RESEARCH ARTICLE
Au oma ic assessmen o he ca diomyocy e
de elopmen s ages om con ocal
mic oscopy images using deep con olu ional
ne wo ks
Pa el S
ˇk aba
´nekID
1
*, Alexand a Zah adnı
´ko a
´j .ID
2,3
1Ins i u e o Au oma ion and Compu e Science, B no Uni e si y o Technology, B no, Czech Republic,
2Ins i u e o Molecula Physiology and Gene ics, Cen e o Biosciences SAS, B a isla a, Slo akia,
3Depa men o Cellula Ca diology, Ins . o Expe imen al Endoc inology, Biomedical Resea ch Cen e SAS,
B a isla a, Slo akia
*pa el.sk abanek@ u .cz
Abs ac
Compu e assis ed image acquisi ion echniques, including con ocal mic oscopy, equi e
e icien ools o an au oma ic so ing o as amoun o gene a ed image da a. The com-
plexi y o he classi ica ion p ocess, absence o adequa e ools, and insu icien amoun o
e e ence da a has made he au oma ed p ocessing o images challenging. Mas e ing o
his issue would allow implemen a ion o s a is ical analysis in esea ch a eas such as in
esea ch on o ma ion o - ubules in ca diac myocy es. We de eloped a sys em aimed a
au oma ic assessmen o ca diomyocy e de elopmen s ages (SAACS). The sys em clas-
si ies con ocal images o ca diomyocy es wi h luo escen dye s ained sa colemma. We
based SAACS on a densely connec ed con olu ional ne wo k (DenseNe ) opology. We
c ea ed a se o labelled sou ce images, p oposed an app op ia e da a augmen a ion
echnique and designed a class p obabili y g aph. We showed ha he DenseNe opol-
ogy, in combina ion wi h he augmen a ion echnique is sui able o he gi en ask, and
ha high- esolu ion images a e ins umen al o image ca ego iza ion. SAACS, in combi-
na ion wi h he au oma ic high- h oughpu con ocal imaging, will allow applica ion o s a-
is ical analysis in he esea ch o he ubula sys em de elopmen o emodelling and
loss.
In oduc ion
The ca diac muscle cells, ca diomyocy es, con ac o p opel blood low [1]. In adul hea ,
en icula myocy es con ain a sys em o memb aneous ans e sal ubules ( - ubules) con in-
ual wi h he sa colemmal memb ane [2]. T- ubules o m du ing pos na al g ow h and ma u a-
ion o ca diac myocy es and a e p one o emodelling unde physiological o pa hological
ca diac hype ophy [3]. As he in eg i y o he ubula sys em is essen ial o he co ec unc-
ion o adul ca diac myocy es, unde s anding o hei o ma ion, loss and emodelling, and
PLOS ONE | h ps://doi.o g/10.1371/jou nal.pone.0216720 May 30, 2019 1 / 18
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OPEN ACCESS
Ci a ion: S
ˇk aba
´nek P, Zah adnı
´ko a
´A, j . (2019)
Au oma ic assessmen o he ca diomyocy e
de elopmen s ages om con ocal mic oscopy
images using deep con olu ional ne wo ks. PLoS
ONE 14(5): e0216720. h ps://doi.o g/10.1371/
jou nal.pone.0216720
Edi o : Thomas Ab aham, Pennsyl ania S a e
He shey College o Medicine, UNITED STATES
Recei ed: Decembe 4, 2018
Accep ed: Ap il 26, 2019
Published: May 30, 2019
Copy igh : ©2019 S
ˇk aba
´nek, Zah adnı
´ko a
´. This
is an open access a icle dis ibu ed unde he
e ms o he C ea i e Commons A ibu ion
License, which pe mi s un es ic ed use,
dis ibu ion, and ep oduc ion in any medium,
p o ided he o iginal au ho and sou ce a e
c edi ed.
Da a A ailabili y S a emen : The da a unde lying
his s udy ha e been deposi ed o Figsha e and
may be accessed ia h ps:// igsha e.com/a icles/
da ase s_zip/8063369. All o he ele an da a a e
wi hin he pape and i s Suppo ing In o ma ion
iles.
Funding: The wo k was suppo ed by na ional
schola ship p og amme o he Slo ak Republic
(PS), h ps://www.schola ships.sk/; Slo ak
Resea ch and De elopmen Agency (SRDA, APVV),
ac o s in luencing hese p ocesses is pa amoun o bo h he s udy o exci a ion-con ac ion
coupling, as well as o he de elopmen o ma u e human induced plu ipo en s em cell
de i ed ca diomyocy es wi h co ec pheno ype [4].
