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\begin{document}

\title{Functional near-infrared spectroscopy for human brain age group
classification by machine learning}



\author[1]{Martti Ilvesmäki}%
\author[1]{Hany Ferdinando}%
\author[2]{Kai Noponen}%
\author[2]{Tapio Seppänen}%
\author[1]{Vesa Korhonen}%
\author[1]{Vesa Kiviniemi}%
\author[1]{Teemu Myllylä}%
\affil[1]{Oulun yliopisto}%
\affil[2]{Oulun Yliopisto Konenaon ja signaalianalyysin tutkimuskeskus}%


\vspace{-1em}



  
  \date{June 18, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Aging brain undergoes multiple structural and functional changes. These
may contribute to an increased risk of neurodegenerative disease (NDD)
and other age-related diseases, highlighting the importance of assessing
deviations from healthy brain aging trajectory. In this human brain
study, 50 healthy adults were investigated by functional near-infrared
spectroscopy (fNIRS). A resting state single channel multiwavelength
fNIRS was measured from the forehead in a supine position. The subjects
were divided into four age groups. A machine learning approach was
utilized for age group classification by using support vector machine
and random forest learners with nested cross-validation. The results
suggest brain aging effects being more distinct in the oldest age group
and a difference in the brain aging for the subjects of the in-between
groups. Our study shows high potential for the use of fNIRS in the
analysis of brain aging.%
\end{abstract}%



\sloppy


RESEARCH ARTICLE

\textbf{Functional near-infrared spectroscopy for human brain age group
classification by machine learning}

Martti Ilvesm\selectlanguage{ngerman}äki\textsuperscript{1}* \textbar{} Hany
Ferdinando\textsuperscript{1} \textbar{} Kai
Noponen\textsuperscript{2}\textbar{} Tapio Seppänen\textsuperscript{2}
\textbar{} Vesa Korhonen\textsuperscript{1},\textsuperscript{3}
\textbar{} Vesa Kiviniemi\textsuperscript{1},\textsuperscript{3}
\textbar{} Teemu Myllylä\textsuperscript{1},\textsuperscript{4}

1 Research Unit of Health Sciences and Technology, University of Oulu,
Oulu, Finland

2 Center for Machine Vision and Signal Analysis Research Unit,
University of Oulu, Oulu, Finland

3 Department of Diagnostic Radiology, Oulu University Hospital, Finland

4 Optoelectronics and Measurement Techniques Research Unit, University
of Oulu, Oulu, Finland

\textbf{*~Correspondence}

Martti Ilvesmäki, University of Oulu, Pentti Kaiteran katu 1, 90570
Oulu, Finland

Martti.ilvesmaeki@oulu.fi Aging brain undergoes multiple structural and
functional changes. These may contribute to an increased risk of
neurodegenerative disease (NDD) and other age-related diseases,
highlighting the importance of assessing deviations from healthy brain
aging trajectory. In this human brain study, 50 healthy adults were
investigated by functional near-infrared spectroscopy (fNIRS). A resting
state single channel multiwavelength fNIRS was measured from the
forehead in a supine position. The subjects were divided into four age
groups. A machine learning approach was utilized for age group
classification by using support vector machine and random forest
learners with nested cross-validation. The results suggest brain aging
effects being more distinct in the oldest age group and a difference in
the brain aging for the subjects of the in-between groups. Our study
shows high potential for the use of fNIRS in the analysis of brain
aging.

