Unipolar Electrogram Eigenvalue Distribution Analysis for the Identification of Atrial Fibrosis

Unipola Elec og am Eigen alue Dis ibu ion Analysis o he Iden i ica ion o A ial Fib osis Jenni e Riccio1, Sa a Roche 2, Lau a Ma ´ ınez-Ma eu2, Alejand o Alcaine3,1, Ja ie Saiz2, Juan Pablo Ma ´ ınez1,3, Pablo Laguna1,3 1BSICoS, I3A, IIS A ag´ on, Uni e sidad de Za agoza, Za agoza, Spain 2Ci2B, Uni e si a Poli ` ecnica de Val` encia, Valencia, Spain 3CIBER en Bioingenie ´ ıa, Bioma e iales y Nanomedicina (CIBER-BBN), Spain Abs ac A ial ib osis plays an impo an ole in he pa hogene- sis o a ial ib illa ion (AF). Low bipola elec og ams (b- EGMs) peak- o-peak ol age a eas indica e sca issue and a e conside ed a ge s o AF subs a e abla ion. Howe e , his app oach igno es he spa io empo al in o ma ion em- bedded in he signal and he dependence o b-EGMs on ca he e o ien a ion. This wo k p oposes an app oach o de ec ib osis based on he eigen alue dominance a io (EIGDR) in an ensemble (clique) o unipola elec og ams (u-EGMs). A 2-D issue wi h a cen al ci cula pa ch o ib osis has been simula ed using he Cou emanche cellu- la model. Maps o EIGDR ha e been compu ed using wo sizes o elec ode cliques, om he o iginal u-EGMs wi hin he ensemble o a e a ime alignmen o hese signals. Pe o mance o each map in de ec ing ib osis has been e alua ed using ecei e ope a ing cha ac e is ic cu es and de ec ion accu acy. Bes esul s achie e an a ea un- de he cu e (AUC) o 0.98 and an accu acy (ACC) o 1 when we use as ma ke he gain in eigen alue dominance p oduced by he ensemble alignmen . 1. In oduc ion A ial ib osis ep esen s a s uc u al abno mali y o he a ium, which al e s he elec ical conduc ion and ex- ci abili y o he issue. Fib oblas s p oli e a ion and hei sec e ion o ex acellula ma ix p o eins, such as collagen, cha ac e ize ib o ic issue [1]. These p o eins a e mainly in ol ed in he epa a i e p ocess o eplace damaged my- oca dial pa enchyma [2]. A ial ib osis is obse ed o be closely ela ed o a ial ib illa ion (AF), e en i hei causal ela ionship is s ill challenging [3]. On he one hand, an ex ensi e ib o ic p ocess in he a ium can p omo e pe sis en AF [3]; on he o he hand, s uc u al a ial emodeling ound in AF p oduces ib osis and al e s issue unc ion [2]. Elec o- physiologically, a ial ib osis p oduces low- ol age in ac- a diac elec og ams (EGMs), which can be iden i ied us- ing elec oana omical mapping (EAM) [4]. Peak- o-peak bipola ol age maps can be cons uc ed h ough da a ob- ained du ing subs a e mapping [5], being bipola ol age an in e es ing ma ke du ing sinus hy hm (SR) as well as in AF. Low- ol age a eas a e ypically de ined as hose wi h peak- o-peak bipola ol age below 0.5 mV du ing SR. Howe e , some d awbacks o his p ocedu e should be pu in e idence. Fi s , peak- o-peak ol age measu e does no p o ide in o ma ion abou mo phological ea u es o empo al end embedded in he signal; he e o e, ol age h esholding does no ake in o accoun he p esence o un- de lying abno mali ies in he a ia. Second, he me hod- ology o de ine low ol age a eas has no been s anda d- ised [6]. Thi d, spa ial he e ogenei y is no accoun ed o . Fou h, low bipola ol age can also be in luenced by o he ac o s han ib osis, such as ac i