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Mo ion A i ac s in Dynamic EEG Reco dings : Expe imen al Obse a ions, Elec ical
Modelling, and Design Conside a ions
© 2024 by he au ho s. Licensee MDPI, Basel, Swi ze land.
Published e sion
Giang ande, Alessand a; Bo e , Albe o; Pii ulainen, Ha i; Ce one, Giacin o Luigi
Giang ande, A., Bo e , A., Pii ulainen, H., & Ce one, G. L. (2024). Mo ion A i ac s in Dynamic
EEG Reco dings : Expe imen al Obse a ions, Elec ical Modelling, and Design Conside a ions.
Senso s, 24(19), A icle 6363. h ps://doi.o g/10.3390/s24196363
2024
Senso s 2024, 24, 6363. h ps://doi.o g/10.3390/s24196363 www.mdpi.com/jou nal/senso s
A icle
Mo ion A i ac s in Dynamic EEG Reco dings: Expe imen al
Obse a ions, Elec ical Modelling, and Design Conside a ions
Alessand a Giang ande 1,2, Albe o Bo e 1, Ha i Pii ulainen 2 and Giacin o Luigi Ce one 1,*
1 Labo a o y o Neu omuscula Sys em and Rehabili a ion Enginee ing, Depa men o Elec onics and
Telecommunica ions, Poli ecnico di To ino, 10129 Tu in, I aly; alessand a.giang ande@poli o.i (A.G.);
albe o.bo e @poli o.i (A.B.); giacin oluigi.ce one@poli o.i (G.L.C.)
2 Facul y o Spo and Heal h Sciences, Uni e si y o Jy äskylä, 40014 Jy äskylä, Finland;
[email p o ec ed]
* Co espondence: giacin oluigi.ce one@poli o.i
Abs ac : Despi e he p og ess in he de elopmen o inno a i e EEG acquisi ion sys ems, hei use
in dynamic applica ions is s ill limi ed by mo ion a i ac s comp omising he in e p e a ion o he
collec ed signals. The e o e, ex ensi e esea ch on he genesis o mo ion a i ac s in EEG eco dings
is s ill needed o op imize exis ing echnologies, shedding ligh on possible solu ions o o e come
he cu en limi a ions. We iden i ied h ee po en ial sou ces o mo ion a i ac s occu ing a h ee
di e en le els o a adi ional biopo en ial acquisi ion chain: he skin-elec ode in e ace, he con-
nec ing cables be ween he de ec ion and he acquisi ion sys ems, and he elec ode-ampli ie sys-
em. The iden i ied sou ces o mo ion a i ac s we e modelled s a ing om expe imen al obse a-
ions ca ied ou on EEG signals. Consequen ly, we designed cus omized EEG elec ode sys ems
aiming a expe imen ally disen angling he possible causes o mo ion a i ac s. Bo h analy ical and
expe imen al obse a ions indica ed wo main esidual si es esponsible o mo ion a i ac s: he
connec ing cables be ween he elec odes and he ampli ie and he sudden changes in elec ode-
skin impedance due o elec ode mo emen s. We concluded ha u he ad ancemen s in EEG ech-
nology should ocus on he ansduc ion s age o he biopo en ials ampli ica ion chain, such as he
elec ode echnology and i s in e acing wi h he acquisi ion sys em.
Keywo ds: elec oencephalog aphy; biomedical ins umen a ion; mo ion a i ac s; he b ain; EEG
elec odes; EEG cap design; elec ode-ampli ie sys em modelling
1. In oduc ion
Among he b ain echnologies, elec oencephalog aphy (EEG) is he mos sui able
o in es iga ing he co ical senso imo o in eg a ion p ocesses du ing dynamic asks
hanks o i s excellen spa io empo al esolu ion, high po abili y, and ela i ely low cos s
[1]. Recen ha dwa e de elopmen s allowed o he acquisi ion o biosignals h ough
wi eless, minia u ized, and po able de ices, ex ending he ange o signal acquisi ions
also ou side lab en i onmen s [2–6]. The oppo uni ies a ising om he a ailabili y o
hese de ices a e, howe e , no ully exploi ed in p ac ice due o he equen p esence o
mo ion a i ac s co up ing dynamic EEG signals. These a i ac s a e undesi ed signals
wi h an ampli ude o e en wo o de s o magni ude g ea e han one o he signals o
in e es , hus s ongly comp omising he co ec in e p e a ion o co ical signals [7,8]. In
he as majo i y o he cases, mo ion a i ac s a e ime-locked o he pe o med mo e-
men s and g ea ly a iable in e ms o shape, epea abili y, and spec al con en , hus be-
ing ha d o impossible o emo e [9,10]. Indeed, mo ion a i ac s can be obse ed bo h a
low equencies as baseline shi s and a high equencies as spike-like a ia ions [8].
The e o e, pos -p ocessing echniques a e no always e ec i e in emo ing hese a i ac s,
conside ing he ela i ely low ypical EEG equency bandwid h (0.1 Hz–100 Hz) [11].
Ci a ion: Giang ande, A.; Bo e , A.;
Pii ulainen, H.; Ce one, G.L. Mo ion
A i ac s in Dynamic EEG
Reco dings: Expe imen al
Obse a ions, Elec ical Modelling,
and Design Conside a ions. Senso s
2024, 24, 6363.
h ps://doi.o g/10.3390/s24196363
Academic Edi o : Chang-Hwan Im
Recei ed: 23 Augus 2024
Re ised: 19 Sep embe 2024
Accep ed: 27 Sep embe 2024
Published: 30 Sep embe 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license
(h ps://c ea i ecommons.o g/license
s/by/4.0/).