\textbf{KEYWORDS}

fNIRS, brain aging, aging, machine learning

\textbf{ABBREVIATIONS} AD, Alzheimer's disease; bacc, balanced accuracy;
CSF, cerebrospinal fluid; CV, cross-validation; DPF, differential path
length factor; dPhaseTE, differential phase transfer entropy; EEG,
electroencephalography; ESSC, envelope-signal spectra correlation; fMRI,
functional magnetic resonance imaging; fAPF, fractional amplitude of
physiological fluctuations; fNIRS, functional near-infrared
spectroscopy; FC, functional connectivity; H\textsubscript{2}O, water,
HbO, oxygenated-hemoglobin; HbR, deoxygenated-hemoglobin; HbT,
total-hemoglobin; LED, light-emitting diodes; LOOCV,
leave-one-out-cross-validation; MBBL, modified beer-lambert law; MCCV,
Monte Carlo cross-validation; MREG, magnetic resonance encephalography;
MRI, magnetic resonance imaging; MRMR, minimum redundancy maximum
relevance; MCI, mild cognitive-impairment ; NDD, neurodegenerative
disease; NIR, near-infrared; PFC, prefrontal cortex; PSD, power spectral
density; SampEn, sample entropy; SD, source-detector; SVM, support
vector machine; TBI: traumatic brain injury

1 \textbar{} INTRODUCTION

The life expectancy of the global population is steadily continuing to
increase {[}1{]}. As aging possess an increased risk of developing
neurodegenerative diseases (NDD), such as Alzheimer's disease (AD), the
better understanding of healthy brain aging process is of importance.
The assessment of the brain aging trajectory is of interest to detect of
deviations from the healthy trajectory, and to monitor the efficacy of
the treatments and interventions. The increased understanding of the
brain aging process can lead to development of improved interventions,
with an aim to delay age-related disease onset and to reduce their
severity in the later years of life.

Brain aging has been widely studied, and multiple interconnected
structural and functional changes have been reported. The changes can be
observed in different scales of interest, such as micro or macro scale.
Some notable changes are DNA damage, which is considered as one of the
key hallmarks of aging, cerebrovascular changes observed as decreased
vessel size, reduced number of capillaries, small infractions and
microbleeds, causing overall decreased cerebral perfusion, changes in
functional connectivity (FC), and regional brain atrophy, manifested in
overall decrease of brain volume and weight. {[}2{]} In recent years,
neuroimaging methods such as magnetic resonance imaging (MRI) and
electroencephalography (EEG) have been utilized to measure the healthy
brain aging trajectory. The methods commonly aim to quantify the
biological age of the brain, which is assumed to be congruent with the
chronological age of the healthy individuals, while being increased in
the presence of aging related disease and decreased in successful aging
{[}3{]}

Functional near-infrared spectroscopy (fNIRS) presents an intriguing
method for the assessment of aging related-changes in the brain due to
its good temporal resolution, affordability, and portable light-weight
equipment. This enables development of brain health monitoring
applications which can be used in a natural environment. The method is
based on applying light source-detector (SD) pairs with minimum distance
of 2.5 cm to the scalp {[}4{]}, utilizing wavelengths in the optical
window of approximately 650 nm -- 1000 nm, where the near-infrared (NIR)
light is able to propagate through the superficial biological layers of
the skin, skull and cerebrospinal fluid (CSF), reaching the cortical
brain layer {[}5{]}. Finally, the back scattered light is recorded by
the detector pair. By applying modified beer-lambert law (MBBL), the
method can be used to quantify chromophore relative concentrations
{[}6{]}. The method requires selection of at least two wavelengths from
the different sides of the isobestic point of the chromophores of
interest. Commonly the concentration changes of oxygenated-hemoglobin
(HbO) and deoxygenated-hemoglobin (HbR) are monitored, as the cortical
changes are related to the brain metabolism caused by neural activity
{[}5{]}. However, the changes in water (H\textsubscript{2}O) can be
detected in NIR region as well by selecting wavelength accordingly. The
measurement of neurohydrodynamics have been demonstrated recently in the
assessment of glymphatic system by fNIRS {[}7{]}.

fNIRS has been used in multiple aging studies showing evidence for the
use of measurement method in the brain aging assessment. In FC studies
fNIRS has been used successfully to confirm the finding of increased
brain region co-operation, assumed to be due to brain's adaptation to
the structural changes. {[}8{]} Furthermore, Nguyen et al. found
evidence of age-related decreased FC detected during verbal fluency
task, although evidence of age-related changes during oddball and
resting state was not found. {[}9{]}

