Combining Pulsed and DC Gradients in a Clinical MRI-Based Microrobotic Platform to Guide Therapeutic Magnetic Agents in the Vascular Network

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_{Vascular Network}

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: Sylvain Martel

Date: 2013

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Martel, S. (2013). Combining Pulsed and DC Gradients in a Clinical MRI-Based

Microrobotic Platform to Guide Therapeutic Magnetic Agents in the Vascular

Network. International Journal of Advanced Robotic Systems, 10(1).

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10.5772/53513

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International Journal of Advanced Robotic Systems (vol. 10, no 1)

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International Journal of Advanced Robotic Systems











Combining Pulsed and DC Gradients in a

Clinical MRI-Based Microrobotic Platform

to Guide Therapeutic Magnetic Agents in

the Vascular Network

Regular Paper

Sylvain Martel

1,*

1 NanoRobotics Laboratory, Department of Computer and Software Engineering, École Polytechnique de Montréal (EPM), Montréal, Canada * Corresponding author E-mail: sylvain.martel@polymtl.ca

ȱ

Received 9 Jun 2012; Accepted 18 Sep 2012 DOI: 10.5772/53513

‹2013 Martel; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

AbstractȱMagneticȱ Resonanceȱ Navigationȱ (MRN)ȱ reliesȱ onȱ theȱ useȱ ofȱ anȱ upgradedȱ clinicalȱ Magneticȱ Resonanceȱ Imagingȱ(MRI)ȱscannerȱtoȱnavigateȱtherapeutic,ȱimaging,ȱ orȱ diagnosticȱ magneticȱ microȬagentsȱ inȱ theȱ vascularȱ network.ȱ Althoughȱ theȱ highȱ homogeneousȱ fieldȱ inȱ theȱ tunnelȱofȱtheȱMRIȱscannerȱincreasesȱtheȱmagnetizationȱofȱ theȱnavigableȱagentsȱtowardsȱfullȱsaturation,ȱtheȱmagneticȱ gradientsȱsuperposedȱonȱsuchȱaȱhighȱhomogeneousȱfield,ȱ generatedȱbyȱtheȱImagingȱGradientȱCoilsȱ(IGC)ȱtypicallyȱ usedȱforȱMRȬimageȱsliceȱselection,ȱallowȱtheȱinductionȱofȱ pullingȱ forcesȱ toȱ steerȱ suchȱ agentsȱ inȱ theȱ targetedȱ branchesȱatȱtheȱvessel’sȱbifurcations.ȱHowever,ȱincreasingȱ theȱ magnitudeȱ ofȱ suchȱ gradientsȱ leadsȱ toȱ aȱ significantȱ decreaseȱ ofȱ theȱ dutyȱ cycle,ȱ leadingȱ toȱ aȱ substantialȱ reductionȱofȱtheȱeffectiveȱsteeringȱforceȱbeingȱapplied.ȱToȱ increaseȱ suchȱ aȱ dutyȱ cycle,ȱ aȱ Steeringȱ Gradientȱ Coilsȱ (SGC)ȱ assemblyȱ capableȱ ofȱ higherȱ magnitudesȱ whileȱ maintainingȱaȱ100%ȱdutyȱcycleȱcanȱbeȱinstalledȱatȱtheȱcostȱ ofȱ aȱ muchȱ slowerȱ slewȱ rate.ȱ Here,ȱ theȱ useȱ andȱ theȱ potentialȱ effectivenessȱ ofȱ IGCȱ and/orȱ SGCȱ forȱ guidingȱ suchȱagentsȱareȱbrieflyȱinvestigatedȱonȱtheȱbasisȱofȱknownȱ specificationsȱandȱexperimentalȱdata.ȱ

Keywordsȱ Magneticȱ Resonanceȱ Imaging,ȱ Navigableȱ Agents,ȱ Magneticȱ Force,ȱ Targetedȱ Therapiesȱ andȱ Diagnostics,ȱVascularȱNetworkȱ

ȱ

1.ȱIntroductionȱ

Forȱ someȱ typesȱ ofȱ cancer,ȱ enhancedȱ therapeuticȱ efficacyȱ canȱbeȱobtainedȱbyȱdirectȱtargeting,ȱwhereȱaȱminimalȱdoseȱ ofȱdrugȬloadedȱmicrocarriersȱorȱagentsȱcanȱbeȱnavigatedȱ throughȱtheȱshortestȱrouteȱinȱtheȱvascularȱnetworkȱwhileȱ avoidingȱorȱatȱleastȱreducingȱsystemicȱcirculation,ȱwhichȱ mostȱ oftenȱ leadsȱ toȱ aȱ substantialȱ increaseȱ inȱ secondaryȱ toxicityȱ thatȱ mayȱ affectȱ healthyȱ organsȱ [1].ȱ Directȱ targetingȱ requiresȱ theȱ assistanceȱ ofȱ aȱ moreȱ sophisticatedȱ interventionalȱ platformȱ andȱ engineeringȱ techniquesȱ thatȱ alsoȱrelyȱonȱtheȱsynthesisȱofȱnavigableȱtherapeuticȱagentsȱ andȱtheȱassociatedȱmedicalȱinterventionalȱprotocols.ȱ ȱ

Oneȱ suchȱ promisingȱ interventionalȱ platformȱ reliesȱ onȱ aȱ clinicalȱMagneticȱResonanceȱImagingȱ(MRI)ȱscannerȱthatȱ

ȱ

isȱ upgradedȱ toȱ allowȱ Magneticȱ Resonanceȱ Navigationȱ (MRN)ȱ [2]ȱ ofȱ theseȱ navigableȱ agentsȱ alongȱ aȱ plannedȱ trajectoryȱ inȱ theȱ vasculatureȱ inȱ orderȱ toȱ achieveȱ directȱ targeting.ȱ MRNȱ hasȱ alreadyȱ beenȱ testedȱ successfullyȱ ’—ȱ

Ÿ’Ÿ˜ȱ inȱ theȱ carotidȱ arteryȱ ofȱ aȱ livingȱ pigȱ withȱ aȱ 1.5ȱ mmȱ

chromeȬsteelȱ beadȱ andȱ aȱ clinicalȱ MRIȱ scannerȱ usingȱ theȱ Imagingȱ Gradientȱ Coilsȱ (IGC)ȱ toȱ propelȱ theȱ beadȱ backȱ andȱ forthȱ alongȱ theȱ arteryȱ inȱ aȱ controlledȱ fashionȱ [3].ȱ Later,ȱ ~50ȱ ΐmȱ therapeuticȱ agentsȱ knownȱ asȱ Therapeuticȱ MagneticȱMicroCarriersȱ(TMMC)ȱwereȱnavigatedȱthroughȱ theȱ hepaticȱ arteryȱ ofȱ rabbitȱ modelsȱ toȱ reachȱ targetedȱ locationsȱ inȱ theȱ liverȱ [4].ȱ Inȱ theseȱ experiments,ȱ TMMCȱ consistedȱ ofȱ therapeuticsȱ (Doxorubicin)ȱ embeddedȱ withȱ FeCoȱ magneticȱ nanoparticlesȱ (MNP)ȱ withinȱ aȱ sphericalȱ biodegradableȱ polymerȱ (PLGA)ȱ matrix.ȱ Theȱ latterȱ experimentsȱwereȱperformedȱwithȱaȱclinicalȱMRIȱscannerȱ upgradedȱ withȱ aȱ specialȱ gradientȱ coilsȱ assemblyȱ –ȱ referredȱ toȱ asȱ Steeringȱ Gradientȱ Coilsȱ (SGC)ȱ –ȱ installedȱ insideȱ theȱ tunnelȱ ofȱ theȱ scanner.ȱ Unlikeȱ IGC,ȱ SGCȱ wereȱ ableȱ toȱ provideȱ sustainedȱ (100%ȱ dutyȱ cycle)ȱ higherȱ gradientȱ fields,ȱ butȱ withȱ muchȱ slowerȱ slewȱ rates.ȱ Theȱ experienceȱ acquiredȱ byȱ performingȱ MRNȱ usingȱ IGCȱ orȱ SGC,ȱ referredȱ toȱ asȱ IGCȬMRNȱ andȱ SGCȬMRNȱ respectively,ȱ forcedȱ usȱ toȱ reȬevaluateȱ theȱ limitationsȱ inȱ relationȱtoȱtheȱadvantagesȱofȱeachȱapproachȱinȱtheȱcontextȱ ofȱnavigatingȱtherapeuticȱagentsȱinȱtheȱvascularȱnetwork.ȱ Thisȱ isȱ theȱ mainȱ objectiveȱ ofȱ thisȱ paper.ȱ First,ȱ toȱ betterȱ understandȱ theȱ principleȱ ofȱ MRN,ȱ someȱ theoreticalȱ backgroundȱisȱnecessary.ȱ

