Motion Artifacts in Dynamic EEG Recordings : Experimental Observations, Electrical Modelling, and Design Considerations

This is a sel -a chi ed e sion o an o iginal a icle. This e sion may di e om he o iginal in pagina ion and ypog aphic de ails. Au ho (s): Ti le: Yea : Ve sion: Copy igh : Righ s: Righ s u l: Please ci e he o iginal e sion: CC BY 4.0 h ps://c ea i ecommons.o g/licenses/by/4.0/ 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. Re e ences 1. Gwin, J.T.; G amann, K.; Makeig, S.; Fe is, D.P. Remo al o mo emen a i ac om high-densi y EEG eco ded du ing walking and unning. J. Neu ophysiol. 2010, 103, 3526–3534. h ps://doi.o g/10.1152/jn.00105.2010. 2. Ce one, G.L.; Giang ande, A.; Ghislie i, M.; Gazzoni, M.; Pii ulainen, H.; Bo e , A. 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