Nuclear magnetic resonance for wireless magnetic tracking

Domain: physics
Published: 2025-12-02
Editorial outcome: major_revision

Abstract
Wirelesstrackershaveemergedasacrucialtechnologyinminimallyinvasive
medicalprocedureswiththeirremotelocalizationcapabilities.Existing
trackerssufferfromminiaturizationissuesandcomplexdesigns,whichlimit
theirintegrationintomedicaldevices.Wepresentnuclearmagneticresonance
(NMR)magneticsensing,aquantumsensingapproachwithnTsensitivityfor
wirelessmagnetictracking.NMRmagneticsensingenablesmillimeter-scale
trackingaccuracyandversatileminiaturizedtrackerdesignsforminimally
invasivemedicaldevicesinmagneticresonanceimagingscanners.Asexam-
ples,wedemonstrateminiaturemagnetictrackerswithsubmillimeter-scale
diametersforguidewiresandopticfibers,flexiblemagnetictrackersforsoft
devices,andferrofluidictrackersforshape-morphingdevices.Withthe
demonstratedminiaturizationandwiderangeoftrackerdesignpossibilities,
wirelessmagnetictrackingwithNMRispromisingforfutureminimallyinva-
sivemedicaloperations.

Introduction
Recentdevelopmentsinminimallyinvasiveproceduresandmedical
robotichavecreatedagrowingdemandformedicaldevicetracking
methodsinthehumanbody,whereadirectlineofsightisnotpossible.
Currently,medicaldevicetrackingisperformedbymedicalimaging1–6
andcomplementaryremotesensing,suchaselectromagnetic(EM)7–10
andmagneticsensing11–14.However,eachapproachhasspecificdraw-
backs in terms of spatial and temporal resolution, workspace, and
miniaturization of tracking devices. The most widely used medical
imagingmethods,suchasX-rayfluoroscopyandmagneticresonance
imaging(MRI),suffertemporalresolutionissuesbecauseofionizing
radiationexposurefromX-rayortheinherentspatiotemporalresolu-
tion trade-off of MR imaging, respectively. Complementary remote
sensing methods compensate for the temporal resolution issues of
medical image-based tracking methods by introducing field
generators10,11oronboardfieldsensors12–14astrackingdevices.Among
remote sensing approaches, commercial EM sensors7 and onboard
magneticsensors12–15arethemostcommonapproaches.However,the
tetherednatureandrelativelylargesizeofthesetrackerslimittheir
their usage. Wireless EM tracking, including electrical or mechanical
resonators,addressestetherissueswitharelativelysmallsize,espe-
ciallywithrecentlyproposedmechanicalresonators8–10.Despitetheir
small size, these wireless EM trackers limit overall medical device
miniaturizationduetothestructuralrestrictionsofresonatordesign.
As an alternative, wireless magnetic tracking could enable further
miniaturizationandversatiletrackerdesignbyeliminatingstructural
restrictions.However,the µT-levelsensitivityofhall-effectmagnetic
sensorsusedinexistingmagnetictrackingsystemsisnotsufficientfor
trackerminiaturizationbelowthecentimeterscale11.
Therequiredsensitivitycouldbeachievedwithquantumsensing
approaches exploiting quantum properties of matter for magnetic
field measurement16, such as superconducting quantum devices17,
optically pumped magnetic sensors18, electron spin magnetic
resonance19, and nuclear magnetic resonance (NMR) magnetic
sensors20.Whilesomeofthesequantumsensorshavefoundtheirway
intobiomedicalapplicationsinmagneto-encephalographyandcardi-
ography,theyrequirehighhardwareandinstallationcosts,preventing
their mainstream adoption in clinical environments. Among these
quantumsensors,NMRmagneticsensorsofferauniqueopportunity
to be integrated into the hardware of clinically available MRI
scannersand provide inherent potentialfor intraoperative imaging.
Moreover,operatingathighmagneticfields,theNMRmagneticsensor
enablestheuseofsoftmagneticmaterialsfortrackers,whichisnot
possiblewithotherquantumsensors.Thisenablesfurtherminiatur-
izationanddesignversatilityduetohighersaturationmagnetization
andsimplermanufacturingprocessescomparedtopermanentmag-
netictrackers.
Considering the miniaturization and integration limitations of
existingwirelesstrackingmethodsandthepotentialofNMRmagnetic
sensing,wedevelopedawirelessmagnetictrackingsystemusingan
NMRmagneticsensorarray(Fig.1).Welocalizedminiaturizedmag-
netic trackers, such as soft magnetic rigid, hollow trackers, flexible
magnetic trackers, and ferrofluidic trackers, by remotelymeasuring
the magnetic field of a magnetic tracker using the NMR magnetic
sensing in the MRI scanner. The NMR magnetic sensor measures
the magnetic field difference,

Δϕ
δB=γ(cid:1)1 ð1Þ
Δt 0

relativetothebackgroundmagneticfield(B
0
=B
0
^z)oftheMRIscan-
nerinz^directionoftheMRIscannerthroughtherateofphaseaccu-
mulationofnuclearspinprecessioninthefree-inductiondecay(FID)
signal of 1H nuclei in water placed in the sensor20, where γ is the
gyromagneticratioof1Hnuclei(SupplementaryNote1andFig.1).This
nuclearspinfrequency-modulatedmagneticmeasurementprovided
nTmagneticfieldmeasurementsensitivity—threeordersofmagnitude
lower than hall-effect sensors—and a broad magnetic measurement
range of ±700µT for 30kHz excitation BW. The NMR sensors are
integratedintoasensorarraythroughanRFswitchthatconnectsto
theRFhardwareoftheMRIscanner(SupplementaryFig.2).Thissetup
enablessequentialexcitationandacquisitionofFIDsignalswithahigh
temporal resolution of 25Hz due to the short phase accumulation
durationof2.5ms.

Results
MagneticmodellingathighfieldsforNMRmagnetictracking
Traditionally, magnetic tracking is performed using hard magnetic
trackers,suchasNeodymiummagnets,duetotheirhighremanence
magnetization11. However, soft magnetic trackers, such as iron and
spring steel, have higher saturation magnetization values at a high
magneticfield(seeSupplementaryNote2andSupplementaryFig.3);
thus,theyallowfurtherminiaturization.Moreover,unlikehardmag-
netictrackersatlowfields,themagnetizationofsoftmagnetsaligns
substantiallywiththehighB field6,whichdecouplestrackingfromthe
0
tracker orientation (Supplementary Fig. 4). Consequently, we could
modelthemeasuredhigh-fielddipolemagneticfieldas(Supplemen-
taryNote3):

B d ðrÞ=
μ
4 0 π
M3jjz^(cid:3)r
j
j
j
j
r
2
jj
(cid:1)
5
jjrjj2
ð2Þ

whereMisthesaturationmagnetizationofthesoftmagnet,risthe
relativepositionofthemagnettothesensor,z^istheunitvectorinthe
B direction,and||(cid:3)||istheEuclideannorm.Weverifiedthemodelby
0
measuringthemagneticfieldofa1mm-diametersteelbead,0.56emu,
alongpredeterminedchannelsinsidea7-Tesla(7T)preclinicalsmall-
animalMRIscanner(SupplementaryFig.5).Themagneticfieldvalues
variedbetween−7and14µTata2cmdistance(Fig.2b)and−70to
110nTata10cmdistance(Fig.2c),withmodelmatchingbetweenthe
2–8cm range. The observed deviation from the model at close
distances,especiallybetween45°and60°,isduetothecurvatureof
thedipolefield(SupplementaryNote4andSupplementaryFig.6).The
deviationfromthemodelatgreaterdistancesisduetotheinteraction
of the magnetic tracker with the MRI’s superconducting main field
coils(SupplementaryNote 5;SupplementaryFigs.7–8,andSupple-
mentaryMovie1).

Characterizationofmagnetictrackingworkspace
Next, we built a hexagonally placed array of seven NMR magnetic
sensorsformagnetictracking(Fig.2d).EachsensorisplacedinanRF
shieldingcomposedofaluminumfoil(SupplementaryFig.15a),which
eliminates interference between sensors and also the nearby tissue
(see Supplementary Note13). We also introduced a reference NMR
magnetic sensor placed far from the other sensors to monitor the
variation of the background field, which could change substantially
overalongdurationofoperation(SupplementaryFig.9).Then,we
performedagradient-basedsensorpositioncalibrationwithrespectto
the center of the MRI scanner using the gradient hardware of the
scanner(see“Methods”,“sensorarraycalibration”).Weinvestigated
thetheoreticallimitsforworkspaceformagnetictrackingwithNMR
using the soft magnetic dipole model Eq. (2). We model the lower
boundfortrackingprecisionforhexagonalplanarsensorarraysusing
measurement covariance, I=HTR−1H, where H and R are the local
observation matrix and sensor noise covariance matrix. Then, we
couldexpressthestatictrackingprecisionas

Σ/ σ B r5 ð3Þ
MV

whereσ ,r,andVarethesensornoise,thedistancetothesensorplane,
B
and the magnetic tracker volume, respectively. We calculated the
modeledtrackingprecisionfora1emutrackerina2Dplanetogether
withthemeanmagneticfieldmeasuredbytrackingsensors(Fig.2e),
whichshoweda1mmlowerboundoftrackingprecisionin100mm
proximityofthearray.
Next,weperformedtrackingexperimentsonmechanicallycon-
strainedlinearchannelsforgroundtruthwhiletrackingtheguidewire
with a particle filter-based tracking algorithm using magnetic field
measurements(SupplementaryFig.10).Then,weevaluatedthepre-
cision and accuracy of the tracker position. Our tracking results
showed less than 1mm precision, matching our model, and below
2mm accuracy in a 60×80mm2 workspace. We observed that the
deviationfromthedipolemodelprohibitstrackingatalargerwork-
spaceinoursmallanimalMRIscanner.However,theworkspacecould
befurtherexpandedinclinicalMRIscanners.Increasingtrackersize
willincreaseworkspace,accordingtoEq.(3),butitwillreducetrackers’
versatilityandintegrationcapabilities.Thus,wediscussmethodsto
expandtheworkspacebymodifyingthesensors’positionandnumber
intheSupplementaryNote6(SupplementaryFig.11andSupplemen-
taryMovie2).