2.ȱFundamentalȱTheoryȱofȱMRNȱ

Theȱ fundamentalȱ platformȱ ofȱ MRNȱ isȱ theȱ MRIȱ scanner,ȱ whichȱprovidesȱaȱhighȬmagnitudeȱhomogenousȱmagneticȱ fieldȱofȱtypicallyȱ1.5ȱTȱorȱ3ȱTȱforȱclinicalȱscannersȱknownȱ asȱ theȱ Ŗȱ field,ȱ aȱ magneticȱ gradientȱ fieldȱ thatȱ canȱ beȱ orientedȱ inȱ anyȱ directionȱ andȱ anȱ RFȱ field.ȱ Forȱ imaging,ȱ theȱmomentumȱorȱspinȱofȱtheȱhydrogenȱnucleiȱisȱalignedȱ inȱ theȱ directionȱ ofȱ theȱ Ŗȱ field,ȱ whichȱ correspondsȱ toȱ theȱ zȬaxisȱ andȱ thereforeȱ ŖȱǓȱ .ȱ Anȱ RFȱ fieldȱ isȱ thenȱ appliedȱ momentarilyȱtoȱflipȱtheȱspinȱangle.ȱWhenȱtheȱRFȱpulseȱisȱ turnedȱ off,ȱ theȱ spinȱ returnsȱ toȱ itsȱ originalȱ directionȱ towardsȱ theȱ zȬaxisȱ duringȱ aȱ timeȱ periodȱ knownȱ asȱ theȱ relaxationȱ time.ȱ Duringȱ thisȱ relaxationȱ time,ȱ whenȱ theȱ magneticȱ dipolesȱ tendȱ toȱ alignȱ withȱ theȱ magneticȱ field,ȱ theȱscannerȱdetectsȱtheȱreȬemittedȱsignalsȱthatȱareȱusedȱtoȱ constructȱ theȱ MRȬimage.ȱ Toȱ selectȱ aȱ particularȱ regionȱ toȱ beȱ imaged,ȱ linearȱ fieldȱ gradientsȱ createdȱ byȱ threeȱ setsȱ ofȱ orthogonallyȱpositionedȱcoilsȱareȱsuperimposedȱonȱtheȱŖȱ field.ȱ

ȱ

Forȱ MRN,ȱ aȱ displacementȱ ofȱ aȱ magneticȱ agentȱ canȱ occurȱ ifȱ aȱ sufficientlyȱ highȱ pullingȱ forceȱ isȱ induced,ȱ whichȱcanȱonlyȱoccurȱwithȱaȱmagneticȱfieldȱstrengthȱȱ providedȱ byȱ theȱ Ŗȱ fieldȱ andȱ aȱ directionalȱ gradientȱ ǰȱ whereȱ bothȱ areȱ sufficientlyȱ high.ȱ Inȱ theȱ zȬaxis,ȱ theȱ magneticȱfieldȱstrengthȱisȱrelatedȱtoȱtheȱ magneticȱfieldȱ

orȱ magneticȱ fluxȱ densityȱ byȱ theȱ permeabilityȱ ofȱ freeȱ spaceȱΐŖȱ=ȱ4Δ×10Ȭ7ȱH/m:ȱ ȱ  P₀.ȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱ(1)ȱ ByȱinsertingȱaȱferromagneticȱcoreȱwithȱsusceptibilityȱΛȱinȱ suchȱaȱfield,ȱȱisȱincreased:ȱ ȱ  P₀(F) P₀().ȱȱȱȱȱȱȱȱȱȱȱȱȱ(2)ȱ Inȱ(2),ȱȱisȱtheȱmagnetizationȱofȱtheȱferromagneticȱmaterial.ȱ Forȱ ȱ ǃȱ 1.5ȱ T,ȱ asȱ inȱ typicalȱ clinicalȱ MRIȱ scanners,ȱ allȱ ferromagneticȱ materialsȱ haveȱ theirȱ magnetizationȱ atȱ saturationȱ (especiallyȱ inȱ 3ȱ Tȱ scanners)ȱ orȱ veryȱ closeȱ toȱ saturationȱ (forȱ 1.5ȱ Tȱ scanners).ȱ Therefore,ȱ weȱ assumeȱ hereȱ saturationȱ magnetizationȱ whereȱ ȱ isȱ replacedȱ byȱ .ȱ Inȱ thisȱcase,ȱtheȱmagneticȱforceȱinducedȱbyȱtheȱMRIȱscannerȱonȱ theȱnavigableȱmagneticȱagentȱcanȱbeȱcomputedȱasȱ ȱ G_ ˜ _



_˜ ’



_£,ȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱ(3)ȱ withȱtheȱgradientȱoperatorȱbeingȱdefinedȱasȱ ȱ  ¡ ¢ £ ªw w wº ’ «_{w w w} » ¬ ¼ .ȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱȱ(4)ȱ Inȱ(3),ȱtheȱdutyȱcycleȱȱisȱtheȱratioȱofȱtheȱdurationȱΘȱofȱtheȱ appliedȱ magneticȱ gradientȱ usedȱ toȱ induceȱ aȱ directionalȱ pullingȱ forceȱ ,ȱ referredȱ toȱ asȱ theȱ pullingȱ gradientȱ orȱ steeringȱ gradientȱ whenȱ theȱ bloodȱ flowȱ velocityȱ isȱ usedȱ toȱ propelȱtheȱnavigableȱagent,ȱtoȱtheȱtotalȱperiodȱȱwhereȱȱisȱ includedȱinȱtheȱintervalȱ[0,ȱ1]ȱwithȱȱ=ȱ1ȱrepresentingȱaȱ100%ȱ dutyȱ cycle.ȱ Althoughȱ theȱ goalȱ forȱ providingȱ theȱ maximumȱ pullingȱorȱsteeringȱforceȱisȱtoȱhaveȱȱĺȱ1,ȱseveralȱfactorsȱcanȱ reduceȱ,ȱandȱoneȱofȱtheȱmainȱfactorsȱbesideȱtheȱtimeȱtakenȱ forȱMRȬtrackingȱorȱimagingȱisȱtheȱcoolingȱissue.ȱForȱIGC,ȱtheȱ reductionȱinȱtheȱdutyȱcycleȱwouldȱdependȱonȱtheȱmagnitudeȱ ofȱtheȱgradientȱbeingȱgenerated,ȱwhichȱwouldȱdependȱonȱtheȱ electricalȱcurrentȱbeingȱappliedȱonȱeachȱaxisȱ(orȱchannel)ȱtoȱ generateȱaȱdirectionalȱmagneticȱforce:ȱ ȱ                  £ £ £  ª º ªw w w º « _{» ˜ ˜} « » « » _{w w w} ¬ ¼ « » ¬ ¼ .ȱȱȱȱȱȱ(5)ȱ TheȱnextȱsectionȱprovidesȱdifferentȱvaluesȱofȱȱforȱanȱIGCȱ assemblyȱ capableȱ ofȱ generatingȱ magneticȱ gradientsȱ inȱ excessȱ ofȱ 400ȱ mTȱ ȉmȬ1_{.ȱ Basedȱ onȱ theoreticalȱ analysisȱ andȱ} experimentsȱthisȱassemblyȱisȱsufficientȱforȱtheȱsteeringȱofȱ MRȬnavigableȱtherapeuticȱagentsȱwithȱdiametersȱasȱsmallȱ asȱ ~50ȱ ΐmȱ inȱ theȱ arteriolesȱ underȱ realȱ humanȱ physiologicalȱconditions.ȱ