Senso s 2024, 24, 6363 2 o 20
Whils wa ele -based o blind sou ce sepa a ion echniques a e obus echniques excel-
ling in emo ing physiological and epea able EEG a i ac s (e.g., eye blinks), hei e ec-
i eness in he con ex o mo ion a i ac emo al collapses. Indeed, i emains obscu e o
wha ex en hey exclusi ely emo e a i ac s, en i ely p ese ing he con en o he phys-
iological b ain signals [9,12]. O e he pas yea s, di e en solu ions ha e been p oposed
o mi iga e he eco ding o mo ion a i ac s, including he use o ac i e elec odes [13].
Al hough ac i e elec odes we e pa icula ly e ec i e in ejec ing powe line in e e ence
a ising om he capaci i e coupling be ween connec ing cables and powe line sou ce,
hey ha e been p o en compa able o passi e elec odes in educing mo ion a i ac s du -
ing dynamic eco dings [14]. Con e sely, hey con ibu e o inc easing he encumb ance
o he acquisi ion sys em, limi ing i s po abili y and usabili y in dynamic con ex s. O he
inno a i e solu ions p e en ing he ising o mo ion a i ac s conce n he de elopmen o
de ec ion sys ems based on ex iles, as hey showed a educed sensi i i y o mo ion a i-
ac s. Howe e , hei use is s ic ly limi ed o hai less co ical egions (i.e., on al and
empo al a eas) and, he e o e, no compa ible wi h comp ehensi e s udies on he ole o
he pa ie al senso imo o co ices in mo emen con ol [15].
Despi e hese e o s, he genesis o mo ion a i ac s in EEG eco dings s ill emains
a poo ly unde s ood opic. The e o e, gi en he inc easing in e es in dynamic EEG e-
co dings in na u alis ic, dynamic condi ions [16–18], i is c ucial o gain a deep unde -
s anding and o model he basic phenomena leading o he genesis o mo ion a i ac s o
op imize exis ing echnologies and o de elop new solu ions o high-quali y EEG de ec-
ion.
Biopo en ial signal acquisi ion can be a ec ed by he mu ual in e ac ion and supe -
imposi ion o mul iple ac o s occu ing a di e en s ages o he eco dings (e.g., expe i-
men al se up p epa a ion, de ec ion, and acquisi ion echnology) [19–21]. Al hough i is
di icul o disen angle he sou ces o mo ion a i ac s in he expe imen al p ac ice, a
model-based app oach desc ibing he basic phenomena unde lying he gene a ion o mo-
ion a i ac s is he eby p oposed. Speci ically, in he ollowing disse a ion, we aim o p o-
ide u he insigh s in o he ole o acquisi ion elec onics, connec ing cables, and elec-
ode echnology in EEG eco dings, bo h om analy ical and expe imen al pe spec i es.
To achie e his, we (i) ca ied ou obse a ions on EEG signals du ing eal expe imen s,
(ii) iden i ied and modelled he possible a i ac sou ces, (iii) designed cus omized EEG
elec ode sys ems aimed a showing he in luence o he de ec ion sys em’s ea u es in
EEG dynamic eco dings, and (i ) pe o med a case s udy aimed a gi ing u he
g ounds o he p e iously modelled phenomena behind he genesis o EEG mo ion a i-
ac s.
2. Obse a ions
Po en ial sou ces o mo ion a i ac s can a ise a each o he h ee main s ages cons i-
u ing a adi ional biopo en ial acquisi ion chain [22,23]: (i) he skin-elec ode in e ace
(i.e., ansduc ion s age), (ii) he elec ode-ampli ie connec ing cables, and (iii) he elec-
ode-ampli ie sys em (i.e., acquisi ion s age). O he possible sou ces o a i ac s a ec ing
he EEG signals (e.g., eye mo emen s and en i onmen - ela ed a i ac s) we e ou o he
scope o he cu en disse a ion as hey a e ei he easily handled o can be ea ed as a
pa icula case o he desc ibed ones. Following his app oach, we we e able o in es iga e
he main ac o s ha can in luence he ou come o biopo en ial signal eco dings. Fi s ly,
he ela i e mo emen be ween he elec ode and he skin c ea es a consequen al e a ion
o he ion dis ibu ion a he elec ode-skin in e ace ha would be ead as an addi i e
a i ac signal wi h espec o hose o in e es [19]. Secondly, due o iboelec ic phenom-
ena [24], he ic ion and de o ma ion o he cable insula o caused by he mo emen s o
he cables gene a e an addi i e inpu ol age po en ial ha will be ampli ied oge he wi h
he signal o in e es [25]. Thi dly, in case o poo elec ode-skin con ac (e.g., due o a
b isk, pa ial de achmen o he elec odes), mo emen s migh also igge a modula ion
o he esidual inpu - e e ed Powe Line In e e ence (PLI). In he nex sec ions, we
Senso s 2024, 24, 6363 3 o 20
p o ide some examples aken om he abo emen ioned a i ac ual phenomena based on
he obse a ions o eal eco dings. These examples will hen be used as s a ing poin s
o he ollowing elec ical modelling.
2.1. A i ac s A ising om Phenomena a he Elec ode-Skin In e ace
Figu e 1 shows an example o mo ion a i ac s co up ing indi idual channels (i.e.,
CP1 o , o a lesse ex en , Pz o he pa ie al co ex) o a se o EEG signals eco ded du ing
o e g ound walking. Such mo ion a i ac s can be desc ibed as ela i ely slow changes in
he baseline ol age po en ial highly co ela ed wi h he main equency o he mo emen .