Integrationofminiaturizedwirelessmagnetictrackers
To demonstrate tracker miniaturization, we developed guidewires
withspringsteeltrackersatthedistalend.Thehighsaturationmag-
netizationofsteel,reaching1.7×106A/m2,enablesamagneticmoment
of1emuwithin0.56mm3,thesmallestwirelesstracker(Supplemen-
taryTable1andSupplementaryFig.13).Thesmallsizeallowedusto
integratethetrackerin0.8mm-diameterguidewires(Fig.3a).Trackers
for smaller guidewires would also be possible with different aspect
ratios(SupplementaryFig.14).Later,weillustratedwirelesstrackingin
anexvivoporcinebrain,simulatinganeedleinsertionoperationinto
thebrain(Fig.3b).Weinsertedastraightcatheterinthebrainandtook
pre-operationalMRimagesofthebrainusinganimagingsurfacecoil
shownin Fig. 3c,d. Next, wemanuallyswitched the RF connection
fromthesurfacecoiltotheNMRsensorarray.Then,wecalibratedthe
background field with the diamagnetic brain tissue, which caused
1–2µT variation on different sensors (Supplementary Fig. 15), and
trackedtheguidewireinthecatheterinrealtimewithNMRmagnetic
tracking (Supplementary Movies 3 and 4). We observed that the
magnetic tracking matched with the catheter’s image artifact with
0.78±0.30mmaccuracy,where±SDisa95%confidenceinterval.
ThemainbenefitofminiaturizationwithNMRmagneticsensingis
thehigherversatilityindesigningfunctionaldevices.Whileprevious
wirelesstrackingmethodsobstructmedicaldevices10,wecoulddesign
hollowstructurestoprovideaworkingchannel.Todemonstratethe
potential,wecreatedamagneticallytrackedlaserfiberusingamicro-
machinedhollowirontracker,smallerthan0.8mmindiameter,atthe
distal end (Fig. 4a and Supplementary Movie 5). We showed that
magnetictrackingcouldbeperformedin3Dspacewhilethelaserwas
continuouslyoperated(Fig.4b,c).Wemeasuredatrackingaccuracyof
2.10±0.80mmwithrespecttotheclosestpointinthecenterofthe
spiral channel, which is close to the 3mm diameter of the channel
(SupplementaryFig.16).Next,weintegratedtheminiaturizedtracker
with1.3emumagneticmomentintoacustom-madeendoscopecam-
erasystem,andperformedtrackinginexvivoonaporcineesophagus
todemonstratewirelesstrackingwhileperformingendoscopevideo
capturing(seeSupplementaryMovie6andSupplementaryFig.17).

Deformablemagneticsofttrackers
Tofurtherhighlighttheversatilityofthetrackerdesign,wedeveloped
flexiblemagnetictrackersmadeofmagneticsoftcompositematerials
(Fig.5a).Softmagneticmicroparticle-embeddedelastomericmaterials
haverecentlyemergedinminiaturizedcontinuumrobots2;however,
thelowmagneticmomentsofthesesoftmagnetspreventtheirusein
magnetic tracking with previous approaches. We created a curved
guidewirewithflexiblemagnetictrackerswith1.35emususinga3µL
75% iron microparticle-silicone elastomer mixture at the distal end
(SupplementaryFig.18).Todemonstratefunctionality,weperformed
repeatedmanualnavigationexperimentsinside3D-printedchannels
(Fig. 5b and Supplementary Movie 7). We observed high-accuracy
trackingoflessthan0.72±0.67mmwhentheflexibletrackerwasina
straightconfiguration.However,thetrackingerrorincreasedashighas
4.3mm as the guidewire approached the sensor array (Fig. 5c). We
discussedtheshapeeffectsofflexiblemagnetictrackersintheSup-
plementaryNote7(SupplementaryFig.19).
Finally, we illustrated the potential for ferrofluidic magnetic
trackers using a balloon catheter filled with an iron-oxide (Fe O )
2 3
nanoparticle solution (Fig. 6). Ferrofluids provide the potential for
reconfigurableandshape-changingmagneticsystems21.However,the
low magnetization of ferrofluids has prohibited them from being
tracked magnetically using previous magnetic tracking methods
(Supplementary Fig. 20). First, we showed that the NMR magnetic
sensingcouldbeusedtomonitortheinflationoftheballoon(Sup-
plementary Fig. 21 and Supplementary Movie 8). Next, we demon-
strated magnetic tracking of the ferrofluid-injected balloon with
1.75mL volume and 0.25emu magnetic moment (Supplementary
Movie9andFig.6b).Althoughtrackingprecisionisreducedduetolow
magnetic moment (Supplementary Fig. 22), the maximum tracking
error reaches 5.5mm when the balloon approaches the sensors,
remaining within the large volume of the balloon (Supplemen-
taryNote8).

Methods
Magneticsensor
TheNMRsensorcomprisesa5-turninductivecoilof400μmdiameter
copperwireswrappedaroundacylindricalglasscapillarywithanouter
diameterof4mmandaheightof5mm(Fig.2a).Afterthewinding,the
capillariesarefilledwithdeionizedwaterandsealedpermanentlywith
epoxy (Loctite 401) to prevent evaporation. We use two constant
matchingcapacitors,ranging from0.5 to1pF,andone0.5to12pF
rangetuningcapacitor(KnowlesVoltronics)totunethefrequencyof
theresonatorcircuitto300MHzandmatchittoa50Ωimpedance.
The sensor is placed inside an aluminum-shielded box to prevent
crosstalkbetweenneighboringsensorsandreducetheeffectsofhigh-
frequencynoises.Acapacitivebalancednetworkisusedtotuneand
matchthecoilsthroughaniterativeprocessoftuningandadjusting
the matching capacitors while connected to a Network Analyzer
(KeysightE5061B).Thematchingcapacitorsaremanuallyselectedfor
eachRFcoil.

Sensorswitch
ThesensorswitchisdesignedusinganRFswitch(HMC253ALC4,
AnalogDevices)controlledbyanArduinoUno(SupplementaryFig.2).
TheArduinoisconnectedtothetrigger-outchannelofthe7TpreclinicalMRIscanner(Biospec30/70,Bruker,
Germany)andthreeinputchannelsoftheRFswitchusingoptocou-
plers(FOD8001,Onsemi)topreventanynoiseoriginatinginexternal
systems.ALi-ionbattery,combinedwithanultra-highPSRR(power
supplyrejectionratio)voltageregulator(LT3097,AnalogDevicesInc.),
powersuptheRFswitch.ExceptfortheRFswitchingboard,allthe
other components of the system were placed outside of the MRI
scanner.TheconnectionswiththeRFswitcharemadethroughnon-
magnetic BNC cables (mmcx connectors, Clinch Connectivity Solu-
tionsJohnson).TheArduinocodesweepseightchannelsinsequence
by changing channels in response to a trigger signal from an MRI
scanner.

NMRsequence
TheNMRsequenceformagneticfieldmeasurementiscomposedof
basicfreeinductiondecay(FID)measurementsandatrigger-outsignal
forsynchronizationwiththesensorswitch(SupplementaryFig.2).The
trigger-outallowsArduinotoswitchamongthedifferentsensorswhile
theNMRsequenceoperates,withoutexplicitlyknowingwhichsensor
isbeingmeasured.TosynchronizetheArduinoandthesequence,we
resetthesensorcounterintheArduinocodeifanNMRsignalisnot
receivedformorethan2s.IntheNMRsequence,weusedanexcitation
pulsewithasincshape,0.2msRFduration(T ),31.05kHztransmis-
RF
sion bandwidth (BW), 32µW RF power, and a readout with 2.5ms
acquisitiontime,250sampling,100kHzreceiverBW.Therepetition
time for a single sensor is 5ms, and for an eight-sensor array, it is
40ms.Theparametersareusedinallmagneticsensingexperiments.

Magneticfieldcalculation
ThephaseoftheFIDsignaliscalculatedusingtherealandimaginary
parts provided by the scanner, and phase unwrapping is applied
(SupplementaryFig.1a,b).Thefirst50phasedatapoints(0.5ms)of
thephasesignalarediscardedduetothesettlingtimeofthereceiver
and electronics in the readout system. Additionally, the inhomoge-
neousB1field,accompaniedbytheattenuatingnatureoftheFIDsig-
nal,introducesnonlinearphaseaccumulationovertimeuntilthetotal
noise dominates the signal amplitude (Supplementary Fig. 1b). To
quantifythiseffect,wecalculatedSNRbycomparingthemaximumof
thefilteredFFTwiththeamplitudeofdeviationfromthecurveasa
function of acquisition time (Supplementary Fig. 1c); thus, only the
following200datapointsareusedforfurtherprocessing.Thephase
slopeiscalculatedusinglinearfitting,andthemagneticfieldiscal-
culatedusingEq.(1).WeusedEigenandFFTWlibrariesinC++forreal-
timesignalprocessing.

Sensorarraycalibration
Thecalibrationroutineiscomposedofbackgroundfieldandsensor
positioncalibrations.ThebackgroundfieldΔBvarieswithshimming
configuration,thepatient’stissue,andthemainfieldcoiltemperature.
Therefore,weneedtoperformaΔBcalibration.Instationarycondi-
tions,wecollect10sofmagneticfieldmeasurementswithallsensors
tocalculatethemean(µ ΔB )andstandarddeviation(σ)oftheΔBindi-
viduallyforeachsensor(SupplementaryFig.15b,c).Wesubtractµ ΔB
fromthesensorreadingduringoperationanduseσintheparticlefilter
forsensornoise.
Next,weperformsensorpositioncalibrationusingthegradient
hardwareoftheMRIscanner.Weapplyknowngradientvalues(G)in
positiveandnegativedirectionsinthex-y-zaxesfor5sinpositiveand
negativedirectionsandrecordmagneticfieldmeasurementsfromall
sensors(SupplementaryFig.15d,e).Later,the averagefieldineach
direction is calculated for each sensor, and then we calculate each
sensor’spositionusing

rs i = 1 B s + i
2 G
+B(cid:1) s i ð4Þ

wherers isthepositionoftheithsensorrelativetothecenterofthe
i
MRIscanner,B+ andB(cid:1)arethemeasuredaveragemagneticfieldsin
s s
i i
positive and negative directions. To cancel the sensor geometry
imperfection error, we averaged the measured value in opposite
directionstocalculatethepositionineachdirection.
Asthepositionsofsensorsareacrucialfactorintrackingpreci-
sion,wedesignedanexperimenttodeterminecalibrationaccuracyin
variousconditions(SupplementaryFig.15d–i).Thecalibrationprocess
wasrepeated10timesforthesystemwithsevensensors,bothwithand
withoutthepatient’sstage,andwithaporcinebrainsampleonthe
stage.Underallconditions,weachievedanerroroflessthan5µmin
thexandzdirectionsandlessthan10µmintheydirection.Duetothe
sensors’ asymmetric profile in the y direction, we observed more
errors.Moreover,weobservedanaveragesensornoiseof8nTinall
experiments,withnonotabledifference.

Dipolemeasurement
Acustomstagecomposedofdifferentchannelstructuresandknown
sensor positions was 3D printed using PLA material to validate the
dipolemodel(SupplementaryFig.5).Later,sensorheadswereposi-
tionedinsidethedesignatedlocationsandconnectedtoamatching
circuit. This method, combined with the triangled 3-sensor setup,
ensured the precision ofthepositionandangleof the sensor com-
paredtothechannelsandB field,respectively.The1mm-diameter
0
steel bead magnetic tracker was moved manually with 5mm incre-
mentalstepsduringtheexperimentusingathinguidewirewithdelays
of3sineachstep.