Se e al de elopmen al s ages o - ubule o ma ion we e iden i ied in con ocal mic oscopy
images o luo escen ly labelled sa colemma o ca diomyocy es om g owing a hea s; how-
e e , high a iabili y among myocy es o he same hea was obse ed and he e o e he indi-
idual s ages could no be simply assigned o speci ic pe iod o hea de elopmen [5]. An
al e na i e o quan i ica ion o - ubules in single myocy es could be applica ion o s a is ical
me hods on a la ge popula ion o ca diomyocy es. This s a is ical e alua ion would allow
assessmen o he - ubule de elopmen , loss, and emodelling in di e en age g oups o unde
di e en condi ions. Cu en mic oscopy echnologies, including con ocal mic oscopy, enable
au oma ic collec ion o la ge amoun s o images; hus, allowing implemen a ion o he s a is i-
cal e alua ion o - ubule o ma ion.
Di e en sampling modes a e used in ca diomyocy e esea ch while aking mic oscopy
images. In one, he expe iden i ies and manually localizes indi idual myocy es in a ield o
iew. The ma ked a eas a e hen scanned [6]. Al e na i ely, signals a e eco ded a low spa-
ial esolu ion and measu ed om he whole ield o iew. All ob ained images may be la e
manually p ocessed by he expe [7]. Bo h al e na i es a e sui able when a small numbe o
a ge objec s should be cap u ed, e.g. when eco ding unc ional da a om li e cells, whe e
se e al measu emen s a e made om he same cell o cul u e pla e well. S a is ical analysis
o mo phological ea u es, on he o he hand, equi es a high numbe o images o a ious
indi idually eco ded cells. These images can be easily ob ained om he whole cul u e well
o mic oscope slide o ixed cells using mosaic scanning unc ionali y o mode n con ocal
mic oscopes. Un o una ely, only a pa o such c ea ed da ase con ains high quali y images
o whole and heal hy myocy es. The es o he da ase consis s o emp y images, images o
dead ca diomyocy es, ou -o - ocus images and images o cell agmen s. Thus, be o e he
da a can be s a is ically analysed, he p ope images in he da ase s mus be iden i ied and
so ed.
So a , when a emp ing o quan i y he - ubule complexi y in ca diac myocy es, expe
needs o iden i y heal hy myocy es in he sample and eco d high quali y images, which a e
hen quan i ied using 2D spa ial Fou ie ans o m [8–11] o s e eological analysis [5]. To s a-
is ically analyse he whole popula ion, he expe would need o assign he - ubule de elop-
men s age o each obse ed image o a ca diomyocy e acco ding o a complex se o objec
ea u es and classi ica ion ules. Such an app oach is imp ac ical and p one o subjec i e
e o s. Conside ing he amoun o da a equi ed o he s a is ical analysis, au oma ic classi i-
ca ion o he images would be mo e app op ia e. As he ca diomyocy es a e objec s o high
complexi y and show subs an ial mo phological a iabili y, he au oma ic classi ica ion is hin-
de ed by lack o implemen ed me hods.
The au oma ic classi ica ion o images is a ypical compu e ision ask known as gene ic
objec ca ego iza ion [12]. The s a e-o - he-a image ca ego iza ion sys ems ely on deep con-
olu ional ne wo ks (deep Con Ne s) [13]. Deep Con Ne s na u ally in eg a e ea u e ex ac-
ion and classi ica ion in o one compac uni . Be o e hei u iliza ion, hey mus be ained and
e alua ed on se s o labelled samples. Key ac o s in luencing pe o mance o a ained deep
Con Ne -based image ca ego iza ion sys em a e he quali y o he used aining se and a
lea ning capaci y o he ne wo k.
The quali y o a aining se is mainly in luenced by selec ion o aining samples, hei
co ec ca ego iza ion, and he o al numbe o samples o each ca ego y in he aining se
[14]. A class balance issue mus be also conside ed whene e class-sensi i e lea ning me hod is
used [15]. In mic oscopy image analysis, a limi ed amoun o sou ce da a is usually a ailable
Au oma ic assessmen o he ca diomyocy e de elopmen s ages om mic oscopy images using deep Con Ne s
PLOS ONE | h ps://doi.o g/10.1371/jou nal.pone.0216720 May 30, 2019 2 / 18
15-0302 (A. Zah adnı
´ko a
´), h p://www.ap .sk/
agen u a.h ml?lang=en; Vedecka
´g an o a
´
agen u
´ a Minis e s a s
ˇkols a, edy, y
´skumu a
s
ˇpo u Slo enskej epubliky a Slo enskej akade
´mie
ied (VEGA), 2/0095/15 and VEGA 2/0143/17
(AZj ), h p:// ega.sa .sk/. This publica ion is also a
esul o implemen a ion o he p ojec ITMS
26230120006, suppo ed by he Resea ch and
De elopmen Ope a ional P og am unded by he
Eu opean Regional De elopmen Fund, h ps://ec.
eu opa.eu/ egional_policy/EN/a las/p og ammes/
2014-2020/slo akia/2014sk16 op001. The
unde s had no ole in s udy design, da a collec ion
and analysis, decision o publish, o p epa a ion o
he manusc ip .