a ion di ec ion, elec ode size, in e elec ode dis ance and il e ing [4], [6], as well as by echnical p oblems such as poo elec ode con ac in ana omically di icul si es (e.g. he pulmona y eins) o i s ins abili y in ime. In o de o o e come hese limi a ions, in his wo k we p opose he dominan - o- emaining eigen alue dominance a io (EIGDR) o unipola EGMs (u-EGMs) as a measu e o he ol age wa e on oughness and co ela e i wi h he p esence o ib osis. We compu e maps o eigen alues a ios conside ing wo di e en elec ode clique a ange- men s (ECA) and we e alua ed he abili y o each map o de ec a ib osis pa ch in he con ex o a simula ion s udy. Maps ha e been c ea ed om he whole leng h o u-EGMs, using 0oand 45oca he e o ien a ions wi h espec o he wa e on p opaga ion. 2. Ma e ials A 2-D a ial issue o 4x4 cm o hexahed ic elemen s simula ed wi h 100 µm esolu ion using he Cou emanche Compu ing in Ca diology 2020; Vol 47 Page 1 ISSN: 2325-887X DOI: 10.22489/CinC.2020.434 cellula model [7] has been used. Conduc ion he e ogene- i y induced by ch onic AF in le a ium has been consid- e ed in he model. The simula ed issue includes a ci cula pa ch o di use ib osis ha ing a diame e o 2 cm, whe e 20% nodes ha e andomly been assigned he Malecka model o ib oblas s [8] and a conduc i i y educ ion o 30%. Le xk(n)be he u-EGMs compu ed wi h a sampling equency o 1 kHz a a high-densi y mul i-elec ode a ay (MEA) o 15×15 elec odes, k∈ {1,...,225}, loca ed a si es (i, j), i, j ∈ {1, .., 15}. The MEA has an in e - elec ode dis ance d= 2 mm, is cen e ed in he issue slice and loca ed a 1 mm dis ance om he issue su ace. Each simula ed u-EGM is 500 ms long and con ains a single ac- i a ion (depola iza ion plus epola iza ion) co esponding o one sinus bea . 3. Me hods 3.1. Eigen alue analysis In his wo k, we p opose and assess EIGDR om u- EGMs a each 3×3 and 2×2 clique om he MEA, as ib osis ma ke s. Eigen alues we e ob ained om he spa ial co a iance ma ix o bo h o iginal and aligned u- EGMs wi hin clique ensembles. Signals ha e been aligned as p oposed in [9], acco ding o he maximum c oss- co ela ion wi h espec o he highes ampli ude u-EGM. Fo each elec odes clique, he a io Ro he dominan - o- emaining eigen alues, compu ed as: R=λ1 PK k=2 λk ,(1) whe e Kis he numbe o u-EGMs xk(n)in he clique ensemble (4 o 9 in his s udy), is es ima ed o quan i y EIGDR. Fo a heo e ical analysis o EIGDR, he model xk(n) = αks(n−τk) + k(n) + k(n)(2) is conside ed o he u-EGMs xk(n)a he k h elec ode, whe e s(n)is he clean and space in a ian u-EGM in he case o a plane wa e p opaga ion, τkis he delay o he k h u-EGM s(n−τk)wi h espec o he ime e e ence in he ensemble, αkis a pa ame e accoun ing o u-EGM ampli- ude (dec eased a ib osis, αk<1, wi h espec o no mal issue, αk= 1), k(n) ep esen s he u-EGM ib o ic com- ponen (absen in no mal issue), and k(n)is he noise componen o he k h u-EGM. The ene gy o s(n)is de- no ed by Es, and Es0 ep esen s he ene gy o i s de i a i e s0(n). The delays τka e cha ac e ized by hei a iance, β2σ2 θ, wi h β > 1 in ib osis, a ac o accoun ing in e sely o ib osis gene a ed speed educ ion ela i e o no mal issue whe e β=1. αkis modelled as andom a iable wi h mean E[αk] = αand a iance σ2 α. Noise is con- side ed o be ze