2.ȱIGCȬMRNȱ

TheȱmainȱadvantageȱofȱusingȱtheȱIGCȱforȱMRNȱisȱthatȱtheȱ sameȱcoilsȱcanȱbeȱusedȱforȱbothȱMRȬtrackingȱforȱgatheringȱ

positionalȱ dataȱ aboutȱ theȱ navigableȱ agentsȱ forȱ theȱ servoingȱ controlȱ purpose,ȱ andȱ MRȬsteeringȱ ofȱ theȱ agentsȱ towardsȱtheȱtargetedȱregion.ȱForȱtheȱIGCȱdesignȱusedȱforȱ MRȬimagingȱ (orȱ tracking),ȱ severalȱ specificationsȱ areȱ considered,ȱ suchȱ asȱ linearity,ȱ selfȬinductance,ȱ resistance,ȱ storedȱ energy,ȱ dissipatedȱ power,ȱ andȱ externalȱ fields.ȱ Indeed,ȱ althoughȱ nonȬlinearityȱ ofȱ theȱ gradientȱ resultsȱ inȱ imageȱ distortion,ȱ itȱ isȱ notȱ asȱ criticalȱ whenȱ usedȱ toȱ generateȱ steeringȱ gradients.ȱ Theȱ selfȬinductanceȱ isȱ responsibleȱforȱlongerȱswitchingȱtimesȱ(slowerȱslewȱrates)ȱ andȱ suchȱ selfȬinductanceȱ mustȱ beȱ minimizedȱ forȱ bothȱ cases,ȱi.e.,ȱforȱMRȬimagingȱorȱtrackingȱandȱ steering.ȱThisȱ isȱ alsoȱ trueȱ forȱ theȱ storedȱ energyȱ inȱ theȱ gradientȱ coil,ȱ whichȱ isȱ definedȱ asȱ theȱ squaredȱ amplitudeȱ ofȱ theȱ magneticȱ fieldȱ integratedȱ overȱ theȱ volumeȱ ofȱ theȱ coil,ȱ whereȱ suchȱ storedȱ energyȱ increasesȱ rapidlyȱ ifȱ theȱ magneticȱfieldsȱandȱtheȱvolumeȱofȱtheȱcoilȱareȱincreased,ȱ leadingȱ toȱ aȱ correspondingȱ linearȱ increaseȱ ofȱ theȱ selfȬ inductance.ȱ Forȱ aȱ givenȱ electricalȱ currentȱ circulatingȱ inȱ theȱ gradientȱ coil,ȱ theȱ dissipatedȱ powerȱ inȱ theȱ coilȱ isȱ proportionalȱ toȱ theȱ ohmicȱ resistance,ȱ whichȱ shouldȱ beȱ minimizedȱ inȱbothȱ cases.ȱ Anotherȱ aspectȱ isȱ eddyȱcurrentȱ inducedȱ inȱ neighbouredȱ coils,ȱ whichȱ mustȱ beȱeliminatedȱ orȱ atȱ leastȱ minimizedȱ dueȱ toȱ undesirableȱ effects.ȱ Higherȱ eddyȱ currentsȱ areȱ expectedȱ withȱ strongerȱ appliedȱ magneticȱfields,ȱgreaterȱelectricalȱconductivityȱofȱtheȱcoilsȱ and/orȱ fasterȱ switchingȱ gradients.ȱ Asȱ such,ȱ typicalȱ IGCȱ assembliesȱ includeȱ aȱ shieldingȱ coil,ȱ concentricȱ withȱ theȱ firstȱcoilȱ butȱ onȱ aȱ largerȱ radiusȱ withȱ anȱ electricalȱ currentȱ circulatingȱinȱtheȱoppositeȱdirection.ȱThisȱisȱreferredȱtoȱasȱ activeȱ shielding.ȱ Activeȱ shieldingȱ leadsȱ toȱ theȱ needȱ forȱ moreȱ energyȱ toȱ maintainȱ theȱ sameȱ gradientȱ fieldȱ whileȱ requiringȱ moreȱ volumeȱ toȱ implementȱ theȱ IGCȱ assembly.ȱ Butȱincreasingȱtheȱmagnitudeȱofȱtheȱgradientȱfieldȱcanȱbeȱ beneficialȱforȱimagingȱ(orȱtracking)ȱandȱsteering.ȱForȱMRȬ imaging,ȱsuchȱanȱincreaseȱwouldȱleadȱtoȱthinnerȱslicesȱorȱ imageȱ planesȱ andȱ anȱ increaseȱ inȱ spatialȱ resolutionȱ whileȱ providingȱhigherȱpullingȱforcesȱforȱsteeringȱpurpose.ȱȱ ȱ

Butȱ powerȱ dissipationȱ isȱ aȱ realȱ constraintȱ whenȱ operatingȱ IGCȱ atȱ highȱ magnitudes.ȱ Forȱ instance,ȱ letȱ usȱ considerȱ anȱ activelyȱ shieldedȱ IGCȱ withȱ anȱ innerȱ andȱ externalȱdiameterȱofȱ150ȱmmȱandȱ240ȱmm,ȱrespectively,ȱ whichȱ canȱ beȱ placedȱ insideȱ theȱ tunnelȱ ofȱ aȱ Siemensȱ Magnetomȱ Sonataȱ clinicalȱ MRIȱ scanner.ȱ Theȱ IGCȱ isȱ poweredȱ byȱ itsȱ ownȱ setȱ ofȱ amplifiersȱ suchȱ thatȱ noȱ softwareȱ orȱ hardwareȱ modificationsȱ onȱ theȱ clinicalȱ scannerȱ areȱ requiredȱ forȱ operationsȱ withȱ magneticȱ gradientsȱ atȱ leastȱ tenȱ timesȱ thoseȱ generatedȱ byȱ theȱ IGCȱ ofȱ theȱ clinicalȱ scannerȱ whileȱ takingȱ advantageȱ ofȱ itsȱ Ŗȱ fieldȱ ofȱ 1.5T.ȱ ȱ Thisȱ removableȱ IGCȱ isȱ capableȱ ofȱ generatingȱ aȱ maximumȱ gradientȱ ofȱ 450ȱ mTȱ ȉȱ mȬ1_{ȱ withȱ aȱ} riseȱtimeȱofȱ100ȱΐs.ȱButȱbyȱdoingȱso,ȱȱwillȱbeȱdecreasedȱ substantiallyȱ inȱ orderȱ toȱ maintainȱ theȱ internalȱ temperatureȱ withinȱ theȱ operationalȱ limitȱ characterizedȱ atȱ 45o_{Cȱ aboveȱ anȱ ambientȱ temperatureȱ ofȱ 20}o_C,ȱ assumingȱ thatȱ waterȱ coolingȱ ofȱ theȱ IGCȱ happensȱ atȱ 5.0ȱ

litresȱ perȱ minuteȱ atȱ 32.5ȱ psiȱ inȱ orderȱ toȱ maintainȱ theȱ maximumȱ heatȱ dissipationȱ ofȱ theȱ IGCȱ assemblyȱ atȱ 500ȱ W.ȱTheȱeffectȱofȱtheȱgradientȱstrengthȱonȱtheȱdutyȱcycleȱ forȱȱ=ȱ1s,ȱwhichȱcorrespondsȱtoȱoneȱcardiacȱcycleȱorȱoneȱ cycleȱ ofȱ pulsatileȱ bloodȱ flow,ȱ isȱ depictedȱ inȱ Fig.ȱ 1,ȱ inȱ whichȱonlyȱoneȱofȱtheȱthreeȱchannelsȱ(x,ȱy,ȱz)ȱisȱactiveȱatȱ anyȱinstant.ȱ ȱ ’ž›ŽȱŗǯȱReductionȱofȱtheȱdutyȱcycleȱwithȱhigherȱgradientȱfieldsȱ forȱeachȱaxisȱgeneratedȱbyȱtheȱremovableȱIGCȱwithȱonlyȱoneȱaxisȱ beingȱactiveȱatȱanyȱinstantȱ