Compe ing in e es s: The au ho s ha e decla ed
ha no compe ing in e es s exis .
[16–18] which is also he case o con ocal mic oscopy images o he ca diomyocy es. The
lack o da a limi s sample selec ion and does no allow c ea ion o a su icien ly la ge and ep-
esen a i e aining se . To o e come hese conce ns, da a augmen a ion echniques, such as
image ansla ions, ho izon al e lec ions [17], o o a ions [16,18] a e ypically applied on
inadequa e se s. The ep esen a i eness o he se s can be u he imp o ed by using images
independen ly ca ego ized by se e al expe s.
The capaci y o a deep Con Ne is p ede e mined by i s opology. A ypical opology o he
ea ly deep Con Ne s is as ollows. The i s le els o a ne wo k consis o con olu ional laye s,
ypically complemen ed wi h ec i ied linea uni ac i a ion unc ions, and o se e al pooling
laye s [13]. Subsequen le els usually con ain ully connec ed laye s including a d opou egu-
la iza ion echnique [19–21]. The ne wo k is ypically closed by a classi ie employing a so -
max unc ion. The laye s in he ne wo k a e a anged in a eed- o wa d manne and he
capaci y o he ne wo k can be inc eased by inc easing he numbe o laye s (a dep h o he
ne wo k) [13]. Such a opology, howe e , does no allow cons uc ion o e y deep ne wo ks
due o a anishing g adien p oblem [22]. Thus, deep Con Ne s based on his opology a e
app op ia e o p oblems wi h a ela i ely simple disc iminabili y o a ge objec s, e.g. o
human epi helial-2 cell image classi ica ion [16], o classi ica ion o glioblas oma mul i o m
and low-g ade glioma [17], o o classi ica ion o ed blood cells in sickle cell anemia [23].
This opology is, howe e , inapp op ia e o he classi ica ion o ca diomyocy e images due
he complexi y o he ca diomyocy es.
Mode n, mo e complex deep Con Ne opologies o e come he anishing g adien p ob-
lem o a la ge ex en ; hence, hey allow cons uc ion o e y deep ne wo ks wi h g ea lea ning
capaci ies. The new opologies con ol he capaci y by a ying wid h o dep h o ne wo ks
[21]. Enla ging a deep Con Ne capaci y h ough inc easing i s wid h is used e.g. in GoogLe-
Ne [24,25], whe e se e al sub-ne wo ks a e connec ed in pa allel a a ious le els o he ne -
wo k. The cu en ends con e ge owa ds inc eased numbe o laye s ( he ne wo k dep h),
while e aining he da a p ocessing linea i y. Topologies, such as Highway Ne wo ks [26],
Residual Ne wo ks [27–29], Deep Py amidal Residual Ne wo ks [30], Densely Connec ed
Con olu ional Ne wo ks (DenseNe s) [31] and C oss-Laye Neu ons Ne wo ks [32], all in o
his ca ego y. All hese opologies show e y good classi ica ion pe o mance e en on da ase s
wi h high in aclass a iabili y.
Gi en he p og ess in compu e ision in las yea s, we decided o de elop a sys em o
au oma ic assessmen o ca diomyocy e de elopmen s ages (SAACS) om con ocal images.
SAACS is aimed o iden i y and classi y whole and heal hy myocy es in a se o images
ob ained while scanning he whole cul u e well o mic oscope slide o ixed cells, whe e he
images a e classi ied acco ding o he de elopmen al s ages o indi idual ca diomyocy es. Con-
side ing he complexi y o he ca diomyocy es and he limi ed numbe o images a ailable o
he o ming o he aining se , we based SAACS on he DenseNe opology. As he o he mod-
e n deep Con Ne opologies, DenseNe opology alle ia es he anishing-g adien p oblem
and i allows c ea ion o ne wo ks wi h high lea ning capaci y. Fu he mo e, acco ding o [31],
ne wo ks o DenseNe opology a e p o ed o be obus agains o e i ing on asks wi h small
aining se s. Fo a u he imp o emen o he aining p ocess, we designed an e icien da a
augmen a ion echnique ha imp o ed classi ica ion pe o mance o SAACS. We show ha
SAACS ained on he augmen ed da ase , consis ing o i een sou ce images o each class
only, was able o iden i y he whole and heal hy myocy es, and di e en ia e among i e ca dio-
myocy e de elopmen s ages. In addi ion, we analysed he in luence o image esolu ion on
SAACS pe o mance and implemen ed a class p obabili y g aph o simpli y he expe e alua-
ion o SAACS pe o mance.