o-mean, Gaussian, whi e and unco ela ed wi h τkand k(n), wi h a iance σ2 . The a iance o he ze o-mean ib o ic componen ac oss clique elec odes is deno ed by σ2 . Fou u-EGMs scena ios o non-aligned (NA) and aligned (A) u-EGMs a non- ib o ic (NF) and ib o ic (F) a eas a e conside ed and hei app oxima e heo e ical eigen alues a e de i ed acco ding o he p ocedu e p e- sen ed in [10]. Table 1 shows he eigen alues λkand EIGDR o he ou scena ios. Fib osis ma ke s: •F om he de i a ions in equa ions p esen ed in Table 1, i is clea ha R>RF, as esul o h ee concomi an e - ec s appea ing simul aneously a ib osis: a) highe mo - phology dispe sion, σ2 , b) lowe ampli ude, α < 1, and c) la ge delays esul ing in la ge misalignmen dispe sion β > 1. Then Ris p oposed as one ma ke o ib osis de ec ion. •Simila ly, o he same wo i s easons, i also esul s ha RA>RA F, sugges ing RAas o he ib osis de ec ion ma ke . •Analyzing he a io ∆RFbe ween EIGDR in non- ib o ic a eas wi h espec o ib o ic ones, ep esen ing he eigen alue concen a ion los by ib osis, and hen a mea- su e o he sepa abili y powe o RFas a ma ke o ib o- sis, we ob ain o misaligned u-EGMs, σ2 θ>0: ∆RF=R RF ≈β2σ2 θEs0+N(σ2 +σ2 ) (α2+σ2 α) σ2 θEs0+Nσ2 .(3) To e alua e how ∆RF a ies wi h he le el o misalign- men σ2 θwe pe o m he de i a i e, ob aining: ∂∆RF ∂σ2 θ ≈ −Es0Nσ2 +σ2 1−β2α2+σ2 α α2+σ2 α(σ2 θEs0+Nσ2 )2. (4) The e m 1−β2α2+σ2 α is ypically >0since in i- b osis βcan ge alues up o 2 and αup o 1/8 [11], esul - ing ha ∂∆RF ∂σ2 θ <0, jus i ying he ad an age o alignmen , since he highe he misalignmen σ2 θ, he lowe he sepa a- bili y capaci y o RF o disc imina e be ween ib osis and non- ib osis, sugges ing ha RA Fis be e sui ed ma ke han RF. •Al e na i ely, he a io ∆RAbe ween EIGDR be o e and a e alignmen , ep esen ing he gain in eigen alue concen a ion p oduced by he ensemble alignmen , is con- side ed. In he case o ib osis, i is eached he alue: ∆RA=RA F RF ≈ Esβ2σ2 θα2+σ2 αEs0+N(σ2 +σ2 ) N(σ2 +σ2 )(Es−β2σ2 θEs0) . (5) To e alua e how ∆RA a ies wi h he le el o ib osis σ2 we also pe o m he de i a i e, ob aining: Page 2 u-EGM model λkEIGDR NA, NF xk(n) = s(n−τk) + k(n)λk≈   (Es−σ2 θEs0)K/N +σ2 , k = 1; σ2 θEs0K/N +σ2 , k = 2; σ2 , k = 3,...,K, R ≈ Es−σ2 θEs0 σ2 θEs0+Nσ2 . A, NF xk(n) = s(n) + k(n)λk≈EsK/N +σ2 , k = 1; σ2 , k = 2,...,K, RA≈Es Nσ2 . NA, F xk(n)=αks(n−τk)+ k(n)+ k(n)λk≈     α2+σ2 α(Es−β2σ2 θEs0)K/N +σ2 +σ2 , k = 1; α2+σ2 αβ2σ2 θEs0K/N +σ2 +σ2 , k = 2; σ2 +σ2 , k = 3, ., K RF≈Es−β2σ2 θEs0 β2σ2 θEs0+ N(σ2 +σ2 ) (α2+σ2 α) A, F xk(n) = αks(n) + k(n) + k(n)λk≈(α2+σ2 αEsK/N +σ2 +σ2 , k = 1; σ2 +σ2 , k = 2,...,K, RA F≈Es N(σ2 +σ2 ) (α2+σ2 α) . Table 1: Models o non-aligned (NA) and aligned (A) u-EGMs a non- ib o ic (NF) and ib o ic (F) a eas, wi h hei espec i e eigen alues λkand eigen alue dominance a ios EIGDR compu ed ollowing he p ocedu e p esen ed in [10] ∂∆RA ∂σ2 ≈−EsNβ2σ2 θα2+σ2 αEs0 N(σ2 +σ2 )2(Es−β2σ2 θEs0) .