Forȱ instance,ȱ toȱ guaranteeȱ aȱ gradientȱ ofȱ 450ȱ mTȱ ȉȱ mȬ1_{ȱ inȱ} anyȱ directions,ȱ ȱ =ȱ 0.043,ȱ whichȱ correspondsȱ toȱ aȱ durationȱΘȱofȱtheȱappliedȱmagneticȱgradientȱofȱonlyȱ43ȱmsȱ everyȱ second.ȱ Aȱ burstȱ modeȱ whereȱ severalȱ gradientȱ pulsesȱareȱappliedȱwithinȱtheȱsameȱȱisȱpossibleȱasȱlongȱasȱ theȱpowerȱdissipationȱisȱkeptȱwithinȱtheȱoperationalȱlimit.ȱ Inȱ suchȱ aȱ case,ȱ theȱ magnitudeȱ ofȱ theȱ gradientsȱ couldȱ beȱ decreasedȱ inȱ orderȱ toȱ maintainȱ theȱ internalȱ temperatureȱ ofȱtheȱIGCȱwithinȱacceptableȱlimits.ȱ

ȱ

However,ȱtheȱslewȱrateȱȦȱatȱsuchȱhigherȱgradientsȱcanȱ poseȱ aȱ threatȱ toȱ theȱ patientȱ [5]ȱ knowingȱ thatȱ theȱ meanȱ thresholdȱlevelsȱareȱ60ȱT/sȱforȱperipheralȱnerveȱsensation,ȱ 90ȱ T/sȱ forȱ peripheralȱ nerveȱ pain,ȱ 900ȱ T/sȱ forȱ respiratoryȱ systemȱ stimulation,ȱ andȱ 3600ȱ T/sȱ forȱ cardiacȱ stimulationȱ [6].ȱ Presently,ȱ forȱ clinicalȱ practicesȱ theȱ FDAȱ guidelinesȱ suggestȱ0Ȭ20ȱT/s,ȱwhichȱlimitsȱgradientȱswitchingȱratesȱtoȱ aȱ factorȱ ofȱ 3ȱ belowȱ theȱ meanȱ Peripheralȱ Nerveȱ Stimulationȱ (PNS)ȱ levelȱ (>ȱ 20ȱ T/sȱ forȱ firstȱ andȱ secondȱ controlledȱ modes,ȱ limitedȱ byȱ humanȱ ethicsȱ committees).ȱ Theȱ typicalȱ operatingȱ rangeȱ forȱ MRȬimagingȱ isȱ 45ȱ T/s,ȱ whichȱsuggestsȱmaximumȱgradientȱamplitudesȱofȱ90ȱmTȱȉȱ mȬ1_{ȱforȱaȱmaximumȱadequateȱriseȱtimeȱofȱ200ȱΐsȱforȱMRIȱ} sequencing.ȱForȱIGCȬMRNȱsequencingȱusingȱ450ȱmTȱȉȱmȬ 1_{,ȱ theȱ minimumȱ acceptableȱ riseȱ timeȱ becomesȱ 11.25ȱ ms,ȱ} whichȱ translatesȱ toȱ aȱ maximumȱ possibleȱ switchingȱ frequencyȱ (assumingȱ thatȱ noȱ MRȬtrackingȱ isȱ performed)ȱ ofȱ 44.44ȱ Hz.ȱ Forȱ operatingȱ withinȱ theȱ FDAȱ recommendationsȱ ofȱ 0Ȭ20ȱ T/s,ȱ theseȱ figuresȱ becomeȱ 22.5ȱ msȱ andȱ 22.22ȱ Hz.ȱ Atȱ theȱ limitȱ ofȱ thisȱ IGC,ȱ i.e.,ȱ forȱ anȱ increaseȱ fromȱ 0ȱ toȱ 450ȱ mTȱ ȉȱ mȬ1_{ȱ inȱ 100ȱ ΐs,ȱ theȱ switchingȱ} rateȱwouldȱcorrespondȱtoȱ450ȱT/s,ȱwhichȱisȱwellȱaboveȱtheȱ thresholdȱ forȱ peripheralȱ nerveȱ painȱ butȱ stillȱ wellȱ belowȱ theȱthresholdȱforȱrespiratoryȱsystemȱstimulation.ȱ

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However,ȱitȱisȱknownȱthatȱtheȱinducedȱcurrentȱproducedȱ byȱ suchȱ gradientsȱ inȱ theȱ patientȱ isȱ proportionalȱ notȱ onlyȱ toȱtheȱslewȱrateȱbutȱalsoȱtoȱtheȱcrossȬsectionalȱareaȱofȱtheȱ bodyȱ beingȱ exposedȱ toȱ suchȱ aȱ varyingȱ magneticȱ field;ȱ therefore,ȱ theȱ orientationȱ ofȱ theȱ steeringȱ gradientsȱ couldȱ beȱ consideredȱinȱ evaluatingȱ theȱ risksȱ forȱ theȱ patient.ȱ Butȱ smallerȱ IGC,ȱ suchȱ asȱ headȬonlyȱ gradientȱ coils,ȱ canȱ gainȱ safety/sensoryȱ thresholdȱ marginsȱ dueȱ bothȱ toȱ theirȱ reducedȱlengthȱandȱtheȱreducedȱcrossȬsectionalȱareaȱoverȱ whichȱ theȱ gradientsȱ occur.ȱ Theȱ gradientȱ efficiencyȱ scalesȱ withȱ theȱ fifthȱ powerȱ ofȱ theȱ radius,ȱ soȱ thatȱ reducingȱ theȱ diameterȱ ofȱ theȱ IGCȱ twoȬfoldȱ canȱ increaseȱ theȱ gradientȱ strengthȱ byȱ aȱ factorȱ ofȱ 32.ȱ Therefore,ȱ aȱ smallerȱ IGCȱ notȱ onlyȱ enablesȱ theȱ useȱ ofȱ largerȱ amplitudesȱ withȱ goodȱ safetyȱ margins,ȱ butȱ alsoȱ makesȱ suchȱ highȱ gradientsȱ practicalȱtoȱimplement.ȱ 3.ȱSGCȬMRNȱ TheȱmainȱadvantageȱofȱinstallingȱanȱSGCȱinsideȱtheȱtunnelȱofȱ aȱclinicalȱMRIȱscannerȱthatȱrequiresȱnoȱsoftwareȱorȱhardwareȱ modificationȱofȱtheȱscanner,ȱisȱtheȱfactȱthatȱtheȱdutyȱcycleȱcanȱ beȱmaintainedȱatȱ100%ȱofȱmaximumȱgradientȱfields,ȱi.e.,ȱȱ=ȱ 1.ȱ Butȱ becauseȱ theȱ SGCȱ assemblyȱ isȱ drivenȱ byȱ threeȱ DCȱ powerȱ suppliesȱ (oneȱ forȱ eachȱ axis),ȱ theȱ slewȱ rateȱ isȱ muchȱ lowerȱ thanȱ forȱ theȱ pulsedȱ gradientsȱ generatedȱ throughȱ theȱ IGC.ȱForȱinstance,ȱforȱaȱgradientȱofȱ450ȱmTȱȉȱmȬ1_{,ȱtheȱriseȱtimeȱ} wasȱ 100ȱ ΐsȱ (extendedȱ toȱ 22.5ȱ msȱ toȱ beȱ withinȱ FDAȱ guidelines)ȱandȱ~350ȱmsȱ(measuredȱexperimentally)ȱduringȱ IGCȬMRNȱ andȱ SGCȬMRN,ȱ respectively.ȱ Suchȱ aȱ longȱ riseȱ timeȱpreventsȱtheȱSGCȱfromȱbeingȱusedȱasȱimagingȱcoilsȱand,ȱ moreȱimportantly,ȱputsȱaȱconstraintȱonȱMRȬimagingȱorȱMRȬ trackingȱduringȱMRN.ȱThisȱisȱdueȱtoȱinterferencesȱbetweenȱ theȱSGCȱandȱtheȱIGC,ȱwherebyȱtheȱSGCȱmustȱbeȱsetȱbackȱtoȱ zeroȱ priorȱ toȱ MRȬtrackingȱ forȱ gatheringȱ positionalȱ informationȱforȱservoingȱcontrol.ȱ

