Distortion-free inside-out imaging for rapid diagnostics of ...Distortion-free inside-out imaging for rapid diagnostics of rechargeable Li-ion cells Konstantin Romanenkoa and Alexej

Distortion-free inside-out imaging for rapid diagnosticsof rechargeable Li-ion cellsKonstantin Romanenkoa and Alexej Jerschowa,1

aDepartment of Chemistry, New York University, New York, NY 10003

Edited by Alexis T. Bell, University of California, Berkeley, CA, and approved August 6, 2019 (received for review April 23, 2019)

Safety risks associated with modern high energy-dense recharge-able cells highlight the need for advanced battery screeningtechnologies. A common rechargeable cell exposed to a uniformmagnetic field creates a characteristic field perturbation dueto the inherent magnetism of electrochemical materials. Theperturbation pattern depends on the design, state of charge,accumulated mechanical defects, and manufacturing flaws of thedevice. The quantification of the induced magnetic field with MRIprovides a basis for noninvasive battery diagnostics. MRI distor-tions and rapid signal decay are the main challenges associatedwith strongly magnetic components present in most commercialcells. These can be avoided by using Single-Point RampedImaging with T1 enhancement (SPRITE). The method is immune toimage artifacts arising from strong background gradients andeddy currents. Due to its superior image quality, SPRITE is highlysensitive to defects and the state of charge distribution in com-mercial Li-ion cells.

inside-out MRI | SPRITE | battery diagnostics | Li-ion batteries

The wide use of portable electronics and rapidly expandingmarket for electric vehicles have driven the demand for high

capacity and safe rechargeable batteries. Challenges arise due tothe presence of flammable materials in cells and their high en-ergy densities. Noninvasive means of diagnostics can facilitateunderstanding of battery failure modes (1–4). MRI is a powerfultool for studying chemical, biological, and solid-state phenomena(5–8). Recently, in situ MRI of model electrochemical devicesshed light on underlying physical and mechanistic processes (9–16). These techniques however could not be used to studycommercial cells due to the conductive casings and small dis-tances between electrodes, which hamper radiofrequency (RF)penetration. An inside-out MRI (ioMRI) approach that over-comes these limitations has been recently introduced (1). Amagnetic field (MF) perturbation created by a cell depends onthe magnetic susceptibility and morphology of its constituents.For example, the source of a strong induced magnetization inlithium-ion cells is often a lithium-intercalation compound. Themagnetic susceptibility changes as a function of the amount ofinserted lithium. Therefore Li intercalation and its state of charge(SOC) could be assessed in cells nondestructively and rapidly byioMRI. Cells can also exhibit unique MF features characteristic oftheir defects.Industrial-scale applications of such battery diagnostics could

also employ rapid MRI methods (e.g., Fast Low Angle Shot –FLASH) (17). These techniques rely on either long evolutiontimes and echo trains, frequency encoding, or slice-selective RFpulses. Conductive and magnetic materials are known to inducesevere MRI artifacts (18–20). Several complications arise: a) Thesignals in the vicinity of such features can decay rapidly due todestructive interferences within voxels, and b) strong backgroundgradients lead to image misregistration. These problems are re-solved with fully phase-encoded MRI. Single-point rampedimaging with T1 enhancement, SPRITE (21–24), has been suc-cessfully employed for imaging of challenging systems (14, 25–28) and is highly suitable for MF visualization in regions withstrong local magnetism. This aspect is particularly important as

incorporation of ferromagnetic materials into commercial bat-teries is a common practice.