Arterial stiffness has been associated with aging and is one of the
leading risk factors for hypertension {[}10{]}. As younger subject's
arteries are more compliant, the mechanical stress to the brain caused
by pulsatility is reduced in comparison to older adults with stiffer
arteries, causing damage to the brain's microvasculature. The arterial
stiffness can be detected from the changed pulse shape form, and the
distinguishing of younger and older adults has been shown to be
successful by fNIRS by using pulse shape parameters. {[}11{]}
Additionally, fNIRS has been used with MRI to show association between
aging related cortical thinning and regional pulsatility. {[}12{]}

fNIRS has been used widely to study aging related changes in prefrontal
cortex (PFC) activation, which is involved in the executive function.
The results have shown age related differences in the PFC activation
{[}13--16{]}. Furthermore, fNIRS has been used to characterize
differences between younger and older adults, and mild
cognitive-impairment (MCI) and AD groups {[}17,18{]}, and to show
age-related differences in within-session trainability of hemodynamic
response. {[}19{]}

The results of the previous findings suggest potential for the use of
fNIRS in the study of aging. To investigate this further, the use of
single channel resting state fNIRS to detect aging caused differences in
healthy adults is studied by utilizing machine learning (ML) methods in
an age group classification task. In addition to traditional analysis of
HbO, HbR and total hemoglobin (HbT) changes, the effects of relative
H\textsubscript{2}O concentration changes and raw fNIRS signals are
used. Multiple features based on the latest fNIRS, EEG and functional
magnetic resonance imaging (fMRI) studies are applied. The results
presented are based on the research conducted for the master's thesis of
Martti Ilvesmäki {[}20{]}.

2 \textbar{} EXPERIMENTAL

2.1 \textbar{} fNIRS measurements and data acquisition

The data collection followed the guidelines established by the
Declaration of Helsinki and the study was approved by the regional
Ethical Committee of Northern Ostrobothnia Hospital District in Oulu
University Hospital. All participants of the study signed informed
consent letters before the measurements. The data was collected with
hospital multi-modal MRI compatible frequency coded fNIRS utilizing high
power light-emitting diodes (LED) coupled to optical fibres, with
modifiable wavelength selection {[}21,22{]}.

Total of 56 healthy controls participated in the study. The participants
restrained from the use of alcohol 12 hours prior the measurements. With
the exception of one individual, the participants were non-smoking. Data
from single optode with 3 cm source detector (SD) separation distance,
placed on the left side of the forehead corresponding to the Fp1 of the
10-20 system of the international federation for EEG electrode
placement, was used with sampling frequency of 800 Hz. The subjects were
in a supine position in resting state during the measurement, which
lasted for approximately 5.5 -- 10 minutes in total. After visual
inspection, the data of six subjects was discarded, as the data of four
subjects had gross movement artefacts and for two subjects the length of
the measurement was insufficient. The final dataset consisted of 50
subjects with mean age of 42.3 ± 15.2 and age range of 23 - 67 (22F,
28M). The signal lengths were unified to the length 5.5 minutes by
selecting signal of corresponding length from the start of the
measurement. It is noteworthy, that the chronological and biological age
of the brain may differ as pathologies, such as schizophrenia, traumatic
brain injury (TBI) and AD, have been shown to affect the aging
trajectory of the brain {[}23--25{]}. Thus, although the subjects in the
study were considered as healthy controls and thus the chronological age
is assumed to be similar to the subject's brain age, the true brain age
is not known. Therefore, a potential undiagnosed pathology could affect
the results of the study.

The used wavelengths of 690 nm, 830 nm and 980 nm were selected due to
the absorption being dominated by HbR, HbO and H\textsubscript{2}O
respectively in the corresponding wavelength. Additionally, wavelength
of 810 nm was used, which is close to the isobestic point of the
hemoglobin.

\textbf{2.2 \textbar{} Signal processing and feature extraction}

All the signal processing, machine learning and data-analysis methods
were implemented by using MATLAB version R2022b. Figure 1 illustrates
the signal processing methods used, from signal acquisition until
feature extraction.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{FIGURE 1} Feature extraction pipeline. The four-wavelength fNIRS
data is collected from the subjects and several pre-processing methods
are applied before extracting the features.

