Accele a ed and Accu a e Myoca dial T1 Mapping wi h
PENGUIN: Combining Deep Lea ning wi h Ex ended
Phase G aph Modeling
Ca a ina N. Ca alho1,2, And eia S. Gaspa 1, Ri a G. Nunes 1, and Te esa Co eia2,3
1Ins i u e o Sys ems and Robo ics - Lisboa and Depa men o Bioenginee ing, Ins i u o Supe io Técnico, Uni e sidade de
Lisboa, Lisbon, Po ugal; 2Cen e o Ma ine Sciences (CCMAR), Fa o, Po ugal; 3School o Biomedical Enginee ing and Imaging
Sciences, King's College London, London, Uni ed Kingdom
Synopsis
Mo i a ion: Myoca dial T1 mapping sequences ypically equi e mul iple b ea h-hold scans, leading o
limi ed spa ial esolu ion, pa ien discom o and mo ion a i ac s. Mo eo e , mapping is gene ally
accomplished h ough h ee-pa ame e exponen ial ing, which may comp omise he accu acy o he
es ima ion due o he model’s simplici y.
Goal(s): Imp o e T1 mapping es ima ion accu acy, while also educing acquisi ion and econs uc ion imes.
App oach: We p opose a physics-in o med deep lea ning ne wo k o ob ain myoca dial T1 maps di ec ly
om unde sampled k-space ollowing he Ex ended Phase G aph o mula ion.
Resul s: Ou me hod is able o es ima e T1 maps o accele a ion ac o s 4 and 8× wi h minimal e o .
Impac : We p opose a no el physics-based deep lea ning me hod ha pe o ms accele a ed myoca dial T1
mapping di ec ly om unde sampled kspace acquisi ions conside ing he Ex ended Phase G aph
o mula ion, g ea ly imp o ing he accu acy o he es ima ed T1 alues while sho ening
acquisi ion/ econs uc ion imes.
In oduc ion
Model-based Deep Lea ning (DL) has become inc easingly popula o accele a ed MRI econs uc ion and
quan i a i e mapping. DL a chi ec u es ha pe o m quan i a i e mapping di ec ly om accele a ed k-space
ha e been p oposed o T1 and T2 mapping in a ious ana omical egions1–3. Howe e , all o hese app oaches
assume exponen ial eco e y o T1 and T2 mapping, simpli ying he elaxa ion dynamics. A mo e accu a e
way o modeling he signal is o conside he Ex ended Phase G aph (EPG) o mula ion ; howe e , his can
be e y esou ce-consuming, especially in he4 case o ca diac T1 mapping, whe e simula ed signals mus
conside he subjec s’ hea a e (HR). He e, we p opose modi ying ou PhasE G aph sigNal and G adien s
QUan i a i e In e ence machiNe (PENGUIN)5, ini ially p oposed o b ain T2 mapping, o accele a e
myoca dial T1 mapping, whils conside ing he EPG o mula ion. Compa ed o ou p e ious implemen a ion,
his wo k has he ollowing no el ies: (a) quan i a i e mapping is now pe o med di ec ly om unde sampled
k-space, ins ead o om econs uc ed images; (b) signal in ensi y cu es a e now simula ed no only o a
ange o T1 alues, bu also o a ange o egula HR alues, esul ing in a comp ehensi e dic iona y which
mo es he esou ce bu den away om he in e ence s age and in o he p ep ocessing s age.
Me hods
PENGUIN combines a Recu en In e ence Machine6 wi h a dic iona y o EPG simula ed signal e olu ion
cu es ha p o ides he ne wo k wi h a p e-calcula ed signal model, alle ia ing he compu a ional bu den
du ing in e ence. In his wo k, PENGUIN aims o lea n a maximum a pos e io i
es ima o by un olling he
op imiza ion p ocess wi h a o wa d model gi en by:
𝑑 =𝑈𝐹𝐸(𝑇1) + 𝑁𝑜𝑖𝑠𝑒
whe e d is he acqui ed (unde sampled) k-space da a, U is he unde sampling ope a o , F is he Fou ie
T ans o m, and E is he EPG o mula ion ha p oduces a signal in ensi y 4D image (3D image sampled a
mul iple in e sion imes) gi en a T1 alue. PENGUIN pe o ms J = 2 in e ence s eps o ob ain J es ima es o
he T1 maps, which con ibu e o he loss unc ion used o op imize he ne wo k:
𝐿 = 1
𝐽+1∑10−𝐽−𝑗+2
𝐽𝐿1 (𝑇1,𝑇1
)
𝐽
𝑗=0 ,
whe e L1 is he L1-no m loss, e alua ed in he myoca dium. PENGUIN ollows he a chi ec u e in Figu e 1.
Ne wo ks we e ained in an NVIDIA Quad o RTX 8000 GPU, ADAM op imize , lea ning a e=1e-4, 300
epochs, conside ing C = 64 and C = 256 channels o accele a ion ac o s 4 and 8, espec i ely.
Da a we e ob ained om MICCAI’s 2023 CMR econs uc ion challenge 7. T1 mapping was conduc ed
ollowing a MOLLI sequence which acqui ed 9 images (4-(1)-3-(1)-2), sho axis (SA) iew only,
FOV=360×307 mm2 , spa ial esolu ion=1.4×1.4 mm , slice hickness=5.0 mm, TR=2.67 ms, TE=1.13 ms,
pa ial Fou ie =7/8, and GRAPPA ac o =2, on a 3T MAGNETOM Vida Siemens scanne . We conside ed
only he single coil, ully-sampled da ase and slices 1-4; subjec s #001-#100 we e used o aining, #101-
#110 o alida ion, and #111-#120 o es ing. K-space da a we e unde sampled e ospec i ely, ollowing
a adial k- sampling ajec o y wi h golden angle inc emen s.