Concepts of the Inside-Out SPRITE MethodMRI employs pulsed MF gradients to create a spatial varia-tion of resonance frequencies based on the Zeeman splittingof nuclear spin energy levels. Conceptually, one may definea reciprocal k space, F(k), of spatial frequencies (29, 30),which represents the grid of raw data acquisition points,according to

FðkÞ=X

j

A�rj�exp

�−i2πkrj

�. [1]

An image, A(r), is obtained via a Fourier transformation of F(k). AnMR signal is acquired for discrete values of the vector k = γ g t (2π)−1,where γ is the nuclear gyromagnetic ratio, g is the MF gradient, andt is time. K-space sampling may be performed by varying either time(frequency encoding) or the gradient magnitude (phase encoding).Single-point MRI relies exclusively on phase encoding (31).Key parameters of the 3D centric-scan SPRITE pulse se-

quence (Fig. 1) are applied MF gradient g(gX gY gZ), gradientramp time TGR, gradient stabilization time TGS, RF pulse flipangle α and pulse duration Pα, phase encoding time TP, repeti-tion period TR, pulse train length NTR, number of interleavesNint, recovery delay between the pulse trains T0. The sequencestarts with a nonselective RF excitation at g = 0 followed by freeprecession during TP and acquisition of a sample of free in-duction decay (FID). Note that TP should exceed a probe “dead”time (10–100 μs). Then, the imaging gradient g is ramped to the

Significance

Rechargeable batteries can pose severe risks due to their flam-mable components in combination with high energy density.These challenges motivate the development of advanced batteryscreening techniques capable of rapid battery assessment. MRI, abroadly accepted method in the healthcare industry, has beenadapted for materials chemistry and energy storage research. Aquantitative MRI approach based on 3D phase encoding by-passes the hurdles associated with strongly magnetic compo-nents that are common in modern batteries (e.g., iPhonemodels). The reported technology is virtually distortion-free andshows a high sensitivity to mechanical defects and the chemicalstate of the electrodes. This approach may enable industrialquality control applications with a high temporal resolution andmay aid in battery development and monitoring.

Author contributions: K.R. and A.J. designed research; K.R. performed research; K.R.contributed new reagents/analytic tools; K.R. analyzed data; and K.R. and A.J. wrotethe paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.1To whom correspondence may be addressed. Email: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1906976116/-/DCSupplemental.

Published online August 30, 2019.

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next value over a period TGR and is allowed to stabilize duringTGS. The following RF excitation, free precession (phaseencoding), and single-point acquisition events take place in thepresence of this gradient. Pα should excite the sample bandwidth

for each gk. Typically, α is a few degrees and Pα is a fewmicroseconds long.Although it is possible to execute the SPRITE loop con-

tinuously until the sampling process is complete, the gradientand RF hardware duty cycles can approach levels that cannotbe sustained reliably by the equipment. The interleaved acquisi-tion allows for control over the temperature inside the gradientcoil system and RF circuit, and improves the image resolution (23,24). The k space is divided into Nint interleaves. One interleaf issampled with a train of NTR “Pα - TP - ACQ” blocks. After eachtrain, a recovery delay T0 ∼ 5 T1 (spin-lattice relaxation time)is required.Since F(k = 0) is a measure of the total spin density (Eq. 1),

commencing k-space sampling at k = 0 enables quantitativemeasurement of the longitudinal magnetization and improvedsignal to noise (SNR) (22). Repetitive RF pulses modulate thelongitudinal magnetization and the k-space envelope. Associatedimage blurring can be controlled by adjusting α (22–25).Assigning gradient values to locations on the Cartesian grid is a

robust and convenient sampling approach (23, 24). In this case,the image reconstruction consists of two simple steps: 1) reor-dering of the raw data into a complex array based on pre-determined gradient tables (gk

X gkY gk

Z), and 2) a fast discreteFourier transformation.Sectoral interleaves employed in this work result in iso-

tropic in-plane blurring (11), Fig. 1B. The k-space matrix NX ×NY × NZ is sampled plane-by-plane along Z. The in-plane tra-jectories (X-Y) are unwinding spirals confined within 8 sectors(Nint = 8).TR is limited by the hardware performance and safety re-

quirements specific to RF and gradient duty cycles. The realisticrange of TR values is from 0.5 to 2 ms.