In such cases, due o he slow and pe iodic changes o he ol age, we hypo hesize ha
hese a i ac s a e gene a ed by ela i e shi s be ween he elec odes and he skin because
o body mo emen s ela ed o he mo o ask. The a i ac localiza ion on a single channel
is likely due o he mo emen o he indi idual explo ing elec ode (i.e., he elec ode
acqui ing he monopola EEG signal o in e es wi h espec o he e e ence elec ode). I
is impo an o highligh ha he example in oduced in Figu e 1 migh be handled
h ough pos -p ocessing echniques. Howe e , i his ype o a i ac simul aneously
a ec s mul iple elec odes, including he e e ence one, he deg ee o signal co up ion
inc eases and he con en ionally adop ed echniques o a i ac emo al a e c i ical o
succeed due o he in ica e supe imposi ion o di e en e ec s.
Figu e 1. Examples o mo ion a i ac s con amina ion on a se o EEG signals eco ded du ing o e -
g ound walking ela ed o he mo emen o single explo ing elec odes (CP1, Pz o e he pa ie al
co ex).
2.2. A i ac s Rela ed o Connec ing Cables Mo emen s
Figu e 2 ep esen s he esul o an expe imen al es ega ding he acquisi ion o EEG
signals om a subjec a es while he expe imen e was manually shaking he cables
connec ing he elec odes o he ampli ie (i.e., a wo s -case scena io). As e iden om he
spec al powe dis ibu ions o Figu e 2B, adi ional signal p ocessing echniques canno
be used o dampen he d ama ic e ec o mo ion a i ac s on EEG signals. Indeed, mo ion
a i ac s ela ed o he connec ing cables ypically occu no ime-locked wi h he
mo emen s wi h a spike-like beha io and hei spec al componen s a e o e lapped wi h
he EEG bandwid h (0.1 Hz–100 Hz). Addi ionally, mo ion a i ac s gene a ed by he
mo emen o he cables a e ha dly epea able, especially in e ms o shape. Fo hese
easons, many il e ing echniques a e no ound o be e ec i e in emo ing non-b ain
ac i i y om he EEG signals [12]. Simila conside a ions ha e been obse ed in he case
o sEMG signals acquisi ions [21].
Senso s 2024, 24, 6363 4 o 20
Figu e 2. Mo ion a i ac s caused by he mo emen o he connec ing cables. (A) EEG signals ec-
o ded wi h he subjec a es while he expe imen e is shaking he cables, wea ing isola ing insu-
la ing glo es. (B) Powe spec a o a ep esen a i e EEG signal wi h and wi hou cable shaking.
2.3. A i ac s Rela ed o he Elec ode-Ampli ie Sys em P ope ies Leading o PLI Modula ion
Figu e 3A shows expe imen al examples o a i ac s due o PLI modula ion on
de ec ed signals. In his case, we hypo hesized ha du ing mo emen , an uns able con ac
a he elec ode-skin in e ace may induce a sudden a ia ion o he elec ode-skin
imbalance be ween he explo ing and e e ence elec odes, leading o a empo a y
inc ease o he inpu - e e ed PLI. Figu e 3B ep esen s a schema iza ion o his
phenomenon. The esidual, inpu - e e ed PLI ( ed sinusoidal signal) is modula ed by he
mo emen ( ep esen ed as he blue bina y signal whe e he le els 0–1 a e espec i ely
e e ed o absence/p esence o elec ode-skin impedance a ia ions due o a mo emen )
p o iding in he ou pu he co up ing signal (black colo ). The e o e, PLI signals
(sinewa e a 50 Hz/60 Hz) a e modula ed in ime by he a ia ions o elec ode-skin
imbalance, esul ing in a i ac s wi h di e en mo phologies. As a esul , he mo emen -
ela ed modula ion is esponsible o changing he spec al con en o he whole eco ded
signal as i in oduces spu ious, unp edic able spec al componen s (di e en om PLI
equency) ha may span h oughou he en i e EEG spec um. These a i ac s a e,
he e o e, pa icula ly challenging no only o be isually iden i ied bu also o be handled
as hey canno be emo ed, e.g., h ough no ch o adap i e il e s [26].
Figu e 3. Examples o PLI modula ion. (A) Th ee eal examples o possible a i ac mo phology due
o he b isk de achmen o elec odes modula ing powe line noise. (B) Schema ic ep esen a ion o
he hypo hesized phenomenon. F om op o bo om: powe -line signal ( ed ace), modula ing sig-
nal modelling he b isk elec ode mo emen (blue ace), esul ing de ec ed signal (black ace) ha
will be supe imposed o he physiological one.

Senso s 2024, 24, 6363 5 o 20
3. Lumped Pa ame e s Modelling
Fo each iden i ied sou ce o mo ion a i ac (Obse a ions 2.1, 2.2, and 2.3), an elec-
ical lumped pa ame e model has been designed o desc ibe and syn hesize sepa a ely
he expe imen ally obse ed phenomena.
3.1. A i ac s A ising om Phenomena a he Elec ode-Skin In e ace
Figu e 4 shows he elec ical model o gene a ion o mo ion a i ac s a ising om he
mo emen o wo explo ing elec odes 𝑒1 and 𝑒2 (ha ing elec ode-skin impedances
espec i ely o 𝑍𝑒1 and 𝑍𝑒2) in he case o monopola con igu a ion (monopola e e ence
elec ode 𝑒𝑟, ha ing impedance 𝑍𝑟). This ci cui has been syn hesized o model common
a i ac s be ween adjacen elec odes due, as an example, o mo emen - ela ed shi s
be ween he elec odes and he skin. A pu ely esis i e ampli ie inpu impedance is
conside ed o simplici y [27–29]. The ol age gene a o (𝑉𝐴𝐸) models a common-mode
mo ion a i ac sou ce as he ol age change gene a ed by he ela i e mo emen s be ween
wo explo ing elec odes. This is assumed as a ealis ic hypo hesis when conside ing, o
example, wo neighbou ing elec odes a ec ed by he same mechanical exci a ion. I is
wo h no ing ha in his elec ical model, we conside ed a single pai o elec odes, bu
he disse a ion can be ex ended o he o al numbe o explo ing elec odes used du ing
EEG measu emen s. In addi ion, simila models can be used o examine he e ec o he
mo emen s a he e e ence elec ode loca ion o bo h e e ence and explo ing elec odes.