Au oma ic assessmen o he ca diomyocy e de elopmen s ages om mic oscopy images using deep Con Ne s
PLOS ONE | h ps://doi.o g/10.1371/jou nal.pone.0216720 May 30, 2019 3 / 18
Ma e ials and me hods
Isola ed ca diomyocy es
E hical s a emen . Animals we e housed and ea ed acco ding o he Eu opean di ec i e
o he p o ec ion o animals used o scien i ic pu poses (2010/63/EU) and wi h he Labo a-
o y Animals Ac No. 377/2012 and he Dec ee 436/2012 Z.z. SR. All p ocedu es we e
app o ed by he S a e Ve e ina y and Food Adminis a ion o he Slo ak Republic (3514/14-
221) and by he E hical commi ee o he Ins i u e o Molecula Physiology and Gene ics, Slo-
ak Academy o Sciences. Adul males and p egnan emales we e om Dob a Voda, Slo akia.
Con ocal mic oscopy. Sa colemma o isola ed ca diomyocy es was s ained using lipo-
philic memb ane p obes (di-8-ANEPPS o FM4-64, Molecula p obes, O egon, US). Images
we e ob ained by he Leica TCS SP2 AOBS con ocal mic oscope (Leica Mic osys ems, Ge -
many) equipped wi h HCX PL APO CS 63x/1.2 NA wa e imme sion objec i e. Fluo opho es
we e exci ed by 488 nm and combined 496 and 514 nm lase ligh . Fluo escence emission was
collec ed om 520 o 800 o 620 nm o 760 nm windows o di-8-ANEPPS o FM 4-64, espec-
i ely. Images we e eco ded in x-y mode wi h 58 nm o 116 nm pe pixel (px) wi h 4× ame
a e aging o inc ease he signal- o-noise a io, wi h he con ocal ape u e se o 1 Ai y uni .
T aining and e alua ion se s
Classi ica ion o objec images. The expe iden i ied he li e and heal hy ca diomyocy es
in images and assigned hem in o 5 de elopmen s ages. The leas de eloped ca diomyocy es
we e conside ed o be a s age 1 while he mos de eloped ones we e assigned s age 5 (Table 1).
We used he s ages o de ine classes o objec images whe e he s ages 1 o 5 co espond o
classes 1 o 5, espec i ely. The es o images in he collec ion (low quali y images o images
which do no con ain whole and heal hy myocy es) belong o he class 0.
Ca diomyocy es wi h no memb ane in agina ions we e ca ego ized as s age 1. S age 2 was
cha ac e ized by p esence o sho (~2 μm), egula ly spaced, pe pendicula in agina ions o
he memb ane and/o indi idual long (>10 μm) ubules. In s age 3, a web o longe ubules
(>10 μm), bo h ans e se and longi udinal, was p esen . A complex sys em o ans e sal
ubules wi h mani es p esence o longe (>2μm) longi udinal ubules and equen a eas
de oid o ubules was classi ied as s age 4. S age 5, p esen in adul ca diomyocy es, was dis in-
guished by a complex sys em o ans e sal ubules, wi h spa se longi udinal s uc u es span-
ning usually no mo e han 1 o 2 sa come es (~2 μm o ~4 μm) illing he whole a ea o he
cell image excep nuclei. Examples o de elopmen s age ca ego ies a e shown in Fig 1.
Sou ce images. Con ocal mic oscopy p oduces high- esolu ion monoch oma ic images
o op ional dimensions. In ou case, images 1024 ×1024 px we e conside ed and each image
con ained no mo e han one a ge objec (ca diomyocy e). An example o o iginal sou ce
image and o i s enhancemen o be e ep esen a ion in he a icle a e shown in Fig 2. As he
Table 1. Cha ac e iza ion o ca diomyocy e de elopmen s ages. Expe s assess ca diomyocy e de elopmen s ages acco ding o pa e ns o longi udinal and ans e sal
ubules, conside ing hei quan i y and cha ac e , and acco ding o he complexi y o he ubula sys em.
s age longi udinal ubules ans e sal ubules sys em complexi y
quan i y cha ac e quan i y cha ac e
1 none - none - no
2 low long low sho no— e y low
3 high long medium medium low—medium
4 medium medium high long high
5 low sho high long high
h ps://doi.o g/10.1371/jou nal.pone.0216720. 001
Au oma ic assessmen o he ca diomyocy e de elopmen s ages om mic oscopy images using deep Con Ne s
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images we e eco ded in he adi ional way (manually by an expe ), a e y limi ed numbe
o app op ia e images was a ailable o o m a aining and an e alua ion se . Ou da ase con-
sis ed o he images analysed in [5], o which we added 12 images o class 5, and all class 0
images. In o al, 18 images o class 1, 23 images o class 2, 22 images o class 3, 22 images o
class 4, and 26 images o class 5 we e a ailable. Compa ed o classes 1 o 5, he numbe o a ail-
able class 0 images was no limi ing. Ou collec ion o sou ce images was imbalanced, which
migh comp omise aining o deep Con Ne s [33]. To deal wi h he imbalanced da a issue, a
andom unde -sampling me hod [34] was used o o m a class-balanced se o sou ce images.