(6) Since o small delays τk,Esβ2σ2 θEs0i esul s ha ∂∆RA ∂σ2 <0, making his ma ke ∆RAbecoming smalle he highe he ib o ic componen σ2 , jus i ying o conside i as a po en ial ib osis ma ke . Also, ∂∆RA ∂α2>0, so he la ge he ib osis, ( educed α2), he u he ge s ∆RA e- duced. Howe e , ∂∆RA ∂β2>0, and since βinc eases in ib osis, i esul s in a coun e ac ing e ec o he ma ke sensi i i y o ib osis. Since ib osis e ec s on u-EGM am- pli ude, α2, and mo phology, σ2 , a e much mo e ma ked han on conduc ion eloci y, β2, [11], i is expec ed ha he i s wo endencies domina e, making he ma ke ∆RA o educe wi h ib osis. Simula ion and eal expe imen s can elucida e he beha iou in p ac ice. 3.2. Assessmen o R,RAand ∆RA o i- b osis de ec ion Maps o R,RAand ∆RAha e been c ea ed p ocess- ing he comple e MEA wi h he elec ode lines in wo o i- en a ions wi h espec o he wa e o m p opaga ion di ec- ion, pa allel (0o) and oblique (45o) and wo ECA (3×3 and 2×2). The 3×3ECA p o ides one EIGDR o each squa ed g oup o nine elec odes wi h diagonal e ices a (i, j), and (i+2, j+2), i, j ∈ {1,...,13}, gi ing a o al o 13 ×13 pixel maps o ma ke s R,RAo ∆RA. The 2×2 ECA p o ides alues a each squa ed g oup o ou elec- odes wi h diagonal e ices a (i, j)and (i+ 1, j + 1), esul ing in maps o 14 ×14 pixels, i, j ∈ {1,...,14}. Recei e ope a ing cha ac e is ic (ROC) cu es ha e been used o e alua e he ma ke s abili y in disc imina ing i- b o ic om non- ib o ic a eas. Fo ha pu pose, a g ound u h mask has been c ea ed labelling hese a eas. Cliques lying in he issue in e ace, i.e., in he line sepa a ing he ib o ic pa ch om non- ib o ic issue, we e no conside ed in he e alua ion. Fo each map, h esholds o ib osis iden i ica ion ha e been a ied o compu e he ROC cu e. The a ea unde he cu e (AUC) and he maximum accu- acy (ACC) ha e been compu ed o each map, as a mea- su e o he abili y o he ma ke o de ec ib osis. AUC/ACC Clique Angle R RA∆RA 3×30o0.88/0.86 0.96/0.95 0.97/0.95 45o0.77/0.75 0.96/0.93 0.98/1 2×20o0.84/0.80 0.85/0.79 0.72/0.70 45o0.76/0.71 0.96/0.93 0.94/0.89 Table 2: AUC and ACC o he h ee di e en me ics 4. Resul s Figu e 1 shows he mean and s anda d de ia ion (SD) o each s udied ma ke R,RAand ∆RAa ib o ic and heal hy simula ed issues, using 2×2 o 3×3 cliques. The h ee ma ke s we e signi ican ly lowe in he heal hy han in he ib o ic issue (Wilcoxon ank-sum es , p < 0.05). RAp esen s he highe a io o ib o ic o heal hy is- sue γ= 2.66 (2.51) o 3×3 (2×2) cliques, being ∆RA he ma ke wi h mo e signi ican di e ences be ween bo h ypes o issue (p < 0.05). Table 2 con ains AUC and ACC o he ma ke s consid- e ed. Resul s show highe alues when ime alignmen o u-EGMs is pe o med, especially when MEA has an o ien- a ion o 45owi h espec o he wa e on di ec ion. The bes disc imina ion powe is ob ained by ∆RA, wi h AUC = 0.97 (0.98) o pa allel (diagonal, whe e ACC = 1) o i- en a ion, using 3×3ECA. Figu e 2 shows he maps o R, RAand ∆RAob ained wi h 3×3 ECA and wi h pa allel ca he e o ien a ion. In he lowe panels, he de ec ed i- b o ic a eas a e shown, using he h esholds ha maximize he de ec ion accu acy o each ma ke . 5. Discussion and Conclusions In his wo k, he eigen alue dominance a ios, EIGDR, o u-EGMs ha e been p oposed and e alua ed using a sim- Page 3 3x3 2x2 0 5 10 15 20 F NF 3x3 2x2 0 100 200 300 400 F NF 3x3 2x2 0 5 10 15 20 25 F NF = 1.72 = 1.56 = 2.51 = 2.66 = 1.49 = 1.55 R RA∆RA Figu e 1: EIGDR ma ke s (R,RAand ∆RA) mean and SD om he wo cliques, 3×3 and 2×2, conside ing bo h MEA o ien a ions, 0oand 45o.