We ocused on his case because i is he mos c i ical one in ligh o he abo emen ioned
obse a ions. Acco ding o he elec ical model o Figu e 4, he ol age di ide be ween
he on -end ampli ie inpu impedances and he elec ode impedances will gene a e he
ollowing inpu - e e ed ol ages a he inpu o he A1 and A2 biopo en ial ampli ie s:
{
𝑉𝑂1𝑖𝑟 =𝑉𝐴𝐸 𝑅𝑖
𝑅𝑖+𝑍𝑒1
𝑉𝑂2𝑖𝑟 =𝑉𝐴𝐸 𝑅𝑖
𝑅𝑖+𝑍𝑒2
(1)
To e alua e how he inpu common mode ol age a i ac (𝑉𝐴𝐸) is ansla ed in o a
di e en ial-mode a i ac a he ampli ie ou pu , we e alua ed he di e ence be ween he
wo ol ages ∆𝑉=𝑉𝑂1𝑖𝑟−𝑉𝑂2𝑖𝑟. Unde he ealis ic hypo hesis ha he inpu ampli ie
impedance is g ea e han he elec ode impedances (i.e., 𝑅𝑖≫𝑍𝑒 ) [30], he ol age
di e ence can be app oxima ed as:
∆𝑉≅𝑉𝐴𝐸∆𝑍𝑒
𝑅𝑖
(2)
This model is well known in he li e a u e as he ol age di ide e ec , and i is o en
used o es ima e he powe line in e e ence ejec ion capabili ies o an elec ode-ampli ie
sys em [21].
I is e iden ha , e en when he sou ce o he a i ac (𝑉𝐴𝐸) is a common mode, he
di e en ial ol ages compu ed a he ou pu o he monopola on -end may no be null,
as hey depend on he a io be ween he elec ode-skin imbalance and he ampli ie inpu
impedance. As a esul , he di e ence be ween he impedance alues ∆𝑍𝑒 should be
minimized as he g ea e he imbalance be ween he elec ode impedances, he g ea e he
ol age di e ences (i.e., a i ac signal ampli ude).
Senso s 2024, 24, 6363 6 o 20
Figu e 4. Elec ical model o mo ion a i ac s caused by mo emen - ela ed shi s o wo explo ing
elec odes (𝒆𝟏 and 𝒆𝟐 , wi h impedances 𝒁𝒆𝟏 and 𝒁𝒆𝟐 ). 𝑹𝒊 ep esen s he ampli ie inpu e-
sis ance. A di e en ial signal acquisi ion in a monopola con igu a ion is ep esen ed.
3.2. A i ac s Rela ed o Connec ing Cables Mo emen s
One o he majo sou ces o cable- ela ed mo ion a i ac s is he iboelec ic e ec ,
causing a ne cha ge accumula ion on he su ace o he cables connec ing he elec odes
o he ampli ie du ing hei ecip ocal mo emen s [25]. The iboelec ic e ec desc ibes
he ans e o elec ic cha ge be ween wo objec s (i.e., he insula ion laye s o
neighbou ing cables) when hey slide agains each o he o e en only when hey come
in o con ac [24,31]. Phenomena like ic ion and de o ma ion o he insula ion laye s o
adjacen cables modi y he elec os a ic ol age acco ding o he cable ma e ial p ope ies,
con ac a ea, ype o con ac , and speed o he a ying ecip ocal dis ance [25]. Wi h he
aim o unde s anding he con ibu ion o he cables’ mo emen o mo ion a i ac s in EEG
eco dings, we modeled wo adjacen cables connec ing wo sepa a ed elec odes o he
ampli ie , as shown in Figu e 5. 𝑹𝒄𝟏, 𝑹𝒄𝟐 a e he elec ical esis ances o he cable
conduc o s ( ypically coppe , esis i i y 𝝆 ≅𝟏𝟔.𝟖 𝐦𝛀∙𝐦𝐦𝟐/𝐦 ), 𝑪𝒊𝟏,𝑪𝒊𝟐 model he
pa asi ic capaci ance due o he cable insula o laye ( hickness 𝒅𝒊, dielec ic cons an 𝜺𝒓)
w apping he inne conduc i e ma e ial, and 𝑪𝑨 ep esen s he elec ical capaci ance due
o he dielec ic (i.e., ai , dielec ic cons an 𝜺𝑨) in be ween wo conduc i e mediums (i.e.,
he cha ged insula o laye s) sepa a ed by a dis ance 𝒅𝑨. S a ing om his model, some
simpli ica ions can be con enien ly in oduced. Fi s , he e ms e e ing o he elec ical
esis ances can be dis ega ded because o hei small con ibu ion o he impedance
magni ude when conside ing s anda d cables wi h a ans e sal sec ion o 0.5 mm2 and a
leng h o 1 cm (~ ens o milli-ohm). Second, unde he hypo hesis o modelling he eac i e
componen s as capaci o s, he equi alen capaci ance o he model can be app oxima ed
o he sole con ibu ion o 𝑪𝑨 as i domina es on he single 𝑪𝒊 because o he g ea e
dielec ic cons an (𝜺𝒓> 𝜺𝑨) and dis ance be ween he pla es (𝒅𝑨>𝒅𝒊). In addi ion, he
mo emen o he cable bundle is expec ed o a ec 𝑪𝑨 mo e han 𝑪𝒊 . Indeed, he
pa ame e 𝒅𝑨 (dis ance among cables) is mos likely o a y h oughou he mo emen s,
which modula es 𝑪𝑨. This, in u n, al e s he o al capaci ance o he model, a ec ing he
elec ical p ope ies o he cables and gene a ing mo ion a i ac s. Indeed, he iboelec ic-
induced elec os a ic ol age consequen ly pola izes he 𝑪𝑨 capaci o , gene a ing a
ol age d op 𝑽𝑨 . The ne cha ge 𝑸𝑨 on he pla es o he capaci o (plana aces
app oxima ion) is p opo ional o he po en ial di e ence 𝑽𝑨 ac oss he wo pla es:
𝑸𝑨=𝑪𝑨𝑽𝑨
(3)
Unde he easonable assump ion ha he ne cha ge, 𝑸𝑨 , accumula ed h ough
iboelec ic e ec emains cons an du ing he cable mo emen , he e will be a di e en ial
ol age change a he inpu o he biopo en ial ampli ie ∆𝐕𝐀=𝐕𝐀𝟏−𝐕𝐀𝟐 . Thus, he
iboelec ic- ela ed ol age d op ∆𝐕𝐀 a he ampli ie inpu can be modelled as an
Senso s 2024, 24, 6363 7 o 20
addi i e, pu ely di e en ial mode ol age, added o he biopo en ial signal o in e es . I
is wo h no ing ha his addi i e signal will be ampli ied by he di e en ial gain which
possibly leads o a ele an con amina ion o he eco ded EEG signals.