To c ea e he se , we andomly selec ed 15 images o each class om he o iginal image collec-
ion. The class-balanced se was used as he base o c ea ing he aining se . The emaining
(unselec ed) images we e used as sou ce images o he e alua ion se . In addi ion, 15 and 9
sou ce images o class 0 we e alloca ed o he aining and he e alua ion se , espec i ely. The
da a a e a ailable a [35].
Da a augmen a ion. The small numbe o sou ce images did no allow e icien aining
(90 images) o c edible e alua ion (46 images) o any deep Con Ne [13]. To o e come his
issue, da a augmen a ion echniques we e used. To p e en al e a ion o - ubule ans e sal
pa e n, which we conside impo an o co ec classi ica ion, non-des uc i e augmen a ion
echniques we e chosen. Speci ically, he sou ce images we e ho izon ally lipped, and bo h
he lipped and he o iginal images we e o a ed by an angle φ2{0, Δφ, 2Δφ,. . ., 2π}, whe e
Dφ¼2p
144 ( i s me hod).
Addi ionally, o enhance he ecogni ion o he objec s o in e es , we ha e de eloped a sec-
ond augmen a ion echnique, which applies he i s me hod on an ex ended se o sou ce
Fig 1. De elopmen s ages o ca diomyocy es. The images o ca diomyocy es a e o de ed om le o igh acco ding o hei
de elopmen al s ages, om he leas o he mos de eloped (s age 1 o s age 5).
h ps://doi.o g/10.1371/jou nal.pone.0216720.g001
Fig 2. Example o a sou ce image. The sou ce images a e monoch oma ic images o spa ial esolu ion 1024 ×1024 px
ob ained using he con ocal mic oscopy. Objec s in sou ce images (a) a e poo ly isible. Wi hin his a icle, we use
images enhanced using in e sion and gamma co ec ion (b).
h ps://doi.o g/10.1371/jou nal.pone.0216720.g002
Au oma ic assessmen o he ca diomyocy e de elopmen s ages om mic oscopy images using deep Con Ne s
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images. The ex ended se consis ed o he o iginal sou ce images and manually modi ied
images. The modi ied images we e based on cu -ou s o a ge objec s (ca diomyocy es). F om
each o iginal sou ce image (Fig 3(a)), he a ge objec was ex ac ed; and om each ex ac ion,
wo new sou ce images we e c ea ed. In bo h images, he a ge objec was placed on a neu al
o noisy backg ound, a a andom posi ion wi hin he image. While he i s new image con-
sis ed only o he a ge objec and he backg ound (Fig 3(b)), he second one (Fig 3(c)) was
enhanced wi h non- a ge objec s ha na u ally occu in he con ocal images. The non- a ge
objec s we e placed andomly in he image, bu hey did no o e lap wi h he a ge objec . In
his way, he sou ce images o classes 1 o 5 we e ex ended. Class 0 images we e ex ended by
30 new unique sou ce images. Thus, he se augmen ed using his echnique was h ee imes
la ge han he se p oduced by he i s da a augmen a ion echnique.
Se up o aining and e alua ion se s. We hypo hesized ha due o he small size
(~0.1 μm o ~0.3 μm in diame e ) and dense spacing (~1.8 μm o ~2.0 μm) o - ubules, high-
esolu ion images a e key o he e icien assessmen o he ca diomyocy e de elopmen
s ages. The a ailable sou ce images we e o dimensions 1024 ×1024 px, wi h esolu ion 58 nm
o 116 nm pe px. To assess he impo ance o image esolu ion on SAACS classi ica ion pe -
o mance, we c ea ed low- esolu ion se s o sou ce images. The o iginal sou ce images we e
esized o 512 ×512 px using a esize me hod wi h bicubic esampling il e in py hon imaging
lib a y 5.0.0, esul ing in esolu ion o 116 nm o 232 nm pe px.
We applied bo h augmen a ion echniques on he esized (512 ×512 px) and he o iginal
(1024 ×1024 px) sou ce images. Using he i s augmen a ion echnique (A), we c ea ed ain-
ing se s T-512-A and T-1024-A, and e alua ion se s E-512-A and E-1024-A. Using he second
augmen a ion echnique (B), we o med aining se s T-512-B and T-1024-B. The aining se s
T-512-A and T-1024-A consis ed o 25 920 labelled objec images, and he e alua ion se s E-
512-A and E-1024-A consis ed o 13 248 labelled objec images. The aining se s T-512-B and
T-1024-B consis ed o 77 760 labelled objec images.
SAACS
DenseNe s. DenseNe s a e deep Con Ne s wi h an ad anced opology. In addi ion o
commonly used con olu ional, pooling and ully connec ed laye s [13], wo composi e build-
ing elemen s, dense blocks (DBs) and ansi ion laye s (TLs), a e used o c ea e a DenseNe
[31].