ȱ

Becauseȱ ofȱ theȱ slowȱ switchingȱ mode,ȱ SGCȬMRNȱ wouldȱ beȱ moreȱ appropriateȱ overȱ IGCȬMRNȱ whenȱ theȱ steeringȱ gradientȱ mustȱ beȱ maintainedȱ forȱ aȱ longerȱ timeȱ periodȱ thanȱ wouldȱ beȱ possibleȱ withȱ theȱ IGCȱ andȱ whereȱ aȱ relativelyȱ fastȱ directionalȱ changeȱ ofȱ theȱ gradientȱ isȱ notȱ required.ȱ Thisȱ wouldȱ implyȱ openȬloopȱ MRNȱ whereȱ servoingȱ wouldȱ notȱ beȱ necessary,ȱ orȱ servoingȱ MRNȱ thatȱ doesȱ notȱ operateȱ underȱ tightȱ realȬtimeȱ constraints.ȱ Anotherȱ interventionȱ thatȱ canȱ takeȱ fullȱ advantageȱ ofȱ theȱ SGCȱ isȱ magneticallyȱ guidedȱ catheterization.ȱ Indeed,ȱ aȱ gradientȱ actingȱ onȱ aȱ magneticallyȱ steeredȱ catheterȱ orȱ guidewireȱ mustȱ typicallyȱ beȱ maintainedȱ longerȱ thanȱ theȱ dutyȱcycleȱofȱtheȱIGCȱatȱhighȱgradientsȱuntilȱtheȱtipȱofȱtheȱ catheterȱ orȱ guidewireȱ isȱ positionedȱ (pushed)ȱ atȱ theȱ entranceȱ ofȱ theȱ nextȱ branchȱ atȱ aȱ vesselȱ bifurcation.ȱ Thisȱ processȱcanȱtakeȱaȱfewȱsecondsȱtoȱbeȱcompleted.ȱ

3.ȱCombiningȱIGCȬMRNȱwithȱSGCȬMRNȱ

TheȱIGCȱcanȱbeȱcombinedȱwithȱtheȱSGCȱtoȱ formȱwhatȱisȱ referredȱtoȱasȱaȱdoubleȬinsert,ȱasȱdepictedȱinȱFig.ȱ2.ȱInȱthisȱ

case,ȱ theȱ IGCȱ isȱ insertedȱ insideȱ theȱ SGCȱ andȱ theȱ doubleȬ insertȱcanȱbeȱplacedȱinsideȱtheȱtunnelȱofȱtheȱclinicalȱMRIȱ scannerȱtoȱtakeȱadvantageȱofȱtheȱŖȱfield.ȱ

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ŽƵďůĞ/ŶƐĞƌƚ

_ȱ ’ž›ŽȱŘǯȱPhotographȱofȱtheȱdoubleȬinsertȱshowingȱtheȱIGCȱ insideȱtheȱSGCȱ

Withȱ theȱ doubleȬinsert,ȱ theȱ advantagesȱ ofȱ bothȱ approachesȱareȱavailableȱforȱMRN.ȱTheȱchoiceȱtoȱuseȱIGCȬ MRNȱ orȱ SGCȬMRNȱ withȱ suchȱ aȱ doubleȬinsertȱ willȱ dependȱonȱtheȱvascularȱcharacteristicsȱalongȱtheȱplannedȱ trajectoryȱ asȱ wellȱ asȱ theȱ characteristicsȱ ofȱ theȱ navigableȱ agents.ȱ Aȱ simpleȱ exampleȱ toȱ demonstrateȱ theȱ fundamentalȱprincipleȱisȱshownȱinȱFig.ȱ3.ȱ

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;ďͿ

ϭ

ϭ

Ϯ

ϯ

Ϯ ϯ

Ě

_ϭ͕Ϯ ȱ ’ž›ŽȱřǯȱMRȬimagesȱofȱtheȱrightȱandȱleftȱrenalȱandȱmesentericȱ arteriesȱshowingȱtwoȱpossibleȱscenariosȱ((a)ȱandȱ(b))ȱforȱMRNȱ alongȱwaypointsȱ1,ȱ2ȱandȱ3ȱ

Inȱ Fig.ȱ 3a,ȱ SGCȬMRNȱ isȱ aȱ potentiallyȱ viableȱ alternativeȱ whereȱ theȱ navigableȱ agentsȱ couldȱ takeȱ advantageȱ ofȱ aȱ longerȱdutyȱcycleȱforȱsteeringȱpurposeȱalongȱtheȱdistanceȱ separatingȱ twoȱ successiveȱ waypointsȱ (e.g.,ȱ ŗǰŘȱbetweenȱ waypointsȱ1ȱandȱ2ȱinȱFig.ȱ3a)ȱandȱwhereȱtheȱdirectionȱofȱ theȱ steeringȱ gradientȱ canȱ remainȱ unchangedȱ betweenȱ waypointsȱ1ȱandȱ3.ȱ

ȱ

Inȱ Fig.ȱ 3b,ȱ aȱ changeȱ inȱ theȱ steeringȱ gradientȱ isȱ necessaryȱ betweenȱ waypointsȱ 2ȱ andȱ 3.ȱ Inȱ thisȱ particularȱ case,ȱ consideringȱ theȱ bloodȱ velocityȱ andȱ theȱ shorterȱ distanceȱ

separatingȱ waypointsȱ 2ȱ andȱ 3,ȱ itȱ becomesȱ obviousȱ thatȱ insufficientȱtimeȱisȱavailableȱtoȱswitchȱtheȱdirectionȱofȱtheȱ SGC.ȱInȱthisȱcase,ȱIGCȬMRNȱisȱlikelyȱtoȱbeȱmoreȱefficientȱ thanȱ SGCȬMRNȱ providedȱ thatȱ theȱ firstȱ bifurcationȱ towardsȱ waypointȱ 2ȱ canȱ beȱ achievedȱ withȱ theȱ IGC.ȱ Anotherȱ alternativeȱ isȱ toȱ useȱ theȱ SGCȱ toȱ performȱ magneticallyȱsteeredȱcatheterizationȱinȱtheȱsegmentȱŗǰŘȱinȱ orderȱtoȱbringȱtheȱtipȱofȱtheȱcatheterȱatȱwaypointȱ2,ȱwhereȱ theȱ navigableȱ agentsȱ wouldȱ beȱ releasedȱ priorȱ toȱ performingȱSGCȬMRN,ȱtowardsȱwaypointȱ3ȱinȱFig.ȱ3b.ȱIfȱ deeperȱ MRNȱ mustȱ beȱ performedȱ towardsȱ anotherȱ waypointȱ beyondȱ waypointȱ 3ȱ requiringȱ aȱ directionalȱ changeȱ ofȱ theȱ steeringȱ gradient,ȱ thenȱ IGCȬMRNȱ couldȱ replaceȱSGCȬMRNȱafterȱreleasingȱtheȱnavigableȱagentsȱatȱ theȱtipȱofȱtheȱcatheter.ȱ