γis he ac o ela ing he mean om ib o ic o non- ib o ic a eas o each ma ke and clique size. 0 1 2 3 4 5 6 7 8 9 10111213 0 1 2 3 4 5 6 7 8 9 10 11 12 13 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10111213 0 1 2 3 4 5 6 7 8 9 10 11 12 13 40 60 80 100 120 140 0 1 2 3 4 5 6 7 8 9 10111213 0 1 2 3 4 5 6 7 8 9 10 11 12 13 8 10 12 14 16 18 R RA∆RA 0 1 2 3 4 5 6 7 8 9 10111213 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 8 9 10111213 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 8 9 10111213 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 0.2 0.4 0.6 0.8 1 Figu e 2: Top panels: maps o R,RAand ∆RA om 3×3 cliques o ca he e o ien a ion o 0o. Ci cle encom- passes ib o ic a ea. Lowe panels: de ec ed ib o ic a eas (b own), using he h esholds ha maximize de ec ion ac- cu acy o each ma ke . Blue (b own) colo inside he ci cle deno es FN (TP), while ou side deno es TN (FP) de ec ion, espec i ely. ula ed a ial issue including a eas wi h ib osis and o he s o no mal issue, in o de o disc imina e hem. In clini- cal se ing, bipola ol age is commonly used as a su o- ga e o a ial ib osis, bu he phenomenon is much mo e complex and ol age canno be conside ed as a subs i- u e o ib osis as assessed by MRI. He e, h ee di e en EIGDR ma ke s ha e been s udied, e alua ing hei abili y in wo possible ECA o wo ca he e - o-wa e on o ien a- ions and conside ing depola iza ion and epola iza ion o he u-EGMs. The p oposed ma ke s a e good candida es o de ec ing ib o ic issue. Resul s in e ms o AUC and ACC con i m he hypo hesis ha educing misalignmen is bene icial and sugges ∆RA, ep esen ing he eigen alue dominance gain by alignmen , as he be e sui ed o i- b o ic a eas iden i ica ion, especially when he 3×3ECA is used. Howe e , hese esul s need o be complemen ed wi h o he simula ion con igu a ions, such as smalle i- b o ic a eas and pa chy ib osis, as well as wi h eal da a, whe e di e en alues o he elec odes size can be es ed and he quali y o issue-elec ode con ac could also be conside ed. Acknowledgmen s Funding comes om EU P og amme H2020 unde he Ma ie Sklodowska-Cu ie G an No 766082 (MY-ATRIA), Gobie no de A ag´ on (BSICoS G oup T39-20R) co unded by FEDER 2014-2020 “Building Eu ope om A agon”, ellowship ACIF/2018/174 om Gene ali a Valenciana, and PID2019-104881RB-I00 om MICINN, Spain. Re e ences [1] Tzeis S, As es as D, Va das P. A ial ib osis: ansla ional conside a ions o he managemen o AF pa ien s. AER Jou nal 2019; 8(1):37–41. [2] Bu s ein B, Na el S. 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Elec o onic coupling be ween human a ial myocy es and ib oblas s al e s myocy e exci abili y and epola iza ion. Biophys. J. 2009; 97:2179–2190. [9] S¨ o nmo L, Laguna P. Bioelec ical Signal P ocessing in Ca diac and Neu ological Applica ions, Else ie (Aca- demic P ess), Ams e dam, 2005. [10] Laguna P e al. Eigen alue-based ime delay es ima ion o epe i i e biomedical signals. Digi al Signal P ocessing 2018; 75:107-119. [11] Vigmond E e al. Pe cola ion as a mechanism o explain a ial ac iona ed elec og ams and een y in a ib o- sis model based on imaging da a. Hea Rhy hm 2016; 13(7):1536-1543. Add ess o co espondence: Jenni e Riccio C/ Ma iano Esquillo s/n, Edi icio I+D+i, Lab 6.1.01 50018 Za agoza, Spain. jen iccio@uniza .es Page 4