Measurementcovariance
Tocalculatethetheoreticallowerboundforthesensingprecisionofa
sensorset,weusedthelocalobservationmatrix,H(x,y,z),bylinear-
izingthesensorfunction,h(r)= [h,h ,h ,…,h ]∈ℝ7,whereristhe
1 2 3 7
positionofthemagnetintheinertialframe,h(x,y,z)isthesensing
i i i i
functionforithsensor

h
i
x
i
,y
i
,z
i
=
μ
4π
0m(cid:2)2z2(cid:1)x2(cid:1)y2
x2
i
+y2
i
+z2
(cid:3)i
2 5
ð5Þ

andx,y,andz arethedistancesbetweenthemagnetandthesensorin
i i i
Eq.(2).ThelocalobservationmatrixintheformoftheJacobianmatrix,
H∈ℝ3×3,iscalculatedby

H=
∂h
∂r
ð6Þ

Thelinearizedstaticsensorprecision,I∈ℝ3×3,iscalculatedas

I=HTR(cid:1)1H ð7Þ

whereR=diag([σ σ σ …,σ ])∈ℝ7×7isdiagonalsensorcovariance
1, 2, 3, 6
matrix.ThediagonalelementsofIgivetheprecisioninσ ,σ andσ
x y, z
directions.Wecalculatedthefinalprecisionby

Σ=
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
σ2+σ2+σ2 ð8Þ
x y z

Particlefilter
AparticlefilterisarecursiveBayesianstateestimationtechniquethat
usestheMonteCarlomethodtoapproximatetheposteriordistribu-
tionoftheestimatedstateinthreesteps:propagation,reweighting,
andresampling31.Ithasbeenusedinthelocalizationofdipole-based
EMtrackers32.Thealgorithmfirstapproximatesthestatedistribution
usingNparticles,whicharedistributeduniformlyoverthestatespace.
Then,inthepropagationstep,itpredictsthenexttimeevolutionof
each particle using a prediction model with noise. Next, in the
reweighting step, it approximates the posterior distribution of the
statebycalculatingtheprobabilityofeachparticlecontributingtothe
observed sensor measurement using a measurement model with
noise. Finally, inthe resampling step, the algorithm samples N new
particlesfromtheapproximatedposteriordistributionandreplaces
theprevioussetofNparticleswithnewparticles.Then,thealgorithm
recursivelyrepeatsitselfforeachtimestepwithnewsensordata.This
methodrecursivelyrefinestheestimatedpositionusingtheobtained
sensordata,generallyconvergingwithin1–2timestepsifNissuffi-
ciently large. To ensure convergence inthe first step, a large initial
particle number, N , is used. Then, in the next step, the particle
0
numberisreducedtoNduringtheresamplingstep.
Toestimatethemagnetictrackerposition,weemployedaparticle
filter-based state estimation model with the state, x=[rT, ΔB]∈ ℝ4,
composedoftrackerpositionand monitored backgroundmagnetic
fieldvariation.Weconsiderthetrackingproblemasastaticprediction
modelandanonlinearmeasurementmodel:

xðk
Þ=xðk(cid:1)1Þ+νðk(cid:1)1Þ ð9Þ

zðk
Þ=Bd ðk
Þ+ΔBðk
Þ+ωðk
Þ ð10Þ

wherekisthetimestepofestimation,zisthemeasurementvector∈
ℝ8,andνandωarethepredictionandmeasurementnoisemodeledas
a Gaussian distribution with covariance Σ ν=diag([σ x , σ y , σ z , σ ΔB ]) ∈
ℝ4×4 and Σ ω=diag([σ
s0
,σ
s1
,….,σ
s7
])∈ ℝ8×8.We used theprediction
noisewithσ x =σ y =σ z =1mmandσ ΔB =0.1nT.Themeasurementnoise
iscalculatedduringthesensorarraycalibration.B (k)=[B (r ),B (r),d d 0 d 1
…,B (r )]T∈ℝ8isthevectorofthesensormeasurementmodelofthe
d 7
sensorsattimestepk.Notethatthereferencesensorisincludedinthe
estimation as the 0th sensor to estimate the change in the
backgroundfield.
WeartedtheparticlefilterwithN =20,000andreducedthe
0
particlenumbertoN=500afterthefirstiterationofestimation.First,
thealgorithmpropagatestheparticlepositionandbackgroundpre-
dictions using Eq. (8).Next, we calculate the expected sensormea-
surement,z(cid:2),foreachparticleusingEq.(9)withthenoiseterm.Then,
we calculate the measurement likelihood for each particle using a
normaldistribution,

P i (cid:2)z i jz =N z(cid:2) i jz,Σ ω ð11Þ

whereiistheindexoftheparticleinNparticles.Later,wescalethe
particleprobabilities,β
=PN Pi ,between0and1.Finally,weresampled
i
theparticlesusingarandomPniumberrfromauniformdistribution(0,
1). To avoid prediction er0rors due to the inhomogeneity effect in
proximitytothesensors,ifanysensormanagementexceeds20μT,
weremovethemeasurementofthecorrespondingsensor,excludeit
from the resampling stage of the particle filter, and estimate the
positionusingtheremainingsensors.

Workspaceexperiment
Tovalidatetheprecisionandaccuracyofthetrackinginthesimulated
workspace, a custom stage with parallel channel structures was 3d
printedusingPLAmaterial(SupplementaryFig.10a).Thestagewas
mechanicallyfixedinsidetheMRIbore,andthechannelswereexten-
dedtotheoutsideoftheMRIusingPTFEtubes.Duringtheexperiment,
after calibration, the magnetic tracker, composed of two 1mm-dia-
metersteelbeads,wasplacedinsideonechannelandmovedmanually
in 5mm incremental steps using a thin guidewire, with a 3-s delay
betweeneachstep.Finally,thepositionswereestimated10timesfor
eachchannelusingtheparticlefilter(SupplementaryFig.10b,c).