Fig 3. Augmen a ion o sou ce images by manually modi ied images. A cu -ou o a ca diomyocy e was c ea ed
om he o iginal sou ce image (a). Placing he ca diomyocy e on a noisy and neu al backg ound, wo manually
modi ied sou ce images (b) and (c) we e c ea ed, espec i ely. The second manually modi ied image (c) was enhanced
by cell agmen s and ou -o - ocus ca diomyocy es. No e ha he displayed images we e in e ed and enhanced using
gamma co ec ion o be e ep esen a ion in he a icle.
h ps://doi.o g/10.1371/jou nal.pone.0216720.g003
Au oma ic assessmen o he ca diomyocy e de elopmen s ages om mic oscopy images using deep Con Ne s
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Dense block. A DB consis s o se e al laye s connec ed in a dense pa e n whe e each
laye akes all p eceding ea u e-maps as i s inpu (Fig 4). The laye s a e connec ed using
conca ena ion and ans o med using a non-linea ans o ma ion. Le us conside a n- h
DB ha is buil in a DenseNe o Llaye s. A non-linea ans o ma ion pe o med wi hin his
DB, placed a he ℓ- h le el wi hin he ne wo k, p oduces ea u e maps x
ℓ
ha a e gi en as
x‘¼H‘ð½xin;xinþ1;. . . ;x‘1�Þ;ð1Þ
whe e H
ℓ
(�) is he ℓ- h non-linea ans o ma ion, ½xin;xinþ1;. . . ;x‘1� e e s o he conca ena-
ion o he ea u e maps xp oduced in laye s i
n
,. . ., (ℓ−1). No e ha xina e ea u e maps ed
in o he inpu o he n- h DB. The inpu o he DB is placed a he i
n
- h le el o he ne wo k,
i
n
<ℓ�o
n
, and o
n
is a le el a which he ou pu o he n- h DB is placed.
The ℓ- h non-linea ans o ma ion H
ℓ
(�) is a composi e unc ion o se e al consecu i e
ope a ions. We used a basic and a bo leneck e sion o he composi e unc ion [31]. The basic
e sion consis s o h ee ope a ions: ba ch no maliza ion (BN) [36], ollowed by a ec i ied lin-
ea uni (ReLU), ollowed by a con olu ion (Con ) [13]. Using a sho no a ion, his e sion
o he unc ion can be w i en as BN-ReLU-Con (h×w, ,s), whe e sis s ide o con olu ional
il e s, is numbe o he il e s, and hand wa e hei heigh and wid h, espec i ely. The
Fig 4. Layou o a gene al dense block. A dense block consis s o dlaye s whe e he laye s a e connec ed using conca ena ion and
ans o med using non-linea ans o ma ions H(�). Typically, a ansi ion laye ollows a dense block. The igu e shows a
hypo he ical dense block o h ee laye s (d= 3) which is placed a he inpu o a ne wo k. Non-linea ans o ma ions H(�) wi hin his
block a e composi e unc ions which consis o he ba ch no maliza ion (BN), he ec i ied linea uni (ReLU) and he con olu ion
(Con ), espec i ely. A he i s , second and hi d laye , h ee, i e and wo con olu ional il e s (
1
= 3,
2
= 5,
3
= 2) o heigh and
wid h 3 ×3 px (h=w= 3) con ol e wi h s ide one (s = 1). The inpu da a o he ne wo k x
0
is a con ocal mic oscopy image o
esolu ion 1024 ×1024 px. A he i s , second and hi d laye o he dense block, ea u e maps x
1
,x
2
and x
3
o dep h h ee, i e and
wo o igina e, espec i ely. Spa ial esolu ions o he ea u e maps a e 1024 ×1024 px. Inpu o each laye is composed o ea u e
maps ha a ose on he p eceding laye s o he dense block, and o he inpu o he block ( he con ocal mic oscopy image x
0
in his
case). The block inpu da a and he ea u e maps a e ca ena ed a he inpu o each laye .
h ps://doi.o g/10.1371/jou nal.pone.0216720.g004
Au oma ic assessmen o he ca diomyocy e de elopmen s ages om mic oscopy images using deep Con Ne s
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bo leneck e sion o he composi e unc ion is de ined as BN-ReLU-Con (1 ×1, 4 , 1)-
BN-ReLU-Con (h×w, ,s). I necessa y, con olu ions we e ze o-padded o keep he ea u e-
map size ixed.
Each DB consis s o dlaye s ei he wi h he basic o wi h he bo leneck e sion o he com-
posi e unc ion. Fo he n- h DB, i holds ha d
n
=o
n
−i
n
. Fo bo h e sions o he composi e
unc ion, he pa ame e s h,w,s, a e iden ical o all laye s wi hin a DB. DBs wi h basic and
bo leneck e sion o he unc ion will be deno ed as DBa(h×w,s, ,d) and DBb(h×w,s, ,d),
espec i ely.