Figu e 5. Model o wo adjacen cables connec ing EEG elec odes o he ampli ie . (A) Schema ic
ep esen a ion o he c oss-sec ion o wo unipola cables sepa a ed by a dis ance 𝐝𝐀 in a medium
(ai , dielec ic cons an 𝛆𝐀). Each cable is composed o a conduc i e wi e ( esis i i y ρ) embedded
in an insula o shea h ( hickness 𝐝𝐢, dielec ic cons an 𝛆𝐫) (B) Equi alen elec ical model o wo
adjacen cables, whe e 𝑹𝒄𝟏,𝟐 ep esen he elec ical esis ances o he conduc i e lead, 𝐂𝐢𝟏,𝟐 model
he pa asi ic capaci ances due o he cable insula o laye and 𝐂𝐀 depic s he elec ical capaci ance
due o he dielec ic 𝛆𝐀. The ed dashed ec angle indica es he simpli ied elec ical model (≃𝐂𝐀).
3.3. A i ac s Rela ed o he Elec ode-Ampli ie Sys em P ope ies Leading o PLI Modula ion
Figu e 6 shows he elec ical model ep esen ing he pa asi ic coupling be ween a
subjec , he powe line, and he elec ode-ampli ie sys em. I is used o model he PLI
modula ion phenomena as a sou ce o mo emen a i ac s in case o a esidual amoun o
PLI a he inpu o he biopo en ial acquisi ion chain. G ound- loa ing ins umen a ion
and monopola elec ode con igu a ion a e ep esen ed oge he wi h a common mode
exci a ion due o pa asi ic coupling be ween he subjec and he powe line [32–35]. I is
well known ha he deg ee o PLI a ec ing biopo en ials depends on he common-mode
ol age a he inpu o he elec ode-ampli ie sys em. This ol age is mainly due o he
pa asi ic capaci i e coupling be ween he subjec , he powe line sou ce and he g ound,
and o he coupling be ween he on -end e e ence and he powe line g ound. Wi h
e e ence o Figu e 6A: 𝑪𝟏 ( ypically anging om 5 pF o 20 pF [21]) ep esen s he
pa asi ic capaci i e coupling be ween he subjec and he ac i e phase o he powe line
[30]; 𝑪𝟐 (~50 pF o 10 nF [21]) models he pa asi ic capaci i e coupling be ween he subjec
and he powe line g ound [21,36]; 𝑪𝒑 ep esen s he pa asi ic coupling be ween he
on -end ampli ie e e ence and he powe line g ound and i anges be ween en pF and
hund eds o pico-Fa ads [28,30,36]. The model o Figu e 6 also includes 𝑽𝑷𝑳 modelling
he common mode exci a ion (i.e., powe line sou ce), 𝑹𝒆𝟏 and 𝑹𝒆𝟐 ep esen ing he
esis i e componen s o he impedance models o he explo ing elec odes and he inpu
esis ances o he on -end ampli ie (𝑹𝒊) [28,37]. Gi en hese assump ions, he common
mode ol age a he inpu o he elec odes-ampli ie sys em 𝑽𝑪 can be compu ed
h ough he The enin equi alen ci cui ex ac ed om he elec ical model o he powe
line- elec ode-ampli ie sys em (Figu e 6B). Whe e:
{
𝑽𝒆𝒒=𝑽𝑷𝑳 𝑪𝟏
𝑪𝟏+𝑪𝟐
𝑪𝒆𝒒=(𝑪𝟏+𝑪𝟐)𝑪𝒑
𝑪𝟏+𝑪𝟐+𝑪𝒑
𝑹𝒆𝒒=(𝑹𝒆𝟐+𝑹𝒊)⨁(𝑹𝒆𝟐+𝑹𝒊)
(4)
Addi ional simpli ica ions can be con enien ly in oduced. Indeed, he inpu
impedance o he on -end ampli ie ci cui 𝑹𝒊 is in he o de o Mega-Ohms, a leas
Senso s 2024, 24, 6363 8 o 20
h ee o de s o magni ude g ea e han he elec ode-skin impedance 𝑹𝒆 ( ens o kΩ i
1cm2 Ag/AgCl a e used) [21]. The e o e, since 𝑹𝒊≫𝑹𝒆, he equi alen esis ance o he
The enin elec ical ci cui is gi en by 𝑹𝒆𝒒≅𝑹𝒊
𝟐. Speci ically, when conside ing a ealis ic
EEG eco ding unde a mul ichannel con igu a ion (i.e., 𝑹𝒆𝑵 wi h N anging om 8 o
128 channels) and conside ing he common monopola con igu a ion ha ing he in e ing
inpu sha ed be ween he channels, he o al esis ance a he monopola e e ence inpu
is ob ained as he pa allel o all he inpu esis ances o each channel, i.e., 𝑹𝒆𝒒 ≅𝑹𝒊
𝑵 .