Guidewireandlasermanufacturing
During the guidewire preparation, we used an MRI-compatible
0.5mm-diameterglassopticfiberastheelasticcoreand0.8mm-dia-
meterTeflontubeswitha0.1mmwallthickness(Adtech,UK).Weglued
a glass fiber, a Teflon tube, and the 0.6mm-diameter 2mm-height
springsteelmagnetictracker.Wepreparedthelaserbyremovingthe
coatingfromthelast2mmoftheopticalfiber.Then,weglueamicro-
machinedirontrackerwithanouterdiameterof0.8mm,aninnerdia-
meterof0.3mm,andalengthof2mm.Later,weassembledtheoptical
fiber with a laser connector and placed a black heat-shrink tube
to prevent light leakage. We prepared the soft guidewire with a
flexible magnetic tracker using a 0.8mm-diameter Teflon tube and
0.5mm-diameteropticfiberasthecore.Atthelast20cmofthedistal
end,wereplacedtheopticfiberwitha0.3mm-diametertungstenwire
withanangledtip.Wefilledthetipwith3µLofsoftmagneticmaterial,
comprising a 75% mass ratio of µm-sized iron powder and Ecoflex.
The endoscope system comprises a 1mm×−1mm miniature camera
(amsNanEye2D)insidea4mmdiameterTeflontube(Adtech,UK)and
two1mmsteelbeadsasthemagnetictracker.Thetrackerisputatthe
backofthecameraandbothofthemarefixedwithepoxyinsidethetip
oftheTeflontube.Finally,thecameraisconnectedthroughacapture
box(amsNANO-FIB-BOX)tosavethevideofeedtocomputer.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Tiryaki et al. describe a novel way to perform magnetic tracking using a soft ferromagnetic marker and an array of NMR probes in an MRI instrument. I’ll start by saying this is probably not the way I would go about tracking using an MRI, but it is an interesting way to do it and might have its advantages. The authors have done a solid job in their performance analysis and their consideration of many different effects, so I think it will be publishable in Nature Communications, but I do have some questions, concerns, and suggestions below that need to be addressed.\n1. I’m not completely clear about the use case for this device. Is this for identifying the location of a catheter during medical procedures, where one wants to overlay the location with an MRI image? Or is it more general and just using the MRI as a big magnet? One of the cited papers was tracking bees, for instance. If it is medical uses, there is a whole field of catheter tracking that has been ignored in the introduction. There are even commercially sold devices that do this for MRI with similar accuracy to the manuscript over a larger volume. I provide a short list here:\nhttps://ajronline.org/doi/10.2214/ajr.183.2.1830391\nhttps://onlinelibrary.wiley.com/doi/10.1002/mrm.24654\nhttps://onlinelibrary.wiley.com/doi/full/10.1002/mrm.20202\nhttps://inventions.techventures.columbia.edu/technologies/wireless-magnetic--1438\nhttps://www.robinmedical.com/endoscout.html\nI’d like the authors to better describe the advantages and weaknesses of their technique in relation to these, because their method is quite different, but the application is not unique.\n2. If the use case is to use the device in conjunction with MRI, there needs to be some discussion and analysis of how well the techniques can coexist as well as the safety implications. Ferromagnetic materials are usually considered incompatible with MRI for a number reasons. A) They distort the image, so they might be able to locate the probe but won’t get a good anatomical image around the probe. (The authors imply this when they mention an image artifact. Is there an image of it?) B) There is RF heating of the metal in the probe. C) There are magnetic forces on the probe (the authors even have a recent Science Advances paper on that subject).\n3. The description of how the location is determined from the NMR measurements is not complete enough to be reproducible. There are no citations listed for the particle filter technique or how it can be used to determine the location of a dipole relative to a number of sensors. It is an interesting way to determine location, rather than trying to solve the inverse problem, and is a critical part of the paper. Has this been done before? Are there citations? What is the starting volume distribution for the 200 test particles in the Monte Carlo simulation? If this is iterative, how many iterations are used? What exactly do you mean by “resample the particles?”\n4. I know that quantum sensors are all the rage right now, but a bulk NMR magnetometer is not a quantum sensor. There are no single spins, quantum entanglement, or quantum interference involved.", "reviewer_2": "This paper proposes a wireless magnetic tracking technology based on nuclear magnetic resonance, demonstrating significant advantages in terms of high sensitivity, miniaturization, and compatibility with MRI systems. The study validates the application potential of NMR magnetic sensors in different types of magnetic trackers (rigid, flexible, hollow, and ferrofluidic) through various experiments and highlights their broad applicability in minimally invasive medical devices. However, despite the novelty of this research, there are several aspects that require further discussion and refinement. Detailed review comments are as follows:\n1. The current system utilizes a planar hexagonal sensor array, which simplifies the hardware design but imposes limitations on localization accuracy along the Z-axis. It is recommended that the authors further investigate the effect of sensor spacing in the Z-direction using a three-dimensional array configuration (e.g., Figure S11.G), in order to quantify the potential improvement in precision and support its clinical applicability.\n2. Although individual NMR magnetic sensors are compact, the current sensor layout (as shown in figure S11) appears to limit the technology's application range, especially for instrument tracking outside the head region. The existing layout may cause interference between the sensors and the patient in other body areas, reducing clinical applicability. The authors are encouraged to explore optimized layout designs for different body regions to expand the technology’s application to more clinical scenarios. Furthermore, as a general-purpose tracking system, requiring layout re-optimization for each body region may significantly complicate its clinical use. The authors are advised to design a highly adaptable universal layout to simplify clinical operations and improve the technology’s potential for broader adoption.\n3. The integration of magnetic trackers with MRI imaging is demonstrated in figure 3, showing that the magnetic tracking data aligns with the artifact of the guidewire in MRI images, enabling precise localization. However, the potential artifacts or interference caused by the magnetic tracker on MRI imaging are not thoroughly discussed. Additionally, there is a lack of comparative MRI images without magnetic trackers, making it difficult to assess their specific impact on imaging quality.\n4. The dipole model currently assumes that the magnetic moment is aligned with the B₀ field (Equation 2). However, for flexible trackers, bending may cause deviations in the magnetic moment direction, which can introduce localization errors. It is encouraged to incorporate a corrected model that accounts for this effect to improve the accuracy of the particle filter-based tracking algorithm.\n5. The paper mentions an ex vivo pig brain navigation experiment but does not provide accompanying video evidence. This omission may affect the reproducibility and credibility of the results. The authors are advised to provide video documentation of the experiment to visually demonstrate the navigation process and its correlation with MRI imaging, thereby enhancing the study’s visualization and reliability.\n6. In lines 59-76 and the supplementary material, the authors provide only a brief overview of the selection and construction methodology for the NMR sensors. There is insufficient explanation regarding the underlying principles of the localization method. It is recommended that the authors include a more detailed explanation of these fundamental principles. For instance, clarification on the Free Induction Decay (FID) signal and the rationale behind designing the NMR sensor with the RF coil encircling a glass tube of water would be beneficial. This addition will help readers grasp the principle-based innovations of this sensor system.\n7. All experiments were conducted using a 7T preclinical animal MRI system (line 89 in the main text), whereas standard clinical MRI systems typically operate at 1.5–3T. Please clarify whether the proposed tracking method is compatible with clinical MRI field strengths.\n8. The background magnetic field appears to have an effect on the localization results. If this is indeed the case, it is recommended that the authors conduct additional localization experiments with the NMR sensing system under varying background fields to investigate this influence.\n9. While Figure S22 demonstrates dual-target localization, the experimental setup is limited to a relatively large inter-target distance (4 cm). It does not evaluate performance in scenarios involving close spacing or overlapping magnetic fields. It is suggested that the authors assess whether accurate dual-target tracking is achievable at smaller separations.\n10. The authors dedicate significant space in the manuscript to describing various miniaturized tracker devices. At line 171 in the main text, an application scenario for the hollow magnetic tracker is mentioned. However, the authors primarily list the positioning performance of these different magnetic trackers within the NMR sensing system, without thoroughly discussing their practical application value. The authors are encouraged to supplement their study with experiments simulating real-world conditions (e.g., ex vivo or in vivo experiments, or integration with commercial equipment) to demonstrate the practical utility of these multiple forms of magnetic trackers.\n11. The paper does not sufficiently demonstrate the advantages of NMR magnetic tracking over electromagnetic (EM) tracking. While EM tracking systems perform well in non-MRI environments, the strengths of NMR magnetic tracking lie in its compatibility with MRI and its high sensitivity. The authors are encouraged to conduct comparative experiments to quantify differences between the two technologies in terms of accuracy, sensitivity, miniaturization, and clinical applicability, thereby better highlighting the unique value of NMR magnetic tracking.\n12. With the continuous improvement of MRI imaging speeds, the relevance of this research warrants further discussion. Faster MRI imaging has alleviated some of the challenges associated with real-time navigation. The authors should further explore the potential synergy between NMR-based magnetic tracking and fast MRI imaging, emphasizing the unique advantages of magnetic tracking in terms of real-time performance and miniaturization.\n13. The paper notes that this method is unsuitable for patients with ferromagnetic implants and faces challenges in environments with dynamic tissues (e.g., the heart or nerves) due to background signal variations. These limitations may hinder the adoption of this technology in complex clinical scenarios. The authors are encouraged to discuss potential solutions to address these limitations.\nIn summary, this paper introduces an innovative NMR-based wireless magnetic tracking technology with advantages in sensitivity, miniaturization, and MRI compatibility. While the research shows great potential, some areas need further improvement, such as optimizing sensor layouts, addressing MRI interference, refining models for flexible trackers, and providing more experimental evidence. Additionally, comparisons with electromagnetic tracking and discussions on clinical limitations and applications would enhance the study's impact and practical relevance."}, "author_response": "We would like to thank the reviewers for their invaluable comments and suggestions on our\nmanuscript. We have addressed the points raised by the reviewers point by point below, which\nsignificantly improved our paper. Our responses are in blue color, and all changes in the revised\nmanuscript are highlighted with yellow color text.\nReviewer #1\nTiryaki et al. describe a novel way to perform magnetic tracking using a soft ferromagnetic marker\nand an array of NMR probes in an MRI instrument. I’ll start by saying this is probably not the way\nI would go about tracking using an MRI, but it is an interesting way to do it and might have its\nadvantages. The authors have done a solid job in their performance analysis and their consideration\nof many different effects, so I think it will be publishable in Nature Communications, but I do have\nsome questions, concerns, and suggestions below that need to be addressed.\nResponse: We thank the reviewer for the kind comments.\nComment 1.1) I’m not completely clear about the use case for this device. Is this for identifying\nthe location of a catheter during medical procedures, where one wants to overlay the location with\nan MRI image? Or is it more general and just using the MRI as a big magnet? One of the cited\npapers was tracking bees, for instance. If it is medical uses, there is a whole field of catheter\ntracking that has been ignored in the introduction. There are even commercially sold devices that\ndo this for MRI with similar accuracy to the manuscript over a larger volume. I provide a short list\nhere:\nhttps://ajronline.org/doi/10.2214/ajr.183.2.1830391\nhttps://onlinelibrary.wiley.com/doi/10.1002/mrm.24654\nhttps://onlinelibrary.wiley.com/doi/full/10.1002/mrm.20202\nhttps://inventions.techventures.columbia.edu/technologies/wireless-magnetic--1438\nhttps://www.robinmedical.com/endoscout.html\nI’d like the authors to better describe the advantages and weaknesses of their technique in relation\nto these, because their method is quite different, but the application is not unique.\nResponse: We thank the reviewer for their comment and the provided literature, which helped us\nfurther highlight the advantage of NMR magnetic tracking.\nThe primary use case and purpose of the proposed wireless magnetic tracking system is to provide\nrapid position feedback for minimally invasive devices, such as catheters, guidewires, and needles,\nwithin an MRI scanner. Consequently, we aim to develop an auxiliary wireless tracking system\nthat operates with preoperative MR images in medical applications, and potentially with real-time\nMR images in the future. We envision that, in the future, MR technology will find increasing use\nas a therapeutic platform, driven by developments in imaging, MR-compatible robotic systems,\nand sensing methods, such as the proposed NMR magnetic tracking. In this sense, no, the MRI\nscanner is not only used as a big magnet.