Total of 209 features were extracted from fNIRS and fNIRS derived
chromophore relative concentration signals {[}20{]}. The differential
path length factor (DPF) used in MBBL was 5.97 and the extinction
coefficients were based on the work of Cope {[}26{]}. The summary of the
features is shown in Table 1. Some of the features have been described
in the latest fNIRS, EEG and fMRI NDD studies while some are common
features, such as signal standard deviation and gender of the subject.
The frequency bandwidths of respiratory (0.1 - 0.6 Hz), cardiac (0.6 - 5
Hz) and full (0.008 - 5 Hz) were utilized when extracting fNIRS
features. In addition to noise attenuation, the bandwidth specific
features are assumed to contain information related to different
physiological events and could contain more predictive power in the
brain aging assessment.

Spectral entropy, fractional amplitude of physiological fluctuations
(fAPF) and relative power derived features have been used in fNIRS and
EEG studies related to aging and AD research {[}18,27--29{]}.
Furthermore, pulse shape derived from fNIRS has been used to distinguish
AD subjects from healthy controls {[}11{]}. Thus, the features were
selected as they are assumed to have potential predictive power in the
age group classification task. In addition, the features of differential
phase transfer entropy (dPhaseTE) {[}30,31{]}, sample entropy (sampEn)
{[}32,33{]}, and correlation between HbT and H\textsubscript{2}O
{[}34{]} were utilized. Unique feature of envelope-signal spectra
correlation (ESSC) was also used. The feature is calculated by computing
the correlation between the power spectral density (PSD) of the signal
and its envelope. The feature describes the relationship between the
spectral power of the original signal and its low frequency component.

\textbf{TABLE 1} List of all features extracted from the fNIRS and
derived relative chromophore concentration signals used in the study.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
\begin{minipage}[b]{0.24\columnwidth}\raggedright\strut
\textbf{Feature} \textbf{name}\strut
\end{minipage} & \begin{minipage}[b]{0.24\columnwidth}\raggedright\strut
\textbf{Number of features} \textbf{per subject}\strut
\end{minipage} & \begin{minipage}[b]{0.24\columnwidth}\raggedright\strut
\textbf{Frequency bands}\strut
\end{minipage} & \begin{minipage}[b]{0.24\columnwidth}\raggedright\strut
\textbf{fNIRS} \textbf{signals}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
HbT vs. H\textsubscript{2}O correlation\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
3\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Full, cardiac, resp*\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Raw, conc**\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
dPhaseTE\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
4 x 3 x 2***\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Full, cardiac, resp\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Conc\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
ESSC\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8 x 3\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Full, cardiac, resp\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Raw, conc\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
fAPF\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8 x 2\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Cardiac, resp\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Raw, conc\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Gender\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
-\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
-\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Pulse Shape of 830nm (mean, min, max, std, iqr)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
5\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Cardiac\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
830 nm\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Relative power (min, mean, 95th quantile, std)\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8 x 2 x 4\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Cardiac, resp\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Raw, conc\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Sample entropy\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8 x 3\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Full, cardiac, resp\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Raw, conc\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Spectral entropy\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8 x 3\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Full, cardiac, resp\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Raw, conc\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Standard deviation\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
8 x 3\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Full, cardiac, resp\strut
\end{minipage} & \begin{minipage}[t]{0.22\columnwidth}\raggedright\strut
Raw, conc\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

* Respiratory bandwidth, ** Relative concentration of the chromophores,
*** dPTE features computed for two directions, e.g., HbO - Water and
Water - HbO.

2.3 \textbar{} Machine learning methods

Random forest ensemble and support vector machines (SVM) with linear,
polynomial and gaussian kernels were selected as learning algorithms.
The feature selection for SVM learners was implemented by using minimum
redundancy maximum relevance (MRMR) algorithm by MATLAB's fscmrmr
function. The hyperparameter optimization was conducted by using
Bayesian optimization with MATLAB's function bayesopt with 60
iterations.