4.ȱMRȬNavigableȱTherapeuticȱAgentsȱ

MRȬnavigableȱtherapeuticȱagentsȱcanȱtakeȱvariousȱforms.ȱ Initialȱ proofsȬofȬconceptȱ wereȱ doneȱ usingȱ MRNȱ agentsȱ knownȱasȱTMMC,ȱwhich,ȱasȱmentionedȱearlier,ȱconsistȱofȱ cancerȱ therapeuticsȱ knownȱ asȱ Doxorubicinȱ (DOX)ȱ embeddedȱ withȱ FeCoȱ magneticȱ nanoparticlesȱ (MNP)ȱ withinȱaȱsphericalȱbiodegradableȱpolymerȱ(PLGA)ȱmatrix.ȱ Moreȱ specifically,ȱ FeCoȱ nanoparticles,ȱ coatedȱ withȱ aȱ 10Ȭ nmȱ graphiteȱ shell,ȱ exhibitedȱ aȱ diameterȱ (Ø)ȱ ofȱ 206ȱ ±ȱ 62ȱ nmȱ andȱ œȱ ofȱ 195ȱ ±ȱ 10ȱ emuȱ gȬ1.ȱ TMMCȱ wereȱ loadedȱ (%,ȱ w/w)ȱ withȱ DOXȱ (3.2ȱ ±ȱ 0.5)ȱ andȱ FeCoȱ nanoparticlesȱ (37ȱ ±ȱ 2.7)ȱ exhibitedȱ theȱ followingȱ properties:ȱ Øȱ =ȱ 53ȱ ±ȱ 19ȱ ΐm,ȱ

œȱ =ȱ 72ȱ ±ȱ 3ȱ emuȱ gȬ1ȱ andȱ aȱ sustainedȱ drugȱ releaseȱ overȱ severalȱdays.ȱ

ȱ

Severalȱ versionsȱ ofȱ TMMCȱ couldȱ beȱ synthesized,ȱ eachȱ versionȱ havingȱ aȱ differentȱ ratioȱ ofȱ magneticȱ materialsȱ versusȱ therapeuticȱ loads.ȱ Indeed,ȱ increasingȱ theȱ amountȱ ofȱ drugȱ inȱ eachȱ MRNȬagentȱ withinȱ theȱ limitȱ ofȱ theȱ synthesisȱ processȱ wouldȱ yieldȱ aȱ higherȱ densityȱ ofȱ therapeuticsȱtoȱbeȱdeliveredȱforȱaȱgivenȱnumberȱofȱagentsȱ beingȱ injected.ȱ Onȱ theȱ otherȱ hand,ȱ byȱ doingȱ so,ȱ theȱ amountȱ ofȱ MNPȱ perȱ agentȱ wouldȱ beȱ decreased,ȱ whichȱ wouldȱ reduceȱ theȱ effectȱ ofȱ theȱ gradientȱ forcesȱ fromȱ theȱ MRNȱ system.ȱ Butȱ increasingȱ theȱ amountȱ ofȱ MNPȱ perȱ agentȱ wouldȱ alsoȱ increaseȱ theȱ dipoleȬdipoleȱ interactionsȱ betweenȱ neighbouredȱ agents,ȱ formingȱ chainȬlikeȱ aggregatesȱ inȱ theȱ shapeȱ ofȱ prolateȱ ellipsoidsȱ withȱ theȱ longitudinalȱaxisȱorientedȱtowardsȱtheȱzȬaxisȱofȱtheȱMRNȱ platform.ȱ Whenȱ navigatingȱ TMMCȱ parallelȱ toȱ theȱ zȬaxis,ȱ applyingȱ tooȱ muchȱ gradientȱ mayȱ increaseȱ theȱ frictionȱ forceȱ betweenȱ theȱ TMMCȱ aggregatesȱ andȱ theȱ vessel’sȱ wall;ȱthisȱwouldȱinfluenceȱtheȱsteeringȱefficacyȱatȱtheȱnextȱ bloodȱ vessel’sȱ bifurcation.ȱ Whenȱ navigatingȱ perpendicularȱ toȱ theȱ zȬaxis,ȱ suchȱ aggregatesȱ couldȱ haveȱ lengthsȱ extendingȱ beyondȱ theȱ diameterȱ ofȱ theȱ nextȱ branchingȱ vessel.ȱ Inȱ thisȱ case,ȱ ifȱ theȱ bloodȱ flowȱ isȱ tooȱ weak,ȱprematureȱembolizationȱofȱtheȱbloodȱvesselsȱcouldȱ occurȱ whereȱ theȱ TMMCȱ aggregatesȱ wouldȱ notȱ proceedȱ furtherȱ towardsȱ theȱ targetedȱ site.ȱ Withȱ sufficientȱ bloodȱ

flowȱ providingȱ theȱ forceȱ necessaryȱ toȱ breakȱ theȱ dipoleȬ dipoleȱinteractiveȱforceȱbetweenȱTMMCȱinȱtheȱaggregates,ȱ aȱ fractionȱ ofȱ eachȱ aggregateȱ couldȱ leadȱ toȱ theȱ otherȱ branchingȱ vesselȱ resultingȱ inȱ aȱ lowerȱ targetingȱ efficacyȱ whileȱincreasingȱtheȱsystemicȱtoxicityȱlevelȱforȱtheȱpatient.ȱ Therefore,ȱ althoughȱ theȱ highȱ gradientsȱ andȱ extendedȱ dutyȱ cyclesȱ areȱ necessaryȱ toȱ achieveȱ adequateȱ targetingȱ efficacy,ȱ cautionȱ mustȱ beȱ practisedȱ soȱ thatȱ theȱ characteristicsȱ ofȱ theȱ navigableȱ agents,ȱ theȱ physiologicalȱ conditionsȱ andȱ inȱ particularȱ theȱ bloodȱ flowȱ rate,ȱ asȱ wellȱ asȱtheȱlengthȱofȱtheȱvessel’sȱsegmentsȱandȱtheȱdirectionȱofȱ theȱ navigableȱ agentsȱ withȱ regardȱ toȱ theȱ zȬaxis,ȱ areȱ allȱ takenȱintoȱaccount.ȱȱ

5.ȱDiscussionȱ

TheȱresultsȱobtainedȱindicateȱthatȱimplementingȱaȱwholeȬ bodyȱ IGCȱ orȱ SGCȱ capableȱ ofȱ achievingȱ sufficientlyȱ highȱ gradientsȱforȱsteeringȱnavigableȱagentsȱinȱtheȱarteriolesȱisȱ notȱ aȱ trivialȱ task,ȱ dueȱ toȱ technologicalȱ limits.ȱ Inȱ theȱ shorterȱ term,ȱ IGCȬMRNȱ andȱ SGCȬMRNȱ couldȱ beȱ conductedȱinȱtheȱlimbsȱorȱtheȱheadȱwhereȱtheȱdiameterȱofȱ theȱ IGCȱ orȱ SGCȱ canȱ beȱ decreased,ȱ facilitatingȱ theȱ implementationȱ ofȱ coilsȱ capableȱ ofȱ generatingȱ steeringȱ gradientsȱ withȱ adequateȱ slewȱ ratesȱ andȱ amplitudes.ȱ UnlikeȱforȱSGCȬMRN,ȱIGCȬMRNȱcouldȱaffectȱtheȱpatientȱ byȱ generatingȱ gradientsȱ wellȱ aboveȱ theȱ thresholdȱ forȱ peripheralȱ nerveȱ pain.ȱ Thisȱ suggestsȱ thatȱ IGCȬMRNȱ sequencesȱ withinȱ FDAȱ recommendationsȱ couldȱ beȱ madeȱ fromȱ alternateȱ imagingȱ andȱ steeringȱ sequencesȱ whereȱ MRIȱsequencesȱhaveȱaȱmaximumȱamplitudeȱofȱ90ȱmTȱȉȱmȬ 1_{ȱ andȱ riseȱ timeȱ ofȱ 200ȱ ΐs,ȱ andȱ steeringȱ gradientsȱ haveȱ aȱ} maximumȱamplitudeȱofȱ450ȱmTȱȉȱmȬ1_{ȱandȱriseȱtimeȱofȱ22.5ȱ} ms.ȱ