T ansi ion laye . Le us conside a TL connec ed a he ou pu o he n- h DB (i.e. he
laye is placed a he (o
n
+ 1)- h le el o he ne wo k). Fea u e maps p oduced by his laye a e
gi en as
xonþ1¼Honþ1ð½xin;xinþ1;. . . ;xon�Þ;ð2Þ
whe e ½xin;xinþ1;...;xon�deno es he conca ena ion o all ea u e maps ha appea in he n- h
DB. The non-linea ans o ma ion Honþ1is also a composi e unc ion. The unc ion was
de ined as BN-ReLU-Con (1 ×1, , 1)-AP(2 ×2, 2), whe e AP(2 ×2, 2) deno es an a e age
pooling wi h pools 2 ×2 and s ide 2 [31]. The unc ion o ansi ion laye s is demons a ed in
Fig 5.
The 1 ×1 con olu ion inco po a ed in he TL allows imp o emen o ne wo k compac -
ness. The numbe o con olu ional il e s con ols he numbe o ea u e maps p oduced by
he TL. Conside ing ha he n- h DB p oduces m
n
ea u e maps, he numbe o ea u e maps
Fig 5. Layou o a ansi ion laye . P ima y, ansi ion laye s educe spa ial esolu ion o he ea u e maps x o educe
he numbe o pa ame e s o he ne wo k. They a e placed behind dense blocks. In his case, he ansi ion laye is
placed behind he dense block om Fig 4. The inpu o he ne wo k x
0
and he ea u e maps x
1
,x
2
,x
3
a e ca ena ed and
p ocessed by he non-linea ans o ma ions H
4
(�). The ans o ma ion is a composi e unc ion which consis s o he
ba ch no maliza ion (BN), he ec i ied linea uni (ReLU), he con olu ion (Con ) and he a e age pooling (AP),
espec i ely. Fi e con olu ion il e s ( = 5) o heigh and wid h 1 ×1 px (h=w= 1) wi h s ide one (s = 1) a e used.
The numbe o he con olu ion il e s con ols he numbe o ea u e maps p oduced by he ansi ion laye , i.e.
dep h o he ea u e maps x
4
is i e in his case. Pools 2 ×2 px and s ide 2 a e used in AP. Thus, he o iginal da a o
spa ial esolu ion 1024 ×1024 px a e educed o 512 ×512 px.
h ps://doi.o g/10.1371/jou nal.pone.0216720.g005
Au oma ic assessmen o he ca diomyocy e de elopmen s ages om mic oscopy images using deep Con Ne s
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p oduced by he (o
n
+ 1)- h TL is gi en as onþ1¼ bymnc, whe e θis a comp ession ac o , and
y2 ½m1
n;1�.
SAACS s uc u e. SAACS is a DenseNe ha pe o ms ea u e ex ac ion and classi ica-
ion on size-no malized objec images. We designed and implemen ed wo a ian s o SAACS
(i.e. wo DenseNe s). One a ian (DenseNe -512) was aimed a objec images o dimensions
512 ×512 px and he second one (DenseNe -1024) a objec images o dimensions 1024 ×1024
px. As he objec images a e monoch oma ic, numbe s o inpu channels o he ne wo ks
(dep hs o he ne wo k inpu s) a e one.
Bo h he DenseNe -512 (Table 2) and he DenseNe -1024 (Table 3) a e opened by one DBa
ollowed by a max pooling laye (MPL). The DBa consis s o one laye (d= 1) wi h 2kcon olu-
ional il e s ( = 2k) wi h ke nels o size 7 ×7 px (h=w= 7), s ide by 2 px (s= 2). The a iable
kis a hype pa ame e de e mining he numbe o il e s in all DBs wi hin he ne wo k. We
used k= 20 and k= 15 o DenseNe -512 and DenseNe -1024, espec i ely. A he MPL, 3 ×3
px (h=w= 3) pools s ide by 2 (s= 2) we e used.
The inne pa s o he ne wo ks consis o se e al DBbs whe e each DBb is ollowed by one
TL. In DenseNe -512, 4 DBbs a e used. They ha e 6, 9, 12 and 15 laye s, espec i ely. In Dense-
Ne -1024, 5 DBbs a e inco po a ed. They ha e 6, 8, 8, 10, and 15 laye s, espec i ely. Bo h he
DenseNe -512 and he DenseNe -1024 a e closed by one addi ional DBb, ollowed by a global
a e age pooling (GAP) and a classi ie . The classi ie consis s o one ully connec ed laye o
six neu ons ollowed by he so max unc ion. The numbe o laye s wi hin he closing DBb is
18 and 15 o he DenseNe -512 and he DenseNe -1024, espec i ely. In bo h a ian s o Den-
seNe s, ke nels o size 3 ×3 px s ide by 1 px a e used in all DBbs, and =k o all o hem. The
comp ession ac o θ= 0.5 is used o bo h ne wo ks. S uc u es o bo h ne wo ks and hei
pa ame e s we e de e mined based on a pilo s udy.
Table 2. S uc u e o he DenseNe -512 classi ying 512 ×512 px con ocal mic oscopy images o ca diomyocy es in o de elopmen s ages.