Due to relatively small sample size used in the study, each test
utilized nested cross-validation (CV) to provide robust and unbiased
performance estimate {[}35{]}. The nested CV protocol is illustrated in
Figure 2. The outer loop consisted of stratified Monte Carlo
cross-validation (MCCV) or K-fold CV depending on the test, while the
inner loop used leave-one-out cross-validation (LOOCV). The inner loop
contained hyperparameter tuning for each model, including
hyperparameters for the feature selection, which in the case of MRMR was
number of selected features based on MRMR feature ranking. For all SVM
learners box constraint was tuned with default search space, while for
polynomial SVM the polynomial order was tuned using search space of
{[}2,3{]}, and for gaussian SVM the kernel scale was tuned using default
search space. For random forest, the tuned hyperparameters were minimum
leaf size and number of predictors to sample with default search space,
and number of trees with {[}5, 1000{]} search space. The overall CV
performance was recorded by using balanced accuracy (bacc). When
analysing the results, the bacc is evaluated either as poor (bacc [?] 60
\%), moderate (\textless{} 60 \% \textless{} bacc [?] 70 \%), good (70 \%
\textless{} bacc [?] 80 \%) or excellent (bacc \textgreater{} 80 \%).

2.3.1 \textbar{} Classification to age groups with pre-defined age
groups

The first classification test was conducted by dividing the data into
four pre-defined age groups. The age thresholds for each group were
selected by aiming for approximately equal sized groups, while still
containing wide age distribution. The age group division is illustrated
in Figure 3. Stratified MCCV with 20-80 \% test-train-split and 1000
iterations was used for the outer CV.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

FIGURE 2 Nested cross-validation protocol used in the study. The inner
loop (light blue) is used for the model selection, while in the outer
loop selected models are trained based on the tuned hyperparameters. The
procedure is repeated N times based on the outer loop CV method,
resulting in the output (green) of estimated performance. For the outer
loop, MCCV was used with pre-defined age groups classification and
K-fold CV in the age threshold tests. The inner loop model selection
included feature selection hyperparameters selection for the MRMR
algorithm used by SVM learners.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{FIGURE 3} Age group division. The bars represent number of
subjects in each age group, while the colours illustrate the
within-class gender distribution.

2.3.2 \textbar{} Classification to age groups with variable age group
thresholds

The effect of varying the age group thresholds was further analysed. Age
grid of 26 to 63 was used to evaluate different thresholds. Instead of
using all the ages between minimum and maximum in the age grid, only the
ages appearing in the data were considered as part of the grid. As a
result, the best corresponding thresholds were found for each classifier
based on the achieved balanced accuracy. For each threshold, stratified
K-fold CV was used with K=5. Figure 4 illustrates the age threshold
finding process for each test.

In the age threshold test 1, all the data was used and split into two
age groups of young and old adults using the aforementioned age grid.
For the test 2, two age thresholds were used and the in-between data was
excluded from the ML pipeline, while the beyond threshold subjects were
sorted in to young and old adult groups. Test 3 used similar method as
test 2, but the in-between data was used as a third rejection class. The
goal of the tests 2 and 3 was to identify how the exclusion or inclusion
of the in-between groups affects the classifiers performance.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{FIGURE 4} Illustration of the age group threshold search
protocol for different age threshold tests. The test 1 was used to find
a single threshold for dividing data into two classes, while the tests 2
and 3 utilized two thresholds for either excluding the data or creating
a third rejection class.