EPG-based simula ions we e implemen ed o he p o ocol desc ibed abo e, HR sampled om 28 o 102
bpm, T1=0:1:2000 ms, T2=50 ms and used o build a dic iona y o complex T1-weigh ed signal in ensi y cu es
o a ying HRs. G ound- u h T1 maps (GT) we e ob ained by pe o ming a pa e n ecogni ion app oach
o e he econs uc ed, ully sampled signal in ensi y images, h ough do p oduc ma ching. In addi ion, we
also pe o med a h ee-pa ame e exponen ial i ing8 o e he econs uc ed images o illus a e he di
e ences be ween exponen ial and EPG-based es ima ion.
Ze o- illed (ZF) and Comp essed Sensing (CS) econs uc ions we e pe o med o compa e wi h
PENGUIN. The CS app oach consis ed in a wa ele -based CS algo i hm o econs uc he images. The
pa e n ecogni ion app oach desc ibed abo e was employed o ob ain he co esponding ZF and CS T1 maps.
Maps we e e alua ed h ough he ela i e e o and he mean s uc u al simila i y index measu emen
(MSSIM) wi h espec o he GT alues.
Resul s
Figu es 2 and 3 illus a e he es ima ed maps wi h ZF, CS and PENGUIN o dis inc es subjec s, slices,
and accele a ion ac o s. T1 maps es ima ed wi h PENGUIN achie ed mean ela i e e o s o 10.1±11.0% and
15.9±15.4%, and mean MSSIM sco es o 0.999±0.001 and 0.998±0.001, o accele a ions 4 and 8×,
espec i ely (Figu e 4).
Figu e 5 depic s he AHA segmen a ion analysis on all es ima ed T1 maps. PENGUIN
equi es only 1.49s and 0.41Gb o RAM o in e a T1 map.
Conclusions & Discussion
We success ully modied PENGUIN o pe o m myoca dial T1 mapping di ec ly om unde sampled k-space
wi h imp o ed accu acy when compa ed o h ee-pa ame e exponen ial-based ing. Mo eo e , PENGUIN
is less esou ce-consuming han CS-based in e ence, since he compu a ional bu den is mo ed o he
p ep ocessing s age. In he u u e, we will inco po a e sensi i i y in o ma ion om mul iple coils (pa allel
imaging) in o he signal model o allow la ge accele a ion a es, and build he dic iona ies conside ing an
addi ional ange o T2 alues o inc eased accu acy.
Acknowledgemen s
This wo k was suppo ed by: NVIDIA GPU ha dwa e g an ; “la Caixa” Founda ion and FCT, I.P
[LCF/PR/HR22/00533]; FCT (SFRH/BD/120006/2016,
PTDC/EMD/EMD/29686/2017; UIDP/50009/2020), P og ama Ope acional Regional de Lisboa 2020
(LISBOA-01-0145-FEDER-029686), LARSyS unding
(DOI: 10.54499/LA/P/0083/2020,10.54499/UIDP/50009/2020,10.54499/UIDB/50009/2020. This esea ch
was suppo ed by FCT h ough p ojec s UIDB/04326/2020 (DOI:10.54499/UIDB/04326/2020),
UIDP/04326/2020 (DOI:10.54499/UIDP/04326/2020) and LA/P/0101/2020 (DOI:10.54499/LA/
P/0101/2020).
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Figu es
Fig 1. PENGUIN a chi ec u e d awn o in e ence s ep j. A each in e ence s ep, he es ima e o he T1 maps
p^j is gi en o he dic iona y o ob ain he signal-in ensi y and co esponding de i a i e a ibu ed o each T1
alue in he map. Wi h hese, he g adien o he nega i e log-likelihood o he model ∇Lj is calcula ed,
conca ena ed o p^j and gi en as inpu o he ne wo k, which ou pu s he inc emen al upda e o he es ima ed
maps.
The ne wo k uses wo memo y ec o s hj o lea n he op imiza ion p ocess.
Fig 2. T1 maps es ima ed wi h he die en me hods applied o 5 dis inc es subjec s ( ows), wi h die en HRs
and accele a ion ac o 4×; om le o igh : g ound- u h (GT), Exponen ial Fi ing, ze o-lled (ZF),
comp essed-sensing (CS), and PENGUIN. The die en slices a e shown in each ame o he anima ion.
Fig 3. G ound- u h (GT) and es ima ed T1 maps wi h ze o-lled (ZF), comp essed-sensing (CS) and
PENGUIN me hods o 1 ep esen a i e subjec , HR=64 bpm, o accele a ion ac o s 4 ( op) and 8×
(bo om).
Fig 4. Violin plo s o he (a) T1 ela i e e o s and (b) MSSIM sco es ob ained wi h ze o-lled (ZF),
comp essed-sensing (CS) and PENGUIN, o accele a ion ac o s 4 and 8×. A wo- ac o ANOVA and
pai wise- es was ca ied ou o iden i y s a is ically signican die ences be ween me hods, indica ed by * (p-
alue<0.05) and *** (p- alue<0.001).
Fig 5. Segmen al dis ibu ion o (a) mean T1 alues and (b) s anda d de ia ion acco ding o he AHA 16-
segmen model, o 2 ep esen a i e subjec s and accele a ion 4×. PENGUIN p o ides esul s ha a e in good
ag eemen wi h he g ound- u h (GT) T1 alues, despi e he lowe a ia ion wi hin each segmen .