ȱ

Catheterizationȱ hasȱ theȱ potentialȱ toȱ helpȱ MRNȱ effectivenessȱbyȱinjectingȱtheȱnavigableȱagentsȱdeeperȱandȱ atȱ strategicȱ locations.ȱ Toȱ doȱ so,ȱ aȱ magneticallyȱ guidedȱ catheterizationȱ procedureȱ usingȱ theȱ SGCȱ orȱ potentiallyȱ theȱ IGCȱ wouldȱ beȱ aȱ greatȱ additionȱ toȱ MRNȬbasedȱ interventionȱ suggestingȱ theȱ useȱ ofȱ aȱ doubleȬinsertȱ forȱ manyȱ cases.ȱ Suchȱ aȱ doubleȬinsertȱ takesȱ upȱ moreȱ volumeȱ inȱ theȱ tunnelȱ ofȱ aȱ clinicalȱ MRIȱ scannerȱ andȱ thereforeȱ restrictsȱ theȱ maximumȱ diameterȱ ofȱ theȱ IGC.ȱ Althoughȱ reducingȱ theȱ diameterȱ ofȱ theȱ IGCȱ helpsȱ inȱ achievingȱ imagingȱ gradientsȱ withȱ properȱ specifications,ȱ suchȱ reductionsȱinȱdiameterȱmayȱlimitȱtheȱregionsȱofȱtheȱbodyȱ thatȱcouldȱbeȱtreated,ȱunlessȱaȱdedicatedȱMRNȱplatformȱisȱ developed.ȱ

Ourȱ experienceȱ inȱ MRNȱ showsȱ thatȱ theȱ decisionȬmakingȱ processȱcanȱbeȱdifficultȱforȱmedicalȱstaff;ȱspecialȱsoftwareȱ interfacesȱcouldȱthereforeȱbeȱhelpfulȱduringȱtheȱplanningȱ phase.ȱ Suchȱ softwareȱ wouldȱ takeȱ intoȱ accountȱ notȱ onlyȱ theȱ characteristicsȱ ofȱ theȱ navigableȱ agentsȱ asȱ wellȱ asȱ theȱ IGCȱ andȱ SGC,ȱ butȱ alsoȱ theȱ physiologicalȱ characteristicsȱ encounteredȱ betweenȱ theȱ plannedȱ injectionȱ andȱ targetedȱ sites.ȱ

ȱ

Anotherȱ aspectȱ toȱ considerȱ isȱ theȱ numberȱ ofȱ repetitiveȱ injectionsȱ toȱ beȱ performed.ȱ Indeed,ȱ dependingȱ onȱ theȱ therapeuticȱ doseȱ toȱ beȱ delivered,ȱ deliveringȱ theȱ requiredȱ doseȱ inȱ onlyȱ oneȱ injectionȱ isȱ unlikely.ȱ Thisȱ isȱ dueȱ toȱ theȱ constrainedȱvolumeȱinȱnarrowerȱvesselsȱandȱthereforeȱtheȱ maximumȱ quantityȱ ofȱ navigableȱ agentsȱ perȱ injection.ȱ Aȱ numberȱ ofȱ injectionsȱ mayȱ impactȱ theȱ heatingȱ ofȱ theȱcoilsȱ orȱ extendȱ substantiallyȱ theȱ overallȱ timeȱ requiredȱ toȱ conductȱsuchȱMRNȬbasedȱinterventions.ȱ

ȱ

Despiteȱ theseȱ constraints,ȱ MRNȱ isȱ aȱ seriousȱ methodȱ forȱ microroboticȬbasedȱtargetedȱinterventionsȱinȱtheȱvascularȱ networkȱ comparedȱ toȱ otherȱ proposedȱ methods.ȱ Forȱ instance,ȱpiezoelectricȱultrasonicȱmicroȬmotorsȱhaveȱbeenȱ proposedȱ andȱ investigatedȱ forȱ ’—ȱ Ÿ’Ÿ˜ȱ microroboticȱ applicationsȱ [7].ȱ ȱ Theȱ advantageȱ ofȱ thisȱ approachȱ isȱ thatȱ noȱ externalȱ sourceȱ isȱ necessaryȱ forȱ generatingȱ theȱ propulsiveȱ orȱ steeringȱ force.ȱ Onȱ theȱ otherȱ hand,ȱ scalingȱ mayȱ proveȱ difficult.ȱ Indeed,ȱ althoughȱ theȱ authorsȱ claimȱ thatȱ theȱ crossȬsectionalȱ dimensionȱ ofȱ theȱ microrobotȱ couldȱ beȱ reducedȱ downȱ toȱ 250ȱ ΐmȱ withoutȱ lossȱ ofȱ performanceȱ comparedȱ toȱ aȱ previousȱ prototypeȱ withȱ aȱ diameterȱ ofȱ 400ȱ ΐm,ȱ theseȱ dimensionsȱ wouldȱ restrictȱ applicationsȱ inȱ theȱ arteriesȱ only.ȱ Anotherȱ concernȱ isȱ theȱ maximumȱ therapeuticȱ payloadsȱ thatȱ couldȱ beȱ deliveredȱ fromȱsuchȱaȱdevice,ȱconsideringȱthatȱonlyȱoneȱdeviceȱcanȱ operateȱ inȱ theȱ arteryȱ atȱ aȱ givenȱ time.ȱ Theȱ factȱ thatȱ theȱ deviceȱ isȱ notȱ madeȱ ofȱ biodegradableȱ materialsȱ suggestsȱ thatȱ itsȱ recoveryȱ wouldȱ beȱ requiredȱ andȱ sinceȱ piezoȬ actuationȱalsoȱrequiresȱrelativelyȱhighȱvoltage,ȱthisȱwouldȱ poseȱ furtherȱ challengesȱ forȱ implementingȱ untetheredȱ versions.ȱ Nonetheless,ȱ suchȱ technologyȱ isȱ promisingȱ forȱ otherȱapplicationsȱinȱtheȱarteries.ȱ

ȱ

Inȱ [8],ȱ theȱ authorsȱ proposeȱ aȱ platformȱ referredȱ toȱ asȱ theȱ EMAȱ systemȱ whichȱ isȱ basedȱ onȱ aȱ pairȱ ofȱ stationaryȱ HelmholtzȬMaxwellȱ coilsȱ andȱ aȱ pairȱ ofȱ rotationalȱ HelmholtzȬMaxwellȱ coilsȱ forȱ manipulatingȱ aȱ microrobotȱ inȱ aȱ 3Ȭdimensionalȱ space.ȱ Aȱ uniformȱ magneticȱ fluxȱ densityȱ isȱ providedȱ byȱ theȱ Helmholtzȱ coilsȱ withȱ theȱ gradientsȱ beingȱ providedȱ byȱ theȱ Maxwellȱ coils.ȱ Theȱ advantageȱofȱthisȱplatformȱisȱthatȱtheȱtorqueȱactingȱonȱtheȱ microrobotȱ isȱ notȱ constrainedȱ toȱ aȱ singleȱ direction,ȱ asȱ isȱ theȱcaseȱforȱMRN.ȱAlthoughȱthisȱcanȱbeȱanȱadvantageȱforȱ shapeȬanisotropicȱ microrobots,ȱ itȱ isȱ notȱ aȱ significantȱ advantageȱ forȱ sphericalȱ implementationsȱ suchȱ asȱ theȱ TMMCȱ orȱ otherȱ potentialȱ shapeȬisotropicȱ microrobots.ȱ Althoughȱ theȱ platformȱ wouldȱ allowȱ rotationalȱ controlȱ ofȱ needleȬlikeȱaggregatesȱofȱTMMC,ȱMRȬimagingȱduringȱtheȱ interventionsȱwouldȱhaveȱtoȱbeȱreplacedȱbyȱotherȱmedicalȱ imagingȱ modalitiesȱ withoutȱ enhancedȱ tissueȱ contrast,ȱ whichȱ isȱ importantȱ inȱ suchȱ targetȱ interventions.ȱ Theȱ systemȱ isȱ alsoȱ bulkyȱ andȱ makesȱ itȱ difficultȱ toȱ generateȱ higherȱ fieldsȱ withinȱ anȱ appropriateȱ workspaceȱ forȱ softȱ magneticȱ materialsȱ withȱ aȱ highȱ magnetizationȱ saturationȱ level.ȱThisȱmayȱnecessitateȱtheȱuseȱofȱpermanentȱmagnetsȱ inȱ theȱ microrobotȱ orȱ theȱ useȱ ofȱ aȱ largerȱ volumeȱ ofȱ softȱ

magneticȱmaterial;ȱinȱbothȱcasesȱthisȱwouldȱleadȱtoȱlargerȱ microrobotsȱ thatȱ mightȱ beȱ constrainedȱ toȱ navigateȱ inȱ largerȱarteries.ȱTheȱrotationalȱmovementȱofȱtheȱcoilsȱalsoȱ reducesȱtheȱresponseȱtimeȱtoȱreȬalignȱtheȱfield,ȱwhichȱmayȱ beȱ aȱ constraintȱ onȱ achievingȱ theȱ requiredȱ realȬtimeȱ performance.ȱ Nonetheless,ȱ theȱ EMAȱ systemȱ hasȱ advantagesȱ thatȱ mayȱ proveȱ toȱ beȱ suitableȱ forȱ specificȱ typesȱofȱinterventionsȱconductedȱinȱarteries.ȱ