3 \textbar{} RESULTS AND DISCUSSION

3.1 \textbar{} Classification with pre-defined age groups

Table 2 illustrates the results of the classification to pre-defined age
groups. The classification between all four groups shows moderate
results with all classifiers reaching bacc between 66 -- 67 \%.
Interestingly, the highest performance is reached in the classification
task of groups A vs. D, where the age difference between the groups is
the largest. The best performing model confusion matrices for the
previously mentioned tasks are shown in the Figure 6. Furthermore, the
performance in binary classification task of younger groups A, B, C vs.
the oldest group D can be seen to decline linearly as the age gap
between groups decreases as shown in the Figure 5. The result indicates
that distinguishing the younger groups from the oldest group is better
when the age gap between the groups is higher. On the other hand, the
binary classification results between the groups A, B and C show poor
performance, suggesting similarity between the groups. The majority of B
and C classifications is done to the group A, which is likely affected
by the class imbalance, group A being the largest. With more balanced
class sizes, more equal proportion of miss-classified samples between
groups A, B and C would be expected in the case of suspected homogenous
samples. Overall, the results suggest no great difference between the
younger groups A, B and C in this study setup, while the age-related
differences become more distinct with the oldest age group.

\textbf{TABLE 2} . The classifiers performance for the age group
classification test with pre-defined age groups. The results include
balanced accuracy and 95 \% confidence intervals inside the brackets.
Polynomial SVM in A vs. D age group classification task achieved the
highest performance (highlighted in bold).\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Task}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Linear SVM}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Polynomial SVM}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Gaussian SVM}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Random Forest}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
A vs. B vs. C vs. D\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
67.05 \% (66.67 -- 67.43)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
66.58 \% (66.21 -- 66.94)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
66.38 \% (66.05 -- 66.70)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
66.09 \% (65.75 -- 66.43)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
A vs. D\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
77.23 \% (76.02 -- 78.45)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{78.98 \%} \textbf{(77.80 -- 80.15)}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
73.68 \% (72.44 -- 74.91)\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
73.46 \% (72.33 -- 74.58)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
B vs. D\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
64.23 \% (62.87 - 65.58)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
63.15 \% (61.78 - 64.52)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
62.63 \% (61.25 - 64.00)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
69.33 \% (67.97 - 70.68)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
C vs. D\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
54.30 \% (53.01 - 55.59)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
52.35 \% (51.15 - 53.55)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
54.68 \% (53.45 - 55.90)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
57.90 \% (56.59 - 59.20)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
B vs. C\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
40.08 \% (38.90 - 41.25)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
41.50 \% (40.29 - 42.71)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
41.68 \% (40.41 - 42.94)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
44.50 \% (43.11 - 45.89)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
A vs. C\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
45.76 \% (44.93 - 46.58)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
53.49 \% (52.23 - 54.75)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
50.04 \% (49.23 - 50.86)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
46.03 \% (45.15 - 46.92)\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
A vs. B\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
46.24 \% (45.41 - 47.07)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
45.86 \% (44.87 - 46.85)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
47.79 \% (47.21 - 48.37)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright\strut
46.25 \% (45.23 - 47.27)\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{FIGURE 5} The best performing models for the classification to
pre-defined age groups A, B, C and D. The chart illustrates the
performance with low and high age gap between the groups.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

(A)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

(B)

\textbf{FIGURE 6} The best performing model normalized confusion
matrices for the classification to pre-defined age groups for the tasks
A vs. B vs. C vs. D (chart A) and A vs. D (chart B).

3.2 \textbar{} Classification with variable age group thresholds

Table 3 shows the results of the age threshold tests for each
classifier. The performance in the age threshold test 1, classification
of the subjects to young and old groups using different age thresholds,
achieved moderate to good performance (bacc: 63.44 -- 71.05 \%). Three
of the classifiers found similar best age threshold (39 -- 41), while
the overall best performing model of linear SVM performed best with an
age threshold of 56. However, it is noteworthy that there is a clear
uneven distribution of subjects when using the suggested age threshold
of 56 (N\_young: 36, N\_old: 14). The class imbalance is similar to one
observed in classification to pre-defined age groups but pronounced more
strongly. On the other hand, it can be observed that the second-best
performing classifier of Gaussian SVM reached the highest performance
with an age threshold of 42, where the achieved performance can be
considered moderate with more balanced classes (N\_young: 27, N\_old:
23). The found best age threshold of 56 matches the threshold used for
group D when using pre-defined age groups. It is visible from Figure 6 A
that in the most cases subjects B and C are classified to group A. The
result indicates that with the current dataset the differences in the
study population seem to be most pronounced with the threshold of 56.
Interestingly, the threshold was in agreement with the class
distribution in Figure 3A.