A

B C

g0 = 0

TR 2TR

TGR TGS

gkZ

gkY

gkX

Pα

TPPα

TP

gk

gk+1

T0

TGSTTTGRTT

Nint × NTR

Fig. 1. (A) Centric-scan SPRITE pulse sequence. (B) Sectoral k-space trajectories.In-plane sampling is repeated for a number of equally spaced kZ values. (C){x-y} and {x-z} views of the battery holder with respect to B0 and B1.

Fig. 2. (A) {y-z} and {x-z} slices through the 3D FLASH image of the battery holder containing an intact iPhone-5 battery. (B) {y-z} and {x-z} slices through the3D io-FLASH map; H2O - containing regions. (C) The io-FLASH map with noisy data masked out.

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The image field of views (FOV) along the principal gradientaxes (PGA) X, Y, and Z are

FOVXYZ = πN�γGXYZTP

�−1, [2]

where GXYZ are the maximum gradient values along PGAs.The phase of the local transverse magnetization accumulated

over the time TP is

φðRÞ= γΔB0ðRÞTP, [3]

where ΔB0(R) = B(R)−B0 is the local perturbation of staticMF associated with the susceptibility contrast. The MR signal mea-sured at location R at time TP after the excitation pulse is described by

SðR,TPÞ= IZsinðαÞexpðiγΔB0ðRÞTPÞexpð−TP=T2 p Þ, [4]

where IZ is the equilibrium magnetization. The time constant T2*describing the rate of magnetization decay

T2p−1 =T−1

2 + γΔBð2πÞ−1 [5]

is determined via spin-spin relaxation rate (1/T2) and MF inho-mogeneity (ΔB) across a voxel. Thus, measuring the phase φ =arctan{Im(S)/Re(S)} as a function of TP (Eq. 3) gives

ΔB0ðRÞ= γ−1dφ=dTP. [6]

AnMFmap can be reconstructed from just 1 SPRITE scan (NTP= 1).Acquiring several phase-encoded points per RF excitation in a single

FID readout is a significant improvement in temporal resolution.Another benefit of this approach is a higher accuracy of the measuredaverage phase due to reduced phase dispersion over the shorter de-lays. Note, since the acquisition occurs in the presence of an appliedMF gradient, each point corresponds to a different FOV. The FOVscan be scaled using an established chirp Z-transform algorithm (23).The duration of an io-SPRITE experiment is

�NXNYNZTR +NintT0

�NTP. [7]

Two-dimensional (N X,Y = 64, N Z = 1, Nint = 8) and 3D acqui-sitions (N X,Y,Z = 64, Nint = 64 × 8) with TR = 1 ms, T0 = 1 s, andNTP = 1 would consume 12 s and 13 min, respectively. The 3Dexperiments can be substantially accelerated, depending on T0and TR (hardware limitations), and the k-space sampling strat-egy. For comparison, an io-FLASH MF map (128 × 128 × 128)requires 10 min with 4 echo times (TE).The accuracy of io-MRI and characteristic MF perturbations

are demonstrated for a cylindrical phantom comprising MnCl2solution (SI Appendix, Note S1 and Fig. S1). io-SPRITE pro-vides excellent accuracy: + 4.5 ppm near the bottom and top ofthe capillary is in good agreement with the expected value(+4.59 ppm).Following points highlight the benefits of the SPRITE design:

1) Immunity to susceptibility and chemical shift artifacts.2) Highly quantitative measurements due to short TP and

centric ordering.3) Flexibility in k-space sampling enables optimization of image

resolution, contrast, measurement time, and gradient and RFduty cycles.

Fig. 3. {y-z} and {x-z} slices through (A) 3D SPRITE image of the battery holder containing an intact iPhone-5 battery and (B) 3D io-SPRITE map (H2O -containing regions; ROI [region of interest]: 53 × 90 mm2; NTP = 1; n = 64, Nint = 64 × 8). (C) An iPhone-5 battery schematic, {y-z} and {x-z} views; the currentcollector and leads are shown in red.