\nMoreover, the current proposed NMR magnetic tracking system utilizes the RF hardware, in\naddition to the MRI scanner’s main static field, to generate the NMR signal. Although we also\nacknowledge that we would undoubtedly benefit from the flexibility of use if we had separate RF\nhardware for the NMR sensors that synchronously operate with the MRI scanner.\nAll that being said, we also believe that NMR magnetic sensing, as a high-sensitivity magnetic\nfield measurement technique, enabled us to highlight the true potential of wireless magnetic\ntracking, which was not previously possible to elucidate with the magnetic sensing methods used\nin magnetic tracking. Therefore, we also try to keep our use cases general, much like the Gleich et\nal.10 with their bee tracking example, while staying within reason, considering medical\napplications in MRI scanners. Furthermore, we also envision that NMR magnetic tracking could\nfind future use outside of MRI scanners, with constructions such as the recently evolving single-\nsided magnetic resonance sensors 29. We also briefly mentioned this potential venue for NMR\nmagnetic tracking in the “Discussion” section\nFurthermore, while clinical use of high-field MRI scanners is becoming popular 26, the integration of NMR\nmagnetic sensor arrays into lower field MRI scanners such as 1.5 T/3 T and emerging ultra-low-field MRI\nscanners could increase the affordability of magnetically guided minimally invasive operations in the future\n27;\nThe Endoscout tracking system, as cited by the reviewer, performs localization by measuring\nmagnetic field changes due to the magnetic gradient coils of the MRI scanner. It is composed of\nthree-axis 7.4 mm fluxmeter coils 15. In this sense, the Endoscout system can be classified as an\nexample of an onboard magnetic sensing approach, which we introduced in the “Introduction”.\nAmong remote sensing approaches, commercial electromagnetic (EM) sensors 7 and onboard\nmagnetic sensors 12–15 are the most common approaches.\nHowever, this system also suffers from the same issues as other tethered onboard magnetic sensing\napproaches, such as larger dimensions, which prohibit integration in small medical tools.\nAlthough the proposed magnetic tracking method is ultimately to complement, not replace, the\nMRI-based tracking methods. We agree with the reviewer that highlighting specific advantages\nand weaknesses enhances the value of our study. Therefore, as reviewers requested, we also\nevaluated the proposed NMR magnetic tracking method in Comparison to MR image-based\ntracking methods suggested by the reviewers, as well as others discussed in the “Discussion”.\nAdditionally, the NMR magnetic sensing technology addresses certain drawbacks of MR image-\nbased tracking. Despite continuous improvements in MRI speed, real-time 3D tracking with\npassive fiducial markers, such as magnetic 22, 19-Fluorine 23, and RF coils24 , and active MRI\npickup coils 25, remains limited by slice thickness 22 and RF-induced tissue heating. In contrast,\nNMR sensors provide continuous 3D tracking without requiring the deposition of RF energy (see\nSupplementary Information), enabling continuous navigation with no risk of heating. Furthermore,\nNMR magnetic sensing eliminates acoustic noise, which in fast MRI-based tracking can exceed\nsafe exposure limits 3,5 and hinder communication between clinicians during interventional MRI\noperations. Because NMR does not rely on MR gradients (figure S23, Movie S8), it is inherently\nsilent, creating a safer acoustic environment for both patients and clinicians. Moreover, NMR\ntracking also functions in air-filled cavities, where most MRI-based tracking methods, except 19F\ntracking 23, fail due to the absence of 1H of the surrounding water or tissue, allowing for the\nuninterrupted tracking of tools such as needles during insertion from outside the skin.\nComment 1.2) If the use case is to use the device in conjunction with MRI, there needs to be some\ndiscussion and analysis of how well the techniques can coexist as well as the safety implications.\nFerromagnetic materials are usually considered incompatible with MRI for a number reasons. A)\nThey distort the image, so they might be able to locate the probe but won’t get a good anatomical\nimage around the probe. (The authors imply this when they mention an image artifact. Is there an\nimage of it?) B) There is RF heating of the metal in the probe. C) There are magnetic forces on the\nprobe (the authors even have a recent Science Advances paper on that subject).\nResponse: We thank the reviewer for the comment. To address MRI compatibility and the safety\nimplications, we have added the following content to the manuscript.\nA) MRI artifact: The magnetic image artifact, which obstructs the anatomical image around the\nclose vicinity of the magnetic trackers, is unavoidable for magnetic trackers in MR images. An\nexample of image artifacts is presented in our previous studies [2022Tiryaki]; however, for the\ncompleteness of this work, we have added a video of guidewire navigation (Movie S9) and\nsnapshots of the artifact (Figure S26) in the “Magnetic Artifact in MR Images” section of the\nSupplementary Materials.\nS11. Magnetic Artifact in MR Images\nPlacing a magnetic tracker inside an MRI machine will disturb the magnetic field in the shape of\na magnetic dipole in three-dimensional space. This disturbance is significant in a volume\nsurrounding the tracker, leading to a substantial change in the NMR frequency of water, as stated\nin Eq. 1. As a result, the volume will not be excited within the utilized RF signal bandwidth,\ncausing complete signal loss in that area. At greater distances from the tracker, the disturbance in\nthe magnetic field is not strong enough to significantly shift the frequency. However, it can still\ndistort the image by affecting the calculations of the gradient fields, which can show itself as a\nskewed image. Two ex vivo experiments using porcine brain were conducted to demonstrate this\neffect in a real tissue. In the first experiment, the tracker was inserted inside the brain in 10 steps,\nand an MR image was taken after each step. The entire process is illustrated in Figure S26 and\nsummarized in Movie S9. In the second experiment, a preoperative image was first taken. Then,\nNMR sensors tracked the tracker’s position throughout the insertion process. Finally, a\npostoperative image was taken. The preoperative and postoperative images are overlaid with the\nestimated position of the tracker. They are shown in Figure S27 as snapshots of the process, and\nthe whole procedure is documented in Movie S2.\nB) RF Heating: The RF heating is a common problem for conductive objects during MRI,\nespecially if the conductive object has a specific geometry, turning the object into an RF resonator.\nFor instance, long conductive wires whose length is comparable to the wavelength of the MRI RF\nsignal, or solenoid coils whose resonance frequency is tuned to the frequency of the MRI RF signal.\nThe conductive magnetic trackers, particularly rigid iron trackers, that we used for NMR tracking\nare too small to exhibit resonance behavior at the RF frequencies used by MRI scanners. The soft\nelastic trackers and the ferrofluid ones, on the other hand, are not conductive enough to cause RF\nheating issues.\nMoreover, we would like to emphasize that MRI-based RF heating issues arise during long-\nduration and continuous imaging. The NMR magnetic sensors do not radiate RF signals outside of\ntheir shielding; therefore, they do not cause any heating issues. To demonstrate the RF safety in\nterms of heating, we performed an RF heating experiment while MR imaging and NMR sensing\nin a saline medium with and without our trackers, and we reported our results in the supplementary\ninformation.\nS13. RF heating experiments\nTo demonstrate that the NMR magnetic tracking does not cause RF-induced heating problems, we\nperformed controlled imaging and sensing experiments. We compared the temperature increase\nduring the extended imaging sequence and sensing in two different sets of experiments. First, the\nexperiments were conducted using 80 ml of 2.6 M saline solution in imaging and sensing mode.\nA hollow tracker was then placed inside the solution, and the experiments were repeated. A\nGradient Echo (GRE) sequence with a repetition time of 10 ms, an RF pulse duration of 0.54 ms,\nand a power of 90 W was used for imaging mode, while the sensing mode remained unchanged.\nEach experiment was conducted over 20 minutes, and sufficient time was allowed for the system\nto stabilize between each experiment. Three temperature sensors were utilised during each\nexperiment, two placed next to the tracker and one far away to measure the environment’s\ntemperature. During the imaging period, we observed a consistent temperature increase due to the\nhigh conductivity of the solution (see Figure S29). However, we noted no significant change in\ntemperature after placing the hollow tracker inside the solution. This is expected because the\ngeometry of the tracker is much smaller than the signal wavelength, resulting in a practically\nnegligible absorption rate. Additionally, no substantial temperature change was detected in the\nsensor mode, which reflects our expectation that no RF radiation exists outside the sensor shielded\nbox.\nFigure S29. Rf heating comparison in imaging and sensing mode inside MRI. Temperature\nmeasurement of 80 ml of 2.6 M saline solution over 20 minutes (A) and with a hollow tracker\ninside the solution (B) in imaging and sensing modes.\nWe also include additional discussion about RF heating in the “Discussion” section, which further\nhighlights the advantage of the proposed NMR magnetic tracking method.\nAdditionally, the NMR magnetic sensing technology addresses certain drawbacks of MR image-\nbased tracking. Despite continuous improvements in MRI speed, real-time 3D tracking with\npassive fiducial markers, such as magnetic 22, 19-Fluorine 23, and RF coils24 , and active MRI\npickup coils 25, remains limited by slice thickness 22 and RF-induced tissue heating. In contrast,\nNMR sensors provide continuous 3D tracking without requiring the deposition of RF energy (see\nSupplementary Information), enabling continuous navigation with no risk of heating.\nC) Magnetic force and torques: We added a “Magnetic Force and Torque Safety” section in the\nSupplementary Information.\nS14. Magnetic force and torque safety\nThe magnetic force and torque are, in general, important safety risks in MRI-compatible devices.\nWe observe magnetic forces at the entrance of the MRI bore due to the high magnetic gradients,\nwhich could reach 20 T/m in 7 Tesla MRI scanners, and magnetic torques at the imaging center of\nthe MRI scanner, where we have high uniform magnetic fields. We calculated the maximum\nmagnetic force exerted on the tracker with a 1 emu magnetic moment using\n𝜕𝐻\n𝐹 = 𝜇 𝑉𝑀 𝑧 , [S20]\n0 𝑠 𝜕𝑧\nas 19 mN in our 7 T MRI scanner 6. A human operator or a mechanical insertion mechanism could\neasily overcome this force. Moreover, the magnetic force on the magnetic tracker disappears once\nthe tracker is at the imaging center. The MR imaging gradient would apply a small force on the\ntracker; however, due to the very low strength of these gradients, typically less than 60 mT/m, the\nmagnetic force during imaging would be in the order of or less than a couple of µN, which would\nbarely vibrate the tip of a guidewire. Since our NMR magnetic tracking does not utilize gradient\ncoils, we do not need to consider imaging gradient-based forces either.\nOn the other hand, the magnetic field at the center of the MRI scanner applies a magnetic torque,\naligning the tracker’s magnetic easy axis with the field direction. Since we used soft magnetic\nmaterials rather than hard magnetic materials, this magnetic torque is much smaller than in our\nprevious work. We calculated the maximum torque acting on the 1 emu tracker with a 0.6 mm\ndiameter and a 2 mm height solid tracker, using6\n𝜏 =\n𝜇0𝑉𝑁𝑀𝑠 2\n. [S21]\ncalculated as 0.3 mN/m, which is an order of magnitude smaller than the torques in our previous\nwork. A flexible tracker with the same 1 emu has much lower torque since the magnetic materials\nare distributed over a larger volume with lower magnetic density. That being said, we should note\nthat there is no literature on the calculation of magnetic torque on flexible magnetic materials\ncomposed of magnetic microparticles and an elastomer matrix at under-saturation conditions.\nComment 1.3) The description of how the location is determined from the NMR measurements is\nnot complete enough to be reproducible. There are no citations listed for the particle filter\ntechnique or how it can be used to determine the location of a dipole relative to a number of\nsensors. It is an interesting way to determine location, rather than trying to solve the inverse\nproblem, and is a critical part of the paper. Has this been done before? Are there citations? What\nis the starting volume distribution for the 200 test particles in the Monte Carlo simulation? If this\nis iterative, how many iterations are used? What exactly do you mean by “resample the particles?”\nResponse: We thank the reviewer for the comment. To increase the reproducibility of the proposed\ntracking method, we have elaborated the description of the particle filter in the “Materials and\nMethods” section in the supplementary materials by adding citations to particle filter techniques.\nTo the best of our knowledge, it is the first time a particle filter is used for magnetic dipole tracking;\nhowever, particle filtering is used for dipole-based tracking in array-based electromagnetic\ntracking 33. We also provided more details on our implementation of the particle filter.\nA particle filter is a recursive Bayesian state estimation technique that uses the Monte Carlo\nmethod to approximate the posterior distribution of the estimated state in three steps: propagation,\nreweighting, and resampling32. It has been used in the localization of dipole-based EM trackers33.