Fu he mo e, in p ac ice, i is gene ally possible o educe he common-mode inpu
ol age 𝑽𝑪 by minimizing he alue o he pa asi ic coupling 𝑪𝒑 be ween he ampli ie ’s
e e ence and he g ound. This esul may be ob ained by designing ba e y powe ed,
g ound- loa ing, and minia u ized sys ems [22,38]. The e o e, he mos common case
wi hin he p esen disse a ion con ex leads o 𝑪𝒆𝒒 ≅𝑪𝒑 since 𝑪𝒑 domina es o e he
combina ion o 𝑪𝟏+𝑪𝟐. Unde hese assump ions, he magni ude o he common mode
ol age ans e unc ion a he inpu o he elec odes-ampli ie sys em 𝑽𝒄 esul s:
|𝑽𝑪|=𝑽𝒆𝒒 𝝎𝑹𝒊
𝑵𝑪𝒑
√𝟏+(𝝎𝑹𝒊
𝑵𝑪𝒑)𝟐
(5)
whe e N is he numbe o EEG channels. Gi en hese conside a ions on he common mode
inpu ol age 𝑽𝑪 , i is well-known [21] ha i is con e ed in o a di e en ial ol age
𝑽𝑰𝑹𝑵𝟓𝟎 acco ding o (6):
𝑽𝑰𝑹𝑵𝟓𝟎=𝑽𝑪(𝑹𝒆𝑵−𝑹𝒆𝟏
𝑹𝒊+𝟏
𝑪𝑴𝑹𝑹)
(6)
whe e he e m (𝑹𝒆𝑵−𝑹𝒆𝟏 ) is he in e elec ode-skin impedances imbalance, Ri and
CMRR a e he ampli ie ’s inpu esis ance and he common mode ejec ion a io (CMRR)
espec i ely. Equa ion (6) enables p ac ical conside a ions ega ding he phenomenon o
he mo emen - ela ed modula ion o 𝑽𝑰𝑹𝑵𝟓𝟎 desc ibed in Sec ion 2.3. Indeed, 𝑽𝑰𝑹𝑵𝟓𝟎
depends on:
• The common mode inpu ol age (𝑽𝑪 ), which depends on bo h he design o he
ampli ie (i.e., 𝑹𝒊 in cases in which a hi d ze o- ol e e ence elec ode is no used,
CP, e c.) and on he expe imen al se up adop ed du ing he eco dings (i.e.,
elec odes p epa a ion, coupling be ween he subjec and he powe line, e c.). Thus,
i can a y acco ding o he mo emen s pe o med du ing he eco dings. Howe e ,
a a ying common mode ol age is unlikely he cause o mo emen a i ac s as i s
a ia ion would ha e an e ec , al hough po en ially di e en , on all he channels and
could consequen ly be emo ed e.g., h ough a common a e age o line e e encing.
• The common mode ejec ion a io (CMRR) o he ampli ie and he inpu ampli ie
esis ance (𝑹𝒊), a e, in u n, dependen on he design o he on -end ampli ie . As a
esul , no mo emen -dependen changes on he CMRR no on 𝑹𝒊 a e expec ed o
occu and he e o e i canno be he cause hinde ing he a ia ion o he 𝑽𝑰𝑹𝑵𝟓𝟎 when
a cons an 𝑽𝑪 is applied.
• The elec odes-skin esis ances imbalance (∆𝑹𝒆). This pa ame e is he only one ha
can explain he obse ed modula ion o powe line in e e ence on speci ic channels.
Indeed, a a single channel le el, he elec odes-skin esis ance imbalance is ob ained
om he ela i e di e ence be ween he esis ance o he explo ing elec ode and he
one aken as a e e ence o he monopola signal de ec ion ∆𝑹𝒆=𝑹𝒆𝑵−𝑹𝒆𝟏. When
pe o ming a mo emen , he single alues o elec ode impedances may be a ec ed
by he changes caused by al e a ion o he skin-elec ode con ac due o e.g.,
ecip ocal mo emen s be ween he elec ode and he skin, hus s ongly con ibu ing
o he con e sion o he common mode exci a ion o a di e en ial one.
Senso s 2024, 24, 6363 15 o 20
Figu e 12. Boxplo o RMS ampli ude alues o 30 EEG signals eco ded wi h he ou elec ode
sys ems du ing es , eadmill walking, and jogging. * p < 0.05 ob ained wi h one-way ANOVA
(Tukey pos -hoc co ec ion).
Figu e 13 ep esen s he ku osis alues dis ibu ions and hei coe icien s o
a ia ion calcula ed on he 30 EEG signals wi h he ou elec ode sys ems in all he
pe o med asks. Acco ding o ou hypo heses, he g ea e he ask dynamics and he
esul ing cable mo emen s, he mo e he e ogeneous he ampli ude signal dis ibu ion
because o a highe occu ence o spike-like a i ac s. The e o e, he highes RMS alues
accompanied by he g ea es a ia ion coe icien s o he ku osis alues we e expec ed o
signals eco ded h ough cabled elec ode sys ems du ing he jogging ask. In line wi h
hese expec a ions, al hough i is no possible o obus ly disen angle cable and elec ode
e ec s in he expe imen al p ac ice as hey bo h con ibu e o an o e all inc ease o he
eco ded signal ampli udes, hese obse a ions sugges ha he mos disc imina ing
ac o in luencing he EEG signals ampli ude is he mo emen o he cables. Indeed,
Figu es 12 and 13 demons a ed ha STN and Lobs e -w caps (i.e., cabled) showed on
a e age highe RMS ampli udes wi h a wide dis ibu ion acco ding o he inc ease o
ask dynamics.