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4) Active spoiling of transverse magnetization during TGRand TGS.

5) Acoustic noise is insignificant.6) Accurate phase encoding is unaffected by the gradient pulse

shape in the switching periods.

Results and DiscussionIn the approach described previously by Ilott et al. (1), the cell isplaced inside the dedicated battery holder, and a series ofFLASH images is acquired with different TEs. Note that the 1HMRI signal originates from the aqueous solution confined inside2 detection volumes of the holder and not from the battery itself(thus the term inside-out was introduced). Fig. 1C shows thearrangement of the cell, the detection volumes, and the direc-tions of the polarizing (B0) and RF (B1) magnetic fields. Theorientation of the cell (Fig. 1C) was selected to minimize Fara-day’s interaction of the oscillating B1 field with electric circuitsinside the battery and improve the B1 homogeneity (9–11).Below, we compare the results of FLASH and SPRITE-based

ioMRI tests of iPhone-5 batteries.These cells contain strongly paramagnetic as well as some

ferromagnetic components. This situation could represent a “nogo zone” for conventional MRI methods employing frequencyencoding and slice-selective pulses. A 3D FLASH image of theholder containing an iPhone-5 battery illustrates this point (Fig.2A). The positions and orientations of the image slices, {x-z} and{y-z}, with respect to the battery are indicated in Fig. 1C. Sincethe battery’s length exceeded the extent of the uniform spot ofthe RF resonator, the upper and lower halves of the battery werescanned separately, and 2 images were combined.

The image regions near the center and the leads (bottom) ofthe cell were severely affected by MF inhomogeneity induced by thespatial variation in susceptibility. The corrupted domains occupieda significant part of the detection volume (Fig. 2A). The metalcomponents present in the battery gave rise to 2 types of MRI ar-tifacts: 1) complete loss of signal due to rapid dephasing of trans-verse magnetization (short T2*) and 2) geometric distortions in theform of high-frequency ripples. A theoretical description of artifactsin gradient-echo MRI is provided by Reichenbach et al. (32).The low-intensity voxels (SNR < 1) contained short-lived

magnetization components with T2* < 0.1 ms (Eq. 3). Thespread of Larmor frequencies γΔB (2π)−1 > 3 kHz on the lengthscale of voxel (∼ 0.4 mm) resulted in total dephasing of thetransverse magnetization over the FLASH TE (2.5 ms). Signifi-cant signal loss can also be associated with the shifting of thegradient echo outside the acquisition window.The source of the geometric distortions is the “contamination”

of the applied frequency encoding gradient by “unaccounted for”background gradients. By design, frequency encoding is thedetection of transverse magnetization in the presence of aconstant and uniform MF gradient. Any arbitrary gradientsadded to this applied gradient will produce unwanted frequencyshifts in k space thus assigning spins to false locations and al-tering true values.Longitudinal slices through an io-FLASH MF map are shown

in Fig. 2B. In order to remove MF components not associatedwith the battery, the MF map of the holder with the emptybattery compartment was used as a reference image. The binarymask applied to this map was calculated from the referenceimage. It shows all voxels containing H2O (i.e., space inside theholder excluding the battery compartment).

Fig. 4. {x-z} and {y-z} slices through 3D io-SPRITE maps of two damaged iPhone-5 batteries: (A) 4 mm hole and leads removed; (B) 16 mm hole and the tophalf of the current collector removed. (H2O - containing regions; ROI [region of interest]: 53 × 90 mm2; NTP = 1; n = 64, Nint = 64 × 8).