\nThe algorithm first approximates the state distribution using N particles, which are distributed\nuniformly over the state space. Then, in the propagation step, it predicts the next time evolution of\neach particle using a prediction model with noise. Next, in the reweighting step, it approximates\nthe posterior distribution of the state by calculating the probability of each particle contributing to\nthe observed sensor measurement using a measurement model with noise. Finally, in the\nresampling step, the algorithm samples N new particles from the approximated posterior\ndistribution and replaces the previous set of N particles with new particles. Then, the algorithm\nrecursively repeats itself for each time step with new sensor data. This method recursively refines\nthe estimated position using the obtained sensor data, generally converging within 1-2 time steps\nif N is sufficiently large. To ensure convergence in the first step, a large initial particle number,\nN0, is used. Then, in the next step, the particle number is reduced to N during the resampling step.\nTo estimate the magnetic tracker position, we employed a particle filter-based state estimation\nmodel with the state, x = [rT, ΔB] ∈ ℝ4, composed of tracker position and monitored background\nmagnetic field variation. We consider the tracking problem as a static prediction model and a\nnonlinear measurement model:\n𝐱(𝑘) = 𝐱(𝑘 −1)+𝜈(𝑘 −1), [S8]\n𝐳(𝑘) = 𝐁 (𝑘)+Δ𝐵(𝑘)+𝜔(𝑘) , [S9]\n𝑑\nwhere k is the time step of estimation, z is the measurement vector ∈ ℝ8, and ν and ω are the\nprediction and measurement noise modeled as a Gaussian distribution with covariance Σ =\nν\ndiag([σ , σ , σ , σ ]) ∈ ℝ4×4 and Σ = diag([σ , σ ,…., σ ]) ∈ ℝ8×8. We used the prediction noise\nx y z ΔB ω s0 s1 s7\nwith σ =σ =σ = 1 mm and σ = 0.1 nT. The measurement noise is calculated during the sensor\nx y z ΔB\narray calibration. B (k) = [B (r ), B (r ), …, B (r )]T ∈ ℝ8 is the vector of the sensor measurement\nd d 0 d 1 d 7\nmodel of the sensors at time step k. Note that the reference sensor is included in the estimation as\nthe 0th sensor to estimate the change in the background field.\nWe started the particle filter with N = 20000, and reduced the particle number to N = 500 after\n0\nthe first iteration of estimation. First, the algorithm propagates the particle position and background\npredictions using Eqn S6. Next, we calculate the expected sensor measurement, 𝐳̅, for each particle\nusing Eqn S7 with the noise term. Then, we calculate the measurement likelihood for each particle\nusing a Normal distribution,\nP(𝐳̅ | 𝐳) = 𝑁 (𝐳̅ | 𝐳,𝚺 ), [S10]\n𝑖 𝑖 𝑖 𝜔\nwhere i is the index of the particle in N particles. Later, we scale the particle probabilities, 𝛽 =\n𝑖\nP𝑖\n, between 0 and 1. Finally, we resampled the particles using a random number r from a uniform\n∑𝑁\n0\n𝑃𝑖\ndistribution (0,1). To avoid prediction errors due to the inhomogeneity effect in proximity to the\nsensors, if any sensor measurement exceeds 20 μT, we remove the measurement of the\ncorresponding sensor, exclude it from the resampling stage of the particle filter, and estimate the\nposition using the remaining sensors.\nComment 1.4) I know that quantum sensors are all the rage right now, but a bulk NMR\nmagnetometer is not a quantum sensor. There are no single spins, quantum entanglement, or\nquantum interference involved.\nResponse: We appreciate the reviewer’s point. NMR magnetometers exploit the quantum property\nof nuclear spin precession in a magnetic field. The Larmor precession, the quantization of spin\nenergy levels, and coherent manipulation via RF pulses are fundamentally quantum mechanical in\nnature. Therefore, we refer to it as a quantum sensor. We updated our description of the quantum\nsensor in the manuscript to clarify what we refer to as a quantum sensor as follows.\nThe required sensitivity could be achieved with quantum sensing approaches exploiting quantum\nproperties of matter for magnetic field measurement 16, such as superconducting quantum devices\n(SQUID) 17, optically pumped magnetic (OPM) sensors 18, electron spin magnetic resonance 19,\nand nuclear magnetic resonance (NMR) magnetic sensors 20.\nAfter carefully investigating the literature on magnetic sensing methods, we observed that only\nsensing methods based on quantum properties, such as SQUID, OPM, ESMR, and NMR sensors,\nhave the potential to provide the required sensitivity for magnetic tracking on smaller scales. We\nwant to use our work as an opportunity to introduce the magnetic tracking problem to the quantum\nsensor community.\nReviewer #2\nThis paper proposes a wireless magnetic tracking technology based on nuclear magnetic\nresonance, demonstrating significant advantages in terms of high sensitivity, miniaturization, and\ncompatibility with MRI systems. The study validates the application potential of NMR magnetic\nsensors in different types of magnetic trackers (rigid, flexible, hollow, and ferrofluidic) through\nvarious experiments and highlights their broad applicability in minimally invasive medical\ndevices. However, despite the novelty of this research, there are several aspects that require further\ndiscussion and refinement. Detailed review comments are as follows:\nResponse: We thank the reviewer for the kind comments.\nComment 2.1) The current system utilizes a planar hexagonal sensor array, which simplifies the\nhardware design but imposes limitations on localization accuracy along the Z-axis. It is\nrecommended that the authors further investigate the effect of sensor spacing in the Z-direction\nusing a three-dimensional array configuration (e.g., Figure S11.G), in order to quantify the\npotential improvement in precision and support its clinical applicability.\nResponse: We appreciate the reviewer’s comment. As suggested, we have expanded the “S5.\nWorkspace Scaling” section to include various 3D configurations and have analyzed their\ncorresponding precision maps, which are shown in the new Figure S.12. Additionally, we prepared\n“Movie S10” to enhance the visualization of the 3D precision map of the arrays. We used the\nexperimental floor noise to estimate the precision map for all 3D configurations in three-\ndimensional space. The following part was added to “S5. Workspace Scaling”:\nWe can achieve a significantly larger workspace by distributing additional sensors in 3D space. In\nour study, we illustrated various 3D sensor array configurations in different medical intervention\nscenarios, focusing on three specific regions of the body while utilizing the experimental noise\nfloor and the mentioned simulation techniques. First, we examined endonasal routes to the skull\nbase using an array of 19 sensors arranged in a triangular format across three rings to cover the\naverage human head. One ring is positioned at the top of the head, while the other two rings\nencircle the forehead and nasal areas. As shown in Figure S12a-c, the 2D precision map indicates\nthat most brain areas have a precision of more than half a millimetre, and there is over 1 mm of\nprecision from the nasal area to the brain at a depth of up to 3 cm. As illustrated in Movie S10, the\nbrain region maintains the half-millimeter precision throughout the entire brain volume.\nNext, we analyzed transfemoral access via the common femoral artery, located about 2 cm below\nthe inguinal ligament. For this analysis, we used the same six-sensor ring array around the thigh,\ndemonstrating the extensive workspace available (Figure S12d-f). The precision map indicates that\nwe can achieve better than 1 mm accuracy up to 7 cm deep into the tissue until we reach the bone.\nBy cascading the rings, we can cover a much larger volume if necessary; in this case, we utilized\na total of 24 sensors arranged in four arrays.\nFinally, we investigated the abdominal area, the largest region. Numerous procedures may require\naccess to internal structures, such as suprapubic cystostomy, which targets the anterior bladder\nwall; peritoneal dialysis (PD) catheter insertion into the peritoneal cavity; or percutaneous\nnephrostomy, which provides access to the kidneys from the posterior flank. To ensure access to\nthe entire abdominal volume, we repeated the triangular configuration three times in succession,\ncreating an array of 39 sensors, which formed a belt around one side of the abdomen (either\nposterior or anterior access). As evident in the 2D precision slice taken 7 cm deep in the body\n(Figure S12g-i), we achieved a precision of over 1 mm across the entire 40 cm width of an average\nbody. By cascading this pattern, we can effectively cover the whole abdominal area, rather than\nfocusing on just one specific procedure. All the analyzed areas are represented in 3D space, with\nthe results showcased in Movie S10.\nFigure S11. Workspace scaling. A) Current sensor array arrangement. B-C) Estimation precision\nas a function of tracker distance (B) and sensor spacing (C). D) Sensor number scaling. E-F)\nComparison of estimation precision with different sensor numbers as a function of distance from\nthe tracker.\nFigure S12. Various 3D sensor arrays for medical interventions. A-C) A 3D array proposed\nfor the head, with its precision map separate (B) and overlaid (C) on the head. D-F) A 3D array\nproposed for the thigh region and its precision map, separate (E) and overlayed (F) on the thigh.\nG-I) A 3D array proposed for the abdominal region and its precision map, separate (H) and\noverlayed (I) on the abdominal region.\nComment 2.2) Although individual NMR magnetic sensors are compact, the current sensor layout\n(as shown in Figure S11) appears to limit the technology’s application range, especially for\ninstrument tracking outside the head region. The existing layout may cause interference between\nthe sensors and the patient in other body areas, reducing clinical applicability. The authors are\nencouraged to explore optimized layout designs for different body regions to expand the\ntechnology’s application to more clinical scenarios. Furthermore, as a general-purpose tracking\nsystem, requiring layout re-optimization for each body region may significantly complicate its\nclinical use.\nResponse: We thank the reviewer for the comments. We realized that we did not mention the\naluminum RF shielding we applied around our sensors, which is, in fact, very important for the\nreproducibility of our results. The aluminum shielding around the sensors isolates the RF signal of\neach NMR coil, preventing interference between sensors and with the tissue. We introduced the\nRF shield in the “Result” part with the following.\nEach sensor is placed in an RF shielding composed of aluminium foil (figure S15a), which\neliminates interference between sensors and also the nearby tissue (see Supplementary\nInformation).\nMoreover, to demonstrate that the sensors do not receive any NMR signal from adjacent sensors\nor nearby tissues due to the shielding, we perform MR imaging experiments with two sensors\nplaced close to a brain tissue. We acquire two sets of slice images: one from a plane passing\nthrough the sensors, and one from a plane passing through the brain, as shown in Figure S28a. We\nobserved that due to the shielding on one of the sensors, the MR images captured from each RF\ncoil did not receive any signal from the water of the other RF coil (Figure S28b-c). From the second\nset of slice images, we observed that while the shielded sensor did not receive any signal from the\nbrain tissue, leaving only imaging noise (Figure S28d), the unshielded sensor received a significant\nsignal from the tissue (Figure S28e). This difference demonstrated that our RF shield effectively\neliminates interference with the patient. We have added these experiments to the Supplementary\nInformation, in a new section titled “RF Shielding”.\nS12.RF Shielding\nEach sensor consists of a miniaturised RF coil, which allows it to excite the volume inside and\naround the coil. This can lead to unintended excitation of nearby sensors or tissues. To minimize\npotential interference from the surrounding environment, the sensor is placed inside an aluminium\nbox serving as an RF shield. To demonstrate the efficacy of the RF shield, we placed two NMR\nsensors, a shielded and an unshielded sensor, on top of a porcine brain, as shown in Figure S28a. We\nperformed 2D MR imaging experiments using the Localizer sequence with an excitation power\nof 80 microwatts, which matches the power used in NMR magnetic sensing. We acquire two sets\nof slice images: one from a plane passing through the sensors, and one from a plane passing\nthrough the brain, as shown in Figure S28a. We observed that due to the shielding on one of the\nsensors, the MR images captured from each RF coil did not receive any signal from the water of\nthe other RF coil (Figure S28b-c). From the second set of slice images, we observed that while the\nshielded sensor did not receive any signal from the brain tissue, leaving only imaging noise (Figure\nS28d), the unshielded sensor received a significant signal from the tissue (Figure S28e). This\nexperiment confirms the shield’s effective role and shows no interference between sensors while\nshielded.\nAs reviewers’ suggestion, we also explored different sensor array layouts, including tracking in\nthe abdominal area, Head region, and thigh, which is added to the “S5. Workspace Scaling” in the\nsupplementary material. Please see Response to Comment 2.1.\nFigure S28. NMR sensor interference with the environment. A) The setup used to study the\nextent of the captured NMR signal with and without shielding. B-C) Sensor head image in the\nupper coronal slice (slice 1) with the shielded sensor (B) and the unshielded sensor. D-E) Image\nof the lower coronal slice (slice2) with the shielded sensor (D) and unshielded sensor (E).\nComment 2.3) The authors are advised to design a highly adaptable universal layout to simplify\nclinical operations and improve the technology’s potential for broader adoption.\nResponse: We agree with the reviewer on the potential benefit of an adaptable universal sensor\nlayout for future applications; however, we believe such a design requires a separate focus study.\nTherefore, we highlighted the potential advantage of such an adaptable universal sensor layout in\nour “Discussion” section as follows.\nIt is possible to create denser NMR magnetic arrays with more sensors or distribute the sensor\narrays with modular layouts around a desired volume to increase the workspace without\ninterference from one another.