.
Figu e 13. Top panel: iolin plo s displaying he median alues o ku osis compu ed o e 1-s
epochs o 30 EEG signals eco ded h ough he ou elec ode sys ems in all he pe o med asks.
Bo om panel: ba diag ams o coe icien s o a ia ion (CV) o ku osis alues o e he EEG elec-
odes in all he pe o med asks.

Senso s 2024, 24, 6363 16 o 20
Figu e 14 shows he co ical esponses a e aged wi h espec o he igh heel s ikes
ac oss s ides (n = 54 walking, n = 70 jogging) conside ing he mos cohe en channels wi h
head accele a ion du ing walking and jogging. Al hough di e en mo phologies o
co ical esponses (e.g., e en showing di e en pola i ies) migh occu a he in a-
elec ode le el, we ound mo ion a i ac s ime-locked o he heel s ikes, wi h high in a-
elec ode epea abili y. In line wi h ou expec a ions and discussions a he elec ical
modelling le el, highe peak- o-peak ampli ude alues we e ob ained o he co ical
esponses eco ded wi h he ET cap when compa ed o he Lobs e cap (24.70 μV s. 7.23
μV and 46.03 μV s. 7.64 μV espec i ely du ing walking and jogging).
Figu e 14. A e aged co ical esponses wi h espec o he igh heel s ike onse we e ob ained om
EEG signals eco ded h ough he ET cap (blue aces) and he Lobs e cap ( iole aces) du ing
walking and jogging mo o asks. Only he mos 6 cohe en EEG signals wi h he head accele a ion
a e displayed.
6. Discussion and Conclusions
The p esen s udy del ed in o he in es iga ion o he genesis o mo ion a i ac s col-
lec ed du ing dynamic EEG eco dings. An in-dep h analysis o he unde lying phenom-
ena h ough elec ical models and expe imen al es s has been pe o med. Gi en he a ail-
abili y o minia u ized and wi eless EEG acquisi ion sys ems, he analy ical app oach
highligh ed wo esidual si es esponsible o mo ion a i ac s con amina ion o EEG sig-
nals: (i) he connec ing cables be ween he elec odes and he ampli ie and (ii) he sudden
changes o elec ode-skin impedance due o he elec odes mo emen s. I is wo h no ing
ha he conduc ed expe imen al se up was no in ended o sepa a ely in es iga e he an-
aly ically desc ibed sou ces o mo ion a i ac s. Indeed, i is unlikely o expe imen ally
disen angle he main causes o mo ion a i ac s as a combined e ec o cables and elec-
odes is expec ed o occu . Ne e heless, he expe imen al esul s showed ha minimiz-
ing he leng h o he EEG elec ode sys ems connec ing cables and ensu ing s able elec-
ode con ac s mi iga es he EEG signal mo ion a i ac s. The e o e, his ou come con ib-
u ed o endo sing he analy ical s udy o he phenomena hinde ing he genesis o EEG
mo ion a i ac s.
The obse ed case s udy was pe o med only on a single subjec . Al hough his may
be conside ed a possible limi a ion o he expe imen al pa o his wo k, i is impo an
o unde line ha he aim o he s udy is no o s udy he collec ion o mo emen a i ac s
among a popula ion, bu a he o alida e a possible elec ical modelling amewo k al-
lowing o be e unde s and possible sou ces o mo ion a i ac s du ing EEG signals col-
lec ion. The e o e, he p ima y aim o he s udy was o collec a se o EEG signals, wi hou
conside a ion o he physiological esponse unde lying he s udied asks ha would e-
qui e a popula ion o subjec s.
Two cus omized EEG elec ode sys ems ha e been designed and p oposed. Da a
analysis on EEG eco ded du ing dynamic asks (i.e., walking and jogging) expe imen-
ally demons a ed ha when he mo emen s o bo h cables and elec odes a e
Senso s 2024, 24, 6363 17 o 20
minimized, i is possible o eco d high-quali y EEG signals e en du ing dynamic mo e-
men s. In ligh o wha was ob ained, p ac ical conside a ions can be d awn up when deal-
ing wi h EEG acquisi ion du ing mo emen s:
• Ampli ie echnology: he s a e-o -a echnology on minia u ized and wi eless EEG
acquisi ion sys ems seems o e icien ly add ess he need o ligh weigh echnology
allowing o enough eedom o mo emen while eco ding b ain signals [2,3,44]. In
his ega d, he use o ac i e elec odes in he sys em elec onics is in insically
demons a ed no o p o ide an app eciable con ibu ion in e ms o mi iga ing mo-
ion a i ac con amina ion on EEG signals. Indeed, hei main con ibu ion is o e-
duce he e ec o capaci i e coupling occu ing downs eam o he elec odes (e.g.,
pa asi ic capaci i e coupling be ween connec ing cables and powe lines) [30]. On he
con a y, hei implemen a ion becomes ine ec ual owa ds elec ode impedance im-
balances occu ing ups eam he elec odes (i.e., ∆𝒁𝒆 om (2)). This inding is in line
wi h wha was shown by Laszlo e al. [14] who expe imen ally showed ha du ing
apid ol age luc ua ions ac i e elec odes a e equally a ec ed by mo emen a i-
ac s ela ed o changes a he elec ode-skin in e ace wi h espec o passi e elec-
odes. Con e sely, he undesi ed esul o using ac i e elec odes in such con ex s is
he inc ease o he o al sys em encumb ance and powe consump ion, hus con-
as ing wi h he need o de elop minia u ized ins umen a ion.