ȱ

Inȱ [9],ȱ aȱ permanentȱ magnetȱ attachedȱ toȱ aȱ roboticȱ armȱ isȱ usedȱtoȱgenerateȱaȱmagneticȱgradientȱforȱlocomotionȱandȱ navigationȱ basedȱ onȱ magneticȱ draggingȱ ofȱ MNPȬbasedȱ devicesȱ forȱ theȱ treatmentȱ ofȱ vascularȱ obstructions.ȱ Theȱ mainȱ advantageȱ ofȱ suchȱ aȱ platformȱ isȱ itsȱ relativeȱ simplicityȱandȱrelativelyȱlowȱcost.ȱButȱsinceȱitȱreliesȱonȱaȱ magneticȱgradientȱonly,ȱitȱmayȱbeȱdifficultȱtoȱachieveȱfullȱ magnetizationȱ ofȱ theȱ MNPȱ orȱ toȱ fullyȱ exploitȱ MNPȱ withȱ highȱ magnetizationȱ saturationȱ levelsȱ unlessȱ operatingȱ relativelyȱ closeȱ toȱ theȱ externalȱ magnet.ȱ Asȱ such,ȱ theȱ methodȱ couldȱ beȱ mostȱ appropriateȱ forȱ operationȱ inȱ arteriesȱ whereȱ theȱ volumeȱ ofȱ magneticȱ materialȱ canȱ beȱ increasedȱ toȱ compensateȱ forȱ interventionsȱ beingȱ performedȱdeeperȱinȱtheȱbody.ȱTheȱfactȱthatȱtheȱgradientȱ isȱ generatedȱ byȱ theȱ mechanicalȱ displacementȱ ofȱ anȱ externalȱ magnetȱ mayȱ haveȱ aȱ significantȱ impactȱ onȱ theȱ realȬtimeȱ performanceȱ ofȱ switchingȱ theȱ directionȱ ofȱ theȱ gradientȱ forȱ targetȱ drugȱ deliveries.ȱ Butȱ forȱ particularȱ interventionsȱ conductedȱ inȱ theȱ arteries,ȱ suchȱ asȱ theȱ treatmentȱofȱvascularȱobstruction,ȱtheȱmethodȱmayȱproveȱ toȱbeȱadequate.ȱ

ȱ

AnotherȱinterestingȱplatformȱisȱtheȱOctoMagȱsystemȱ[10].ȱ Theȱ platformȱ accomplishesȱ aȱ veryȱ highȱ levelȱ ofȱ wirelessȱ controlȱ throughȱ aȱ relativelyȱ largeȱ workspaceȱ characterizedȱbyȱcomplexȱnonȬuniformedȱmagneticȱfieldsȱ byȱ exploitingȱ linearȱ representationsȱ ofȱ coupledȱ fieldȱ distributionsȱ ofȱ multipleȱ softȬmagneticȬcoreȱ electromagnetsȱ actingȱ inȱ concert.ȱ Theȱ systemȱ hasȱ theȱ potentialȱ toȱ beȱ scaledȱ upȱ forȱ humanȱ interventionsȱ withȱ magneticȱgradientsȱcomparableȱtoȱtheȱMRNȱplatformȱbutȱ withȱ aȱ muchȱ lowerȱ magneticȱ fieldȱ atȱ theȱ centreȱ ofȱ theȱ workspace.ȱIndeed,ȱinsteadȱofȱaȱ1.5ȱTȱorȱhigherȱfield,ȱtheȱ fieldȱ mightȱ beȱ asȱ lowȱ asȱ 0.1ȱ T.ȱ Atȱ suchȱ aȱ level,ȱ withȱ theȱ magnetizationȱcurveȱofȱsoftȬmagneticȱMNPȱcharacterizedȱ byȱhighȱmagnetizationȱsaturation,ȱthisȱmayȱtranslateȱtoȱaȱ relativelyȱ lowȱ inducedȱ force,ȱ whichȱ wouldȱ beȱ compensatedȱ byȱ largerȱ microrobots.ȱ Butȱ consideringȱ theȱ difficultyȱ inȱ scalingȱ theȱ MRNȱ platformȱ forȱ anȱ innerȱ diameterȱ capableȱ ofȱ acceptingȱ aȱ humanȱ adult,ȱ suchȱ anȱ approachȱmayȱproveȱquiteȱefficientȱforȱparticularȱwirelessȱ interventionsȱ inȱ theȱ arteriesȱ orȱ forȱ magneticȬbasedȱ catheterizationȱprocedures.ȱ

6.ȱConclusionȱ

Medicalȱ microȬnanoroboticsȱ inȱ theȱ vascularȱ networkȱ isȱ aȱ newȱ fieldȱ ofȱ researchȱ thatȱ hasȱ shownȱ potentialȱ inȱ targetȱ

interventionsȱsuchȱasȱinȱcancerȱtherapiesȱandȱdiagnostics.ȱ Althoughȱtheȱuseȱofȱmagneticȱfieldsȱalreadyȱimplementedȱ inȱ upgradedȱ clinicalȱ MRIȱ scannersȱ isȱ aȱ promisingȱ approachȱ forȱ servoingȱ navigationȱ controlȱ ofȱ navigableȱ agentsȱ inȱ theȱ vascularȱ network,ȱ improvementȱ inȱ coolingȱ ofȱ theȱ coilsȱ forȱ extendingȱ theȱ dutyȱ cycles,ȱ asȱ wellȱ asȱ improvementȱinȱMRȬtrackingȱalgorithms,ȱwouldȱcertainlyȱ helpȱ inȱ translatingȱ thisȱ technologyȱ toȱ wholeȬbodyȱ MRN.ȱ Nonetheless,ȱ experimentalȱ resultsȱ alreadyȱ showȱ greatȱ potentialȱforȱthisȱtechnologyȱforȱcontributingȱtoȱenhancedȱ therapeuticȱ efficacyȱ whileȱ reducingȱ severeȱ secondaryȱ toxicityȱforȱtheȱpatients.ȱ

7.ȱAcknowledgementsȱ

Theȱ authorȱ acknowledgesȱ theȱ participationȱ ofȱ theȱ membersȱofȱtheȱNanoRoboticsȱLaboratory,ȱDrȱSoulezȱandȱ Drȱ Beaudoinȱ fromȱ theȱ Centreȱ Hospitalierȱ deȱ l’Universitéȱ deȱMontréalȱ(CHUM)ȱduringȱtheȱ’—ȱŸ’Ÿ˜ȱexperiments.ȱAtȱ theȱtimeȱofȱtheȱwriting,ȱtheȱauthorȱwasȱsupportedȱbyȱtheȱ Researchȱ Chairȱ ofȱ Écoleȱ Polytechniqueȱ inȱ Nanoroboticsȱ andȱ aȱ Discoveryȱ Grantȱ fromȱ theȱ Nationalȱ Researchȱ CouncilȱofȱCanadaȱ(NSERC).ȱTheȱequipmentȱusedȱinȱthisȱ studyȱ wasȱ acquiredȱ withȱ aȱ grantȱ fromȱ theȱ Canadaȱ FoundationȱforȱInnovationȱ(CFI).ȱȱ

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