\nComment 2.4). The integration of magnetic trackers with MRI imaging is demonstrated in figure\n3, showing that the magnetic tracking data aligns with the artifact of the guidewire in MRI images,\nenabling precise localization. However, the potential artifacts or interference caused by the\nmagnetic tracker on MRI imaging are not thoroughly discussed. Additionally, there is a lack of\ncomparative MRI images without magnetic trackers, making it difficult to assess their specific\nimpact on imaging quality.\nResponse: We thank the reviewer for the valuable suggestion. To give the audience a general idea\nof what a magnetic tracker artifact would look like in MR images, we repeated the tracking\nexperiment in porcine brain tissue first with MR imaging and second with NMR sensing. We added\nthe result in the “S11. Magnetic Artifact in MR Images”. We created videos during both\nexperiments (Movies S2 and S9). We also presented the magnetic artifacts in MR image snapshots\nin Figure S26 from Video S9.\nS11. Magnetic Artifact in MR Images\nPlacing a magnetic tracker inside an MRI machine will disturb the magnetic field in the shape of\na magnetic dipole in three-dimensional space. This disturbance is significant in a volume\nsurrounding the tracker, leading to a substantial change in the NMR frequency of water, as stated\nin Eq. 1. As a result, the volume will not be excited within the utilized RF signal bandwidth,\ncausing complete signal loss in that area. At greater distances from the tracker, the disturbance in\nthe magnetic field is not strong enough to significantly shift the frequency. However, it can still\ndistort the image by affecting the calculations of the gradient fields, which can show itself as a\nskewed image. Two ex vivo experiments using porcine brain were conducted to demonstrate this\neffect in a real tissue. In the first experiment, the tracker was inserted inside the brain in 10 steps,\nand an MR image was taken after each step. The entire process is illustrated in Figure S26 and\nsummarized in Movie S9. In the second experiment, a preoperative image was first taken. Then,\nNMR sensors tracked the tracker’s position throughout the insertion process. Finally, a\npostoperative image was taken. The preoperative and postoperative images are overlaid with the\nestimated position of the tracker. They are shown in Figure S27 as snapshots of the process, and\nthe whole procedure is documented in Movie S2.\nFigure S26. Tracker MR images during insertion inside a porcine brain. Tracker artifacts\nduring the insertion inside a porcine brain in oblique and sagittal planes.\nComment 2.5) The dipole model currently assumes that the magnetic moment is aligned with the\nB₀ field (Equation 2). However, for flexible trackers, bending may cause deviations in the magnetic\nmoment direction, which can introduce localization errors. It is encouraged to incorporate a\ncorrected model that accounts for this effect to improve the accuracy of the particle filter-based\ntracking algorithm.\nResponse: We thank the reviewer for the comment. We agree that a more elaborate magnetic\nmodel, such as a discretized dipole model, could improve the tracking accuracy of the flexible\ntracker. However, we believe that such a complex model requires a more focused investigation in\na separate study, which might be more suitable for a technical journal. Therefore, we preferred to\nleave it for future work, while providing a benchmark for tracking accuracy based on the basic\ndipole assumption.\nComment 2.6) The paper mentions an ex vivo pig brain navigation experiment but does not\nprovide accompanying video evidence. This omission may affect the reproducibility and\ncredibility of the results. The authors are advised to provide video documentation of the experiment\nto visually demonstrate the navigation process and its correlation with MRI imaging, thereby\nenhancing the study’s visualization and reliability.\nResponse: We appreciate the reviewer’s valuable suggestion, which enhanced our comparative\nstudy. To clearly illustrate the process of positioning the magnetic tracker in the ex vivo experiment\nand compare it with the tracker artefact, a new section, “S11. Magnetic Artefact in MR Images”,\nwas added to the supplementary material in which two sets of experiments, one with MR images\nand one with NMR sensing, are demonstrated. In the tracking experiment, a preoperative image\nwas first captured, and after tracking throughout the operation with NMR sensors, a postoperative\nimage was taken. This process is documented in Movie S2, with snapshots presented in Figure\nS27 to demonstrate the navigation process visually.\nS11. Magnetic Artifact in MR Images\nPlacing a magnetic tracker inside an MRI machine will disturb the magnetic field in the shape of\na magnetic dipole in three-dimensional space. This disturbance is significant in a volume\nsurrounding the tracker, leading to a substantial change in the NMR frequency of water, as stated\nin Eq. 1. As a result, the volume will not be excited within the utilized RF signal bandwidth,\ncausing complete signal loss in that area. At greater distances from the tracker, the disturbance in\nthe magnetic field is not strong enough to significantly shift the frequency. However, it can still\ndistort the image by affecting the calculations of the gradient fields, which can show itself as a\nskewed image. Two ex vivo experiments using porcine brain were conducted to demonstrate this\neffect in a real tissue. In the first experiment, the tracker was inserted inside the brain in 10 steps,\nand an MR image was taken after each step. The entire process is illustrated in Figure S26 and\nsummarized in Movie S9. In the second experiment, a preoperative image was first taken. Then,\nNMR sensors tracked the tracker’s position throughout the insertion process. Finally, a\npostoperative image was taken. The preoperative and postoperative images are overlaid with the\nestimated position of the tracker. They are shown in Figure S27 as snapshots of the process, and\nthe whole procedure is documented in Movie S2.\nFigure S27. Tracker navigation inside a porcine brain with pre- and postoperative images.\nComment 2.7) In lines 59-76 and the supplementary material, the authors provide only a brief\noverview of the selection and construction methodology for the NMR sensors. There is insufficient\nexplanation regarding the underlying principles of the localization method. It is recommended that\nthe authors include a more detailed explanation of these fundamental principles. For instance,\nclarification on the Free Induction Decay (FID) signal and the rationale behind designing the NMR\nsensor with the RF coil encircling a glass tube of water would be beneficial. This addition will\nhelp readers grasp the principle-based innovations of this sensor system.\nResponse: We thank the reviewer for their valuable suggestion. We added an extra section, “NMR\nmagnetic sensing,” in the Supplementary Information to further explain the fundamentals of NMR\nsignal generation and provide principles on why the sensor has the mentioned structure.\nNMR magnetic sensing The basis of NMR magnetic sensing resides in the precession of nuclear\nspins in the presence of a background magnetic field (B0) after excitation by an oscillating external\nmagnetic field. In the presence of B0, the net magnetisation of all the spins will redirect in parallel\nwith the field. By superimposing an oscillating magnetic field perpendicular to the background\nfield (called B1), the spins start to precess around the B0 axis with a frequency close to the Larmor\nfrequency, which depends on the gyromagnetic ratio of the specific nuclei and the background\nmagnetic field :\n𝑓\n𝛾 = [S1]\n𝐵0 (𝑇)\nwhere 𝛾, f and 𝐵 are the gyromagnetic ratio(𝐻𝑧/𝑇), the Larmor frequency (Hz), and the\n0\nbackground magnetic field (T), respectively.\nThis precession exhibits a decreasing amplitude of latitude and is characterized as a decaying\noscillating signal. This decaying oscillating signal read by an RF coil is called a free induction\ndecay (FID) signal31. As stated in Eq. 1, the resulting frequency is dependent on the magnitude of\nthe background field (B0), so any change in the B0 will affect the frequency of the FID signal,\nwhich later can be translated to the change in magnetic field:\n𝑓 = 𝛾𝐵 → (𝑓\n0\n+ 𝜿𝑓) = 𝛾(𝐵\n0\n+ 𝜿𝐵) → 𝜿𝐵 = 𝛾−1𝜿𝑓 𝑤ℎ𝑒𝑟𝑒 𝜿𝑓 = Δ𝜙 [S2]\nΔ𝑡\nDeionized (DI) water enclosed in a glass capillary was selected as the base structure for generating\nNMR signals, preventing evaporation over long periods and serving as a solid base for RF coil\nfabrication. This choice ensures that the free induction decay (FID) frequency is compatible with\nthe RF equipment in commercial scanners, allowing for consistent and repeatable results. To\nminimise the nonlinear magnetic effects of a dipole field across large volumes, the amount of water\nused was kept as small as possible. At the same time, ensuring the scanner’s analogue-to-digital\nconverter (ADC) could detect the FID signal’s amplitude within a reasonable acquisition time.\nFinally, an RF transceiver composed of a multi-turn pickup coil and a tuning and matching circuit\nwas constructed around the glass tube to excite the spins and detect the NMR signal in the form of\nFID.\nComment 2.8) All experiments were conducted using a 7T preclinical animal MRI system (line\n89 in the main text), whereas standard clinical MRI systems typically operate at 1.5–3T. Please\nclarify whether the proposed tracking method is compatible with clinical MRI field strengths.\nResponse: We thank the reviewer for the comment. Although we have demonstrated NMR\nmagnetic tracking in a 7T MRI scanner, the same physical principles would be valid for lower\nfield strengths, such as 3T and 1.5T, with a corresponding reduction in signal-to-noise ratio. We\nhave added a related discussion on the reduction in signal level and its effect on tracking\nperformance in different fields to the supplementary material.\nFurthermore, while clinical use of high-field MRI scanners is becoming popular 26, the integration of NMR\nmagnetic sensor arrays into lower field MRI scanners, such as 1.5 T and 3 T, and emerging ultra-low-field MRI\nscanners could increase the affordability of magnetically guided minimally invasive operations in the future\n27; However, we must note that the magnetic sensing precision will decrase with\nthe static field strength since signal-to-noise ratio in MRI scanners scale with ∝ B 7/4 28. Moreover, NMR\n0\nmagnetic sensors constructed in a single-sided MR configuration could allow the use of magnetic tracking\noutside of the MRI scanners 29.\nComment 2.9) The background magnetic field appears to have an effect on the localization\nresults. If this is indeed the case, it is recommended that the authors conduct additional localization\nexperiments with the NMR sensing system under varying background fields to investigate this\ninfluence.\nResponse: Yes, the reviewer is correct. The variation of the background field does affect the\ntracking accuracy. Therefore, we placed the eight NMR magnetic sensors as a reference sensor far\nbehind the sensor array, as shown in Figure S9. As the distance to the magnetic tracker increases\nsubstantially, this sensor enables us to monitor variations in the background field. We use the\nvariation over time in our position tracking algorithm. To clarify this, we add the following in the\n“Result” section.\nWe also introduced a reference NMR magnetic sensor placed far from the other sensors to monitor\nthe variation of the background field, which could change substantially over a long duration of\noperation (figure S9).\nAdditionally, in the supplementary information, we clarified that background field variations have\nbeen monitored.\nTo estimate the magnetic marker position, we used a particle filter-based state estimation model\nwith the state, x = [rT, ΔB] ∈ ℝ4, composed of tracker position and monitored background\nmagnetic field variation.\nComment 2.10) While Figure S22 demonstrates dual-target localization, the experimental setup\nis limited to a relatively large inter-target distance (4 cm). It does not evaluate performance in\nscenarios involving close spacing or overlapping magnetic fields. It is suggested that the authors\nassess whether accurate dual-target tracking is achievable at smaller separations.\nResponse: We appreciate the reviewer’s comment. To further evaluate the performance of our\ntwo-tracker system, we conducted three additional experiments under the same setup, varying the\ninter-target distance from 4 cm to 2 cm and then to 1 cm. We added the results in the\nSupplementary Information.\nWe conducted tracking experiments using two trackers to explore the possibility of a multi-tracker\nsystem with the current number of sensors. A stage featuring parallel channels (Figure S10a) was\nused to move the trackers within the workspace (Figure S24 and S25). The experiment was\nconducted at three different distances: 4cm, 2cm, and 1cm. In each experiment, one tracker was\nmoved 1 cm using a Teflon guidewire, while the other remained stationary. To estimate the\npositions using the particle filter, we increased the number of estimated states in the algorithm\nfrom three to six to account for the second dipole. The particle filter can estimate the positions of\nmultiple trackers simultaneously; however, the accuracy and precision of these estimates decrease\ncompared to single-dipole experiments. When the trackers are spaced 20 mm and 40 mm apart,\nthe particle filter can still estimate their positions within a workspace of 60 mm and 40 mm away\nfrom the sensor array (Figure S24). In contrast, for single tracker scenarios, the workspace, with\naccuracy exceeding 2 mm, extends to 80 mm; however, as trackers are placed closer to each other,\nat 10 mm, the dipole field of two trackers becomes indistinguishable for the particle filter, leading\nto a further reduction in position estimation accuracy (Figure S25). We believe that this problem\ncould be addressed in future robotics systems by incorporating system dynamics into the prediction\nstage of a particle filter.\nFigure S24. Multi-bead experiment with a large distance between trackers. The position\nestimation accuracy of two trackers at a large proximity to each other, in 4 cm (A) and 2 cm (B),\nis investigated.