In the age threshold test 2, where two age thresholds were selected, and
the in-between subjects were excluded from the ML loop, the results show
good to excellent performance with all the classifiers (bacc: 79.09 --
81.50 \%). The lower threshold varies between 27 to 37, while the upper
threshold was between 57 to 62. The performance of the age threshold
test 3 with rejection class can be considered good with all the
classifiers (micro averaged bacc: 72 -- 74.68 \%). Polynomial and
Gaussian SVM, and random forest classifiers performed best with the same
age thresholds (44 -- 62), while linear SVM used different range for the
rejection class (27 -- 57). As visible in Figure 7 confusion matrix of
the best performing model polynomial SVM, most of the predictions were
done in favour of the biggest group of the young subjects, as noticed as
well in the previous tests. The closer examination of class sizes showed
that the biggest class had approximately three times more subjects in
comparison to the other two groups (N\_young: 30, N\_rejection: 9 ,
N\_old: 11 ). The uneven class distribution can result in case where
when the classifier is in doubt it will favour the majority class. The
more balanced case was found with linear SVM model with similar
performance as seen in Figure 7 (D), where the age thresholds for
rejection class of 27 -- 57 yielded more balanced class distribution
(N\_young: 14, N\_old: 12, N\_rejection: 24), although still favouring
one class over the others in the predictions.

The results of the age threshold test 2 and 3 present two interesting
observations. Firstly, the classification performance is higher when the
subjects in-between the young and old age group are excluded from the ML
loop. Secondly, the upper age threshold is fairly constant (57, 62),
while the lower age threshold has more variation (27, 33, 37, 44). The
variation in the age threshold between the classifiers is expected, as
the different classifiers perform differently in the tasks. The between
tests variation with younger threshold with same classifiers could be
explained by the effect caused by homogeneity in the data of the younger
subjects, which is further supported by the results of the
classification task using pre-defined age groups. These findings suggest
a difference in the rate of aging between the subjects, and that the
age-related differences are more distinctly pronounced as the aging
process has progressed further.

\textbf{TABLE 3} The performance of the classifiers in the age threshold
test. The results consist of balanced accuracy of K-fold (K=5)
cross-validation with the selected age thresholds. The results of the
best performing models are bolded.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Test}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Linear SVM}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Polynomial SVM}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Gaussian SVM}\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright\strut
\textbf{Random Forest}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Test 1\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{71.05 \%,} \textbf{th*: 56}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
66.51 \%, th: 41\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
67.37 \%, th: 42\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
63.44 \%, th: 39\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Test 2\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
81.37 \%, ths: 37 - 57\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{81.50 \%,} \textbf{ths: 33 - 62}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
79.09 \%, ths: 33 - 62\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
80.13 \%, ths: 27 - 62\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
Test 3\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
72.00 \%, ths: 27 - 57\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
\textbf{74.68 \%,} \textbf{ths: 44 - 62}\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
73.33 \%, ths: 44 - 62\strut
\end{minipage} & \begin{minipage}[t]{0.19\columnwidth}\raggedright\strut
72.00 \%, ths. 44 - 62\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

*age threshold\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

(A)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

(B)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

(C)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

(D)

\textbf{FIGURE 7} Normalized confusion matrices for the best performing
models in the age threshold tests 1 (A), 2 (B) and 3 (C). Due to notable
class imbalance with the age threshold 3 with the best performing model,
the confusion matrix for the best linear SVM model shown additionally
(D).