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Phase data and local accuracy of the calculated MF field arecompromised the most in these domains with the strongest back-ground gradients. To further demonstrate the limited applicabilityof FLASH, Fig. 2C shows only voxels where the signal magnitudeis above 20% of the overall density image maximum. Although thelocal SNR could be improved by signal averaging (at the expenseof experiment time) the misregistration artifacts will remain. Theycan be mitigated to some degree by increasing the samplingbandwidth and frequency encoding gradient magnitude.SPRITE images illustrate the method’s robustness against dis-

tortions (Fig. 3A). With TP = 0.12 ms, a small T2* - weighting effectwas seen near the center. The MFmap, Fig. 3B, shows well-definedpatterns in the “difficult” regions. Note, io-SPRITE detected afrequency range almost 3 times larger than that of io-FLASH.The “8”-shaped feature near the center of FOV can be at-

tributed to slightly ferromagnetic material inside the cell. Upondisassembly, this material was found to be a part of a Ni-platedtab. The extent of the arrangement is shown in Fig. 3C. Aboveand below the tip of the metal strip, the perturbations approached±20 ppm. An MF variation of 40 ppm over a 5-mm distance isequivalent to an MF gradient of 75 mT m−1. Temporal evolutionsof the signal phase are illustrated for 2 representative locations (SIAppendix, Fig. S2).Fig. 4 shows the MF maps of 2 damaged iPhone-5 batteries.

Fig. 4A shows the effect of a 4-mm-diameter hole punched in thecenter of the lower half of the battery, as indicated on the right.The magnetic tab of this battery was cut and removed from thatlocation. An effect of a 16-mm-diameter hole is demonstrated inFig. 4B. The ferromagnetic metal strip was cut in half and theupper half was extracted. The image shows a striking MF patternassociated with the defect and the leads. Note that the 8-shapedMF pattern in Fig. 3B, observed near the center of the intactbattery disappeared. Instead, the high MF field “cloud” emergedat the tip of the remaining half of the metal strip. Similar pat-terns were seen for the 2 leads at the bottom.MF can be inhomogeneous at the macroscopic level (larger than

a voxel) or the microscopic (subvoxel) scale. In the latter case, smallstructures can be identified due to the partial volume effects evenwith relatively coarse resolution (1 mm) of SPRITE acquisition.Next, we demonstrate the sensitivity of the method to certain

defect features. Fig. 5 shows photographs of an intact PowerStream(PS) cell (A) and the same cell after introducing mechanical

damage (B), Note, the damage did not affect the battery voltage.The defect at the center of the battery was produced by impactswith a metal cylinder of 10-mm diameter. Three impacts were ap-plied to the same spot (0.79 cm2) with the energy of 1.2 J per impactand led to a highly visible imprint of a depth of ∼0.5 mm. A bulgewas formed on the opposite side of the battery. The cell voltage,however, was not affected by this damage.MF maps of the intact (Fig. 5C - FLASH, Fig. 5E - SPRITE)

and damaged (Fig. 5D - FLASH, Fig. 5F - SPRITE) PS cellsshowed noticeable differences. The position and orientation ofthe {x-z} slice with respect to the cell are indicated in Fig. 1C.The MF perturbation by the intact cell was symmetrical andapproached +25 ppm above and below (outside the FOV) thebattery. The damaged battery (Fig. 5 D and F) exhibited noticeableasymmetry of MF. These changes are consistent with simulations ofMF perturbations by “impressions” and “bulges” on the surface ofparamagnetic objects (13).MF perturbations observed by FLASH and SPRITE were

different in magnitude and morphology. According to theSPRITE measurements (Fig. 5 E and F), MF increased by up to6 ppm near the region of impact, while on the opposite side ofthe cell the field decreased by up to 2 ppm. Importantly, theFLASH MF values were found within a much narrower range offrequencies (from −4 to +8 ppm) as compared to the SPRITEdata (from −10 to +25 ppm). The maximum change in MFdetectable by FLASH was close to 1 ppm. FLASH images werealso affected by ripple-like misregistration artifacts seen nearthe battery.The discrepancy between io-SPRITE and io-FLASH measure-

ments is partially attributed to the different extent of T2*weighting, originating from a distribution of Larmor frequencieswithin the voxels