\nFigure S25. Multi-bead experiment with a small distance between trackers. The position\nestimation accuracy of two trackers at a distance of 1 cm in the left (A) and right (B) planes is\ninvestigated.\nComment 2.11) The authors dedicate significant space in the manuscript to describing various\nminiaturized tracker devices. At line 171 in the main text, an application scenario for the hollow\nmagnetic tracker is mentioned. However, the authors primarily list the positioning performance of\nthese different magnetic trackers within the NMR sensing system, without thoroughly discussing\ntheir practical application value. The authors are encouraged to supplement their study with\nexperiments simulating real-world conditions (e.g., ex vivo or in vivo experiments, or integration with\ncommercial equipment) to demonstrate the practical utility of these multiple forms of\nmagnetic trackers.\nResponse: We thank the reviewer for the comment. We agree with the reviewer that in vivo\nexperiments simulating the clinical condition would add value to our study. Unfortunately, at the\ncurrent stage, we lack the experimental capabilities to demonstrate in vivo results. Therefore, we\nfocused on ex vivo experiments. The magnetic tracking experiments in an ex vivo porcine brain\naim to simulate the operation conditions of an MRI-guided needle insertion operation.\nLater, we illustrated wireless tracking in an ex vivo porcine brain, simulating a needle insertion\noperation into the brain (Figure 3b). We inserted a straight catheter in the brain and took pre-\noperational MR images of the brain using an imaging surface coil shown in Figure 3c-d. Next, we\nmanually switched the RF connection from the surface coil to the NMR sensor array. Then, we\ncalibrated the background field with the diamagnetic brain tissue, which caused 1-2 µT variation\non different sensors (Figure S15), and tracked the guidewire in the catheter in real time with NMR\nmagnetic tracking (Movie S2).\nTo further demonstrate the potential of commercial medical equipment, as the reviewer suggested,\nwe prepared a custom-made endoscope camera with a magnetic tracker, and we demonstrated\ntracking in an ex vivo porcine esophagus while performing endoscopic imaging.\nNext, we integrated the miniaturized tracker with 1 emu magnetic moment into a custom-made\nendoscope camera system, and performed tracking in ex vivo on a porcine oesophagus to\ndemonstrate wireless tracking while performing endoscope video capturing (see Movie S4 and\nFigure S17).\nFigure S16. Endoscope camera tip tracking inside the porcine oesophagus. A) Custom made\nendoscope camera system and the Porcine oesophagus used for the operation. B) endoscope\ncamera feed inside the oesophagus. C) Axial view of position tracking throughout the whole\noperation. D) Coronal view of position tracking throughout the whole operation.\nComment 2.12) The paper does not sufficiently demonstrate the advantages of NMR magnetic\ntracking over electromagnetic (EM) tracking. While EM tracking systems perform well in non-\nMRI environments, the strengths of NMR magnetic tracking lie in its compatibility with MRI and\nits high sensitivity. The authors are encouraged to conduct comparative experiments to quantify\ndifferences between the two technologies in terms of accuracy, sensitivity, miniaturization, and\nclinical applicability, thereby better highlighting the unique value of NMR magnetic tracking.\nResponse: We thank the reviewer for the comment. While Magnetic and EM tracking both use\ndipole-based models for tracking, they are distinct in nature due to the magnetic moment\ngeneration method by the tracker. Magnetic tracking uses passive magnetic trackers, while EM\ntracking needs to induce a current in the tracker. Therefore, a direct experimental comparison\nhighlighting the advantage of magnetic tracking over EM and vice versa, similar to one presented\nby Gleich et al.10, between mechanical and electrical EM trackers, would be controversial for\nmagnetic and EM trackers. Moreover, as the reviewer stated, these sensors address the tracking\nproblem in two different operating conditions: low (Non-MRI) and high (MRI) background\nmagnetic fields, both of which have strong clinical potential.\nThat being said, we agree with the reviewer that a meta comparison that places the NMR magnetic\ntracking method next to previous methods in terms of accuracy and miniaturization would be\nbeneficial for benchmarking. Therefore, we have already provided a comparison plot (Figure S13)\nfor miniaturization with a function of workspace and a Table for accuracies (Table 1) in SI, which\nincludes EM tracker examples from the literature. We have updated the Table to refer to the EM\ntrackers more clearly and changed the color of EM tracker dots in Figure S13.\nTable 1. Comparison of wireless tracking systems *Statistics have not been reported explicitly.\nMT: magnetic tracking, MGT: magnetic gradient tracking, EMT: electromagnetic tracking.\nTracking Tracker Temp. Penet. Tracking\nModality\nSize (mm2) Res. Depth Acc.\nSon 11 MT 12.8 × 6.4Ø 5 ms 5 cm 2.1 mm\nGleich10 EMT 1.9 × 0.8Ø 25 ms 30 cm 2 mm at 10 cm*\nSharma 12 MGT 20 × 8Ø 300 ms 40 cm 2 mm at 12 cm*\nOsaki 9 EMT 15 × 4Ø 100 ms 15 cm <1 mm at 15 cm\nArx 13 MGT 6 × 3Ø 100 ms 10 cm <1 mm at 10 cm\nThis work MT 2 × 0.6 Ø 30 ms 8 cm 2 mm at 8 cm\nFigure S13 Miniaturization comparison. It can be seen that in this work, we can track smaller\nvolumes of magnetic material with better accuracy in a similar workspace 9-13. The lower limit of\ntracking accuracy is considered to be 2mm. Blue dots represent magnetic tracking methods, while\ngreen dots represent EM tracking methods.\nTo highlight the advantages of NMR magnetic tracking over wireless EM tracking, we have added\nthe following section to the Discussion section.\nBesides, NMR magnetic sensing provides a larger workspace compared to previous magnetic\ntracking methods 11 and a comparable workspace to wireless EM trackers of the same size 10, with\nsimilar tracking accuracy (Table 1, Figure S13), without the RF-induced heating risks. Although\nour demonstrations have been limited by the size of our preclinical MRI scanner, the NMR\nmagnetic sensing technology offers a potentially larger workspace due to the relatively small size\nof NMR magnetic sensors compared with planar coils used in EM trackers 10. It is possible to\ncreate denser NMR magnetic arrays with more sensors or distribute the sensors around a desired\nvolume to increase the workspace without interference from one another. Increasing sensor\nnumbers could also be used to increase tracking accuracy further; however, this will limit the\ntemporal resolution of tracking and require parallel hardware instead of the current serial hardware.\nImportantly, NMR magnetic sensing also addresses the position-calibration challenges that EM\ntracking systems face during integration with medical imaging. The gradient-based sensor\npositioning enables spatial calibration without the need for external hardware, allowing the\nmagnetic tracker to be registered directly onto MR images (Figure 2f) and enabling single-stage,\nreal-time positioning of stereotactic neurosurgery robots 4. Finally, NMR trackers do not suffer\nfrom the dead-angle issues inherent to EM trackers, since NMR tracking does not require external\nexcitation 9.\nComment 2.13) With the continuous improvement of MRI imaging speeds, the relevance of this\nresearch warrants further discussion. Faster MRI imaging has alleviated some of the challenges\nassociated with real-time navigation. The authors should further explore the potential synergy\nbetween NMR-based magnetic tracking and fast MRI imaging, emphasizing the unique advantages\nof magnetic tracking in terms of real-time performance and miniaturization.\nResponse: We thank the reviewer for the comment. We agree that the improvement in MRI speed\nwill alleviate some real-time navigation challenges, but not address all the drawbacks of MRI-\nbased tracking.\nFirstly, 3D tracking will remain a challenge with MR image-based tracking, since the tracked\nobject may not be visible in an MRI slice throughout the navigation. Although we have\ndemonstrated a potential tracking method with alternating slice positions in our previous work\n22these solutions would still be feasible for a limited workspace. 2D MR projection images with\ntwo orthogonal planes and fast 3D imaging methods might provide real-time tracking alternatives\nin the future; however, the increased imaging speed might be limited by the risk of tissue heating\ndue to the specific absorption rate (SAR) of RF pulses. Additionally, the acoustic noise generated\nby rapidly switching gradient coils during fast MRI would also be a significant limitation for the\nuse of faster imaging sequences during operations. Meanwhile, proposed NMR-based tracking\nmethods do not cause heating since they do not deposit RF energy in the patient and can be used\nwithout generating any acoustic noise, as discussed in the Discussion section.\nSecondly, MR image-based tracking is limited by certain conditions. MRI can only show objects\nin a water or tissue environment; in air, MR images do not provide meaningful information.\nTherefore, we cannot track objects that are fully or partly air-filled parts of the body, such as the\nGI tract. Moreover, we cannot track objects that approach from outside the patient and later\npenetrate the skin, such as needles and biopsy probes. MR image-based tracking would require\nauxiliary tracking methods to track objects until they reach the tissue. In contrast, NMR-based\ntracking can be performed in air, as demonstrated in our experiments.\nTo highlight the additional unique advantages of NMR-based tracking, we include the following\nin the Discussion section.\nAdditionally, the NMR magnetic sensing technology addresses certain drawbacks of MR image-\nbased tracking. Despite continuous improvements in MRI speed, real-time 3D tracking with\npassive fiducial markers, such as magnetic 22, 19-Fluorine 23, and RF coils24 , and active MRI\npickup coils 25, remains limited by slice thickness 22 and RF-induced tissue heating. In contrast,\nNMR sensors provide continuous 3D tracking without requiring the deposition of RF energy (see\nSupplementary Information), enabling continuous navigation with no risk of heating. Furthermore,\nNMR magnetic sensing eliminates acoustic noise, which in fast MRI-based tracking can exceed\nsafe exposure limits 3,5 and hinder communication between clinicians during interventional MRI\noperations. Because NMR does not rely on MR gradients (figure S23, Movie S8), it is inherently\nsilent, creating a safer acoustic environment for both patients and clinicians. Moreover, NMR\ntracking also functions in air-filled cavities, where most MRI-based tracking methods, except 19F\ntracking 23, fail due to the absence of 1H of the surrounding water or tissue, allowing for the\nuninterrupted tracking of tools such as needles during insertion from outside the skin.\nWe envision that the NMR magnetic sensing could also be used in conjunction with 2D MRI and\nrecently emerging MRI-powered magnetic actuation methods, by using an alternating MR\nsequence similar to 5. We can perform high-speed magnetic tracking with NMR simultaneously\nduring slower MR image acquisition, which is safe in terms of RF heating and acoustic noise, and\nwe can also integrate magnetic actuation at the same time. Furthermore, while clinical use of high-\nfield MRI scanners is becoming popular 26, the integration of NMR magnetic sensor arrays into\nlower field MRI scanners such as 1.5 T/3 T and emerging ultra-low-field MRI scanners could\nincrease the affordability of magnetically guided minimally invasive operations in the future 27;\nComment 2.14) The paper notes that this method is unsuitable for patients with ferromagnetic\nimplants and faces challenges in environments with dynamic tissues (e.g., the heart or nerves) due\nto background signal variations. These limitations may hinder the adoption of this technology in\ncomplex clinical scenarios. The authors are encouraged to discuss potential solutions to address\nthese limitations.\nResponse: We thank the reviewer for the comment. Like other MR technologies, NMR magnetic\ntracking can be used for patients with ferromagnetic implants, as these patients may not be able to\nenter the MRI scanner due to the risk of the magnetic gradient fields from the MRI scanner\ndislocating the implant. On the other hand, the dynamic tissue-related background signal variation\nissues could be addressed in the future using an improved prediction model for the motion of the\ntracker and also the dynamic variation of the background. We have added a brief discussion on a\npotential method to address this issue.\nThe second limitation is the difficulty in tracking magnetic trackers from near-moving tissues.\nWhile the magnetization calibration enables tracking near static tissues by subtracting the\ndiamagnetic background, tracking near moving tissues, such as the chest during breathing motion,\nis challenging due to changing background signals 20. This issue could be addressed in the future\nby incorporating the actuation dynamics into the particle filter rather than using a static model, and\nmodifying the proposed background field estimation using basis functions that approximate the\ndynamic component of the background 30, while utilizing more NMR magnetic sensors for\nincreased measurement redundancy.\nIn summary, this paper introduces an innovative NMR-based wireless magnetic tracking\ntechnology with advantages in sensitivity, miniaturization, and MRI compatibility. While the\nresearch shows great potential, some areas need further improvement, such as optimizing sensor\nlayouts, addressing MRI interference, refining models for flexible trackers, and providing more\nexperimental evidence. Additionally, comparisons with electromagnetic tracking and discussions\non clinical limitations and applications would enhance the study’s impact and practical relevance.\nResponse: We thank the reviewer for the kind comments."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I thank the authors for their additional data and thorough responses. I support publication of the manuscript in its current form.", "reviewer_2": "This paper has been well revised. I have no more comments."}, "author_response": ""}]

Decision letter