DBa MPL DBb TL DBb TL DBb TL DBb TL DBb GAP C
h7 3 3 - 3 - 3 - 3 - 3 7 -
w7 3 3 - 3 - 3 - 3 - 3 7 -
s2 2 1 - 1 - 1 - 1 - 1 7 -
2k-k-k-k-k-k- -
d1 - 6 - 9 - 12 - 15 - 18 - -
In he i s ow, he used building componen s a e lis ed wi h espec o hei placemen in he ne wo k ( he i s block is he le mos one); whe e DBa and DBb a e he
basic and he bo leneck e sions o he dense blocks; MPL is he max pooling laye ; TL is he ansi ion laye , GAP deno es he global a e age pooling, and C is used o
a classi ie ha consis s o one ully connec ed laye ollowed by he so max unc ion. The pa ame e s hand wa e he heigh and weigh o he il e ke nel o o he
pool; sis s ide o he ke nel o he pool; is he numbe o il e s a one con olu ion in he dense block; and dis he numbe o laye s in he dense block.
h ps://doi.o g/10.1371/jou nal.pone.0216720. 002
Table 3. S uc u e o he DenseNe -1024 classi ying 1024 ×1024 px con ocal mic oscopy images o ca diomyocy es in o de elopmen s ages.
DBa MPL DBb TL DBb TL DBb TL DBb TL DBb TL DBb GAP C
h7 3 3 - 3 - 3 - 3 - 3 - 3 7 -
w7 3 3 - 3 - 3 - 3 - 3 - 3 7 -
s2 2 1 - 1 - 1 - 1 - 1 - 1 7 -
2k-k-k-k-k-k-k- -
d1 - 6 - 8 - 8 - 10 - 15 - 15 - -
The meaning o he symbols and a iables is explained in Table 2.
h ps://doi.o g/10.1371/jou nal.pone.0216720. 003
Au oma ic assessmen o he ca diomyocy e de elopmen s ages om mic oscopy images using deep Con Ne s
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The de elopmen o SAACS was complica ed by: a) high a iabili y in he ca diomyocy e
shape and s uc u e, and b) lack o sou ce images. To ace hese issues, we based SAACS on
he DenseNe opology and we modi ied he s anda d da a augmen a ion echnique wi h man-
ually adjus ing sou ce images. As bo h issues a e common in biology, we ecommend using
he DenseNe and he augmen a ion echnique in biological applica ions, such as mo phology-
based cell so ing, iden i ica ion o egions o in e es o p ojec s ha oday equi e Ci izen sci-
ence app oach. DenseNe s should be used ins ead o he commonly used ea ly deep Con Ne s
opologies [16,17,23] especially i a ge objec s exhibi high a iabili y in hei shapes and
s uc u es. We also ad ise o use he manually modi ied images whene e only a limi ed collec-
ion o sou ce images is a ailable, especially i he e is p oblem wi h ecogni ion o he objec
o in e es . Conside ing he ac ha he DenseNe s can p ocess any ype o images (mono-
ch oma ic, colou , hype spec al, e c.), DenseNe s in combina ion wi h he da a augmen a ion
echnique a e ideal means o c ea ion o image ca ego iza ion sys ems o a ious asks in
biology.
Suppo ing in o ma ion
S1 File. Implemen a ion o he SAACS in py hon. Codes ha we e used o aining and
e alua ion o he DenseNe -512 and DenseNe -1024, including code which delinea es class
p obabili y g aphs.
(RAR)
Acknowledgmen s
We would like o hank G. Gajdos
ˇı
´ko a
´ o isola ion o adolescen and adul myocy es and A.
Zah adnı
´ko a
´and K. Macko a
´ o pa icipa ion in image acquisi ion. We g ea ly app ecia e
N. Ma ı
´nko a
´, I. Zah adnı
´k and A. Zah adnı
´ko a
´ o cons uc i e c i icism o he manusc ip
and P. Hoope o he English co ec ions.
Au ho Con ibu ions
Concep ualiza ion: Pa el S
ˇk aba
´nek, Alexand a Zah adnı
´ko a
´, j .
Da a cu a ion: Alexand a Zah adnı
´ko a
´, j .
Fo mal analysis: Pa el S
ˇk aba
´nek.
Funding acquisi ion: Alexand a Zah adnı
´ko a
´, j .
Me hodology: Pa el S
ˇk aba
´nek, Alexand a Zah adnı
´ko a
´, j .
Resou ces: Alexand a Zah adnı
´ko a
´, j .
So wa e: Pa el S
ˇk aba
´nek.
Valida ion: Pa el S
ˇk aba
´nek, Alexand a Zah adnı
´ko a
´, j .
Visualiza ion: Pa el S
ˇk aba
´nek.
W i ing – o iginal d a : Pa el S
ˇk aba
´nek, Alexand a Zah adnı
´ko a
´, j .
W i ing – e iew & edi ing: Pa el S
ˇk aba
´nek, Alexand a Zah adnı
´ko a
´, j .
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