• Se up p epa a ion: Gi en ha an ad-hoc p epa a ion o he elec ode si es is manda-
o y o ensu e simila elec ode-skin impedances magni ude among all he channels
(i.e., o minimize ∆𝒁𝒆 o (2) and (6)), i is also p e e able o ensu e a s able skin con-
ac by a oiding empo a y and b isk skin-elec odes de achmen s causing sudden
elec odes impedance changes. This conside a ion applies also when dealing wi h he
monopola e e ence elec ode as i a ec s all he eco ded signals. The e o e, good
p ac ice ecommenda ions ega d he use o adhesi e monopola e e ence elec-
odes, p e e ably placed in body egions wi h limi ed mo emen s (i.e., ea lobe). This
is pa icula ly impo an when eco ding elec ophysiological signals unde a mono-
pola signal con igu a ion as pe u ba ions addi i ely in e e ing wi h he e e ence
signal would a ec all he channels. I could be ha d o comple ely il e ou hese
undesi ed pe u ba ions e.g., by applying a common a e age il e ing due o he su-
pe imposi ion o mul iple con ounding ac o s (i.e., addi i e noise, mo ion a i ac s,
e c.) simul aneously occu ing a he le el o explo ing elec odes. In his ega d, pa -
icula a en ion should be paid when applying e- e e encing echniques, conside -
ing also possible p ocessing- ela ed needs [43].
• Cap echnology: he choice o he EEG elec ode sys em has a non-negligible in lu-
ence on he quali y o he collec ed signals in e ms o mo ion a i ac con amina ion.
Indeed, as expe imen ally sugges ed by he p oposed case s udy, he ideal case
would be o keep he elec odes as ixed as possible such as in he case o he Lobs e
Cap. Howe e , his ype o solu ion, al hough op imal in e ms o he quali y o col-
lec ed signals, holds in insic limi a ions om he applicabili y poin o iew: (i) i is
usable only on ei he bald o sho -hai ed subjec s and (ii) i migh equi e longe
p epa a ion imes. Howe e , conside ing he need o minimiza ion o he connec -
ing cable leng h and ela ed ecip ocal mo emen s o mi iga e he e ec s o iboelec-
ic- ela ed phenomena, embedding he connec ing cables in o he ab ic o he cap
o elec odes such as in he ET Cap could be a good comp omise be ween usabili y
and pe o mance needs. Fu he echnological ad ancemen s should he e o e ocus
on he ansduc ion s age o he biopo en ials ampli ica ion chain such as he elec-
ode echnology and i s in e acing o he acquisi ion sys em.
Al hough he p esen s udy ocused on EEG signals du ing mo emen s gi en hei
g ea clinical signi icance and ela i ely low signal- o-noise a io, simila conside a ions
may be applied o any biopo en ial acqui ed h ough su ace elec odes.
Senso s 2024, 24, 6363 18 o 20
In conclusion, he wo k p esen ed he ein cons i u es a solid and widesp ead ame-
wo k o modelling and unde s anding bio-elec ical phenomena unde lying he collec-
ion o mo ion a i ac s du ing dynamic EEG. The insigh s, explana ions and indings om
his wo k could signi ican ly con ibu e o d i ing echnological de elopmen s and guide
expe imen al se up p ac ices in he ield o dynamic EEG acquisi ions.
7. Pa en
An I alian pa en applica ion has been p oposed by Poli ecnico di To ino o he ET
Cap desc ibed in his s udy. All he au ho s ha e been ecognized as in en o s.
Au ho Con ibu ions: A.G.: concep ualiza ion; da a collec ion; me hodology; da a analysis; da a
isualiza ion and in e p e a ion; w i ing-o iginal d a . A.B.: concep ualiza ion; me hodology; da a
analysis; da a isualiza ion and in e p e a ion; w i ing-o iginal d a . H.P.: concep ualiza ion; me h-
odology; supe ision. G.L.C.: concep ualiza ion; da a collec ion; esou ces; me hodology; da a is-
ualiza ion and in e p e a ion supe ision; w i ing-o iginal d a , supe ision. All au ho s ha e ead
and ag eed o he published e sion o he manusc ip .
Funding: The s udy was suppo ed by he Academy o Finland g an (#296240) o H.P. and PhD
schola ships p omo ed by Poli ecnico di To ino (090804, DET-Senso imo o in eg a ion and co ico-
muscula coupling) and he Facul y o Spo s and Heal h Sciences o he Uni e si y o Jy äskylä o
A.G (Feb ua y-Decembe 2024). G.L.C. holds a JYU ellowship g an om Feb ua y 2023 o Oc obe
2023 (1643/13.00.05.00/2022) p omo ed by he JYU Visi ing Fellow P og amme G an 2023.
Ins i u ional Re iew Boa d S a emen : The s udy was conduc ed in acco dance wi h he Decla a-
ion o Helsinki, and app o ed by he E hics Commi ee o he Uni e si y o Jy äskylä (app o al
numbe : 369/13.00.04.00/2020).
In o med Consen S a emen : In o med consen was ob ained om he subjec in ol ed in he
s udy.
Da a A ailabili y S a emen : The da a a e no publicly a ailable due o p i acy o e hical e-
s ic ions. Howe e , da a a e a ailable upon eques om he co esponding au ho .
Con lic s o In e es : A.B. and G.L.C. a e in ol ed in he ac i i ies o ReC Bioenginee ing Labo a o-
ies, a spin-o o he Labo a o y o Enginee ing o he Neu omuscula Sys em (Poli ecnico di To-
ino, I aly), which p oduces and comme cializes de ices o neu omuscula sys em assessmen . The
indings desc ibed in his pape a e o gene al in e es in he ield o biomedical ins umen a ion
and a e no in ended o p omo e o ad e ise any p oduc o se ices o he company.
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