5: 70.
https://doi.org/10.3390/a11050070