4 \textbar{} CONCLUSION

The two key findings of the study are 1) fNIRS has potential to classify
young and old adults to corresponding age groups with good performance,
and 2) the inclusion and exclusion of the subjects in the young,
in-between and old age groups affects the classification performance
significantly, suggesting different aging rate within these three
groups, i.e., young, in-between, and old groups. As the wavelengths used
in our fNIRS device are sensitive to hemoglobin and water dynamics, the
noticed changes are potentially related to the cerebrovascular and
neurohydrodynamic events. However, it is not clear whether water or
hemoglobin change caused effects are more significant. Furthermore, the
fNIRS was measured from Fp1, and thus the detected changes are only
related to the frontal lobe activity and to the hemodynamic and
neurohydrodynamic differences in the brain. The effect of superficial
layers in fNIRS study of brain aging would be of interest to study more
in detail in the future, by utilizing short SD pair in addition to the
long SD pair.

Several factors accelerating and decelerating brain aging process have
been identified in the literature {[}2{]}. The existence of these
factors could explain the observed changes in classification
performance, when including the subjects in the in-between age groups.
Although the study population was considered healthy, the brain aging
related accelerative and decelerative factors information, such as
alcohol consumption habits and amount of physical activity per week,
were not considered in this study. The analysis of these factors would
be intriguing, as they may delay or expedite the brain aging process.
Furthermore, inclusion of individuals of age over 70 would be of
interest as it has been suggested that brain aging accelerates
significantly afterwards {[}36{]}.

Another intriguing prospect is to use fNIRS in the aging study related
to sleep. Recently it was found that the brain's glymphatic system has
been found to be more active during the sleep {[}37{]} and the aging has
been suggested to affect its function negatively {[}38{]}. As the system
consists of CSF waste clearance, the use of fNIRS to measure the brain
pulsations, which are one of the drivers of the glymphatic system
{[}39{]}, and CSF dynamics with water sensitive fNIRS setup could
provide potential for gaining further insight into the function of the
system in humans, and the effects caused by aging. Furthermore, the EEG
of sleep has been successfully utilized in the brain age prediction
task. {[}28{]} As EEG measured neural activity and fNIRS measured
hemodynamic response are connected by neurovascular coupling effect, it
could be of interest to study if age-related differences become more
pronounced during sleep.

The key limitation of our study is the used relatively small sample
size, as in general the use of large datasets increases the statistical
power in pattern recognition, {[}35{]} and therefore the used datasets
in the brain age studies are usually of large size {[}40{]}. It would be
of great interest in the future to conduct fNIRS brain aging studies
with large, well age distributed, sample population to confirm our
findings. Additionally, use of multi-channel fNIRS could give boarded
picture on the global effects of the aging on brain. Although the used
multi-modal measurement setup included different brain measurement
modalities, such as magnetic encephalography (MREG) and EEG {[}21{]}, in
this study we focused on the analysis of fNIRS and brain aging
specifically due to its novelty in the context. Thus, another area for
future exploration in the fNIRS brain aging studies is to analyse
combination of brain measurement modalities data, such as fNIRS combined
with EEG or MREG. The analysis of different modalities combination would
enhance the information content and provide a comparison of the methods
performance in the brain aging context. However, although suffering from
the lack of data, our study protocol utilized the best practices for ML
research with limited data by utilizing nested cross-validation
framework, with feature and model selection conducted within the inner
loop, for estimating unbiased performance of the models {[}35{]}.
Additionally, we utilized multiple fNIRS signal features, introduced
previously in the study of brain by different measurement modalities.
The findings of our study demonstrate the high potential for the use of
fNIRS in the study of brain aging.

ACKNOWLEDGMENTS

The authors would like to acknowledge CSC -- IT Center for Science,
Finland, for providing the computational resources. The study was
financed by the Academy of Finland Profi6 funding, 6G-Enabling
Sustainable Society (6GESS) programme. Academy of Finland (Terva grant
335723), BF (11146/31/2022), JPND/AoF (357805).

FINANCIAL DISCLOSURE

The authors have no financial conflicts of interest in connection with
this article.

CONFLICT OF INTEREST

The authors have no conflicts of interest in connection with this
article.

DATA AVAILABILITY STATEMENT

Research data are not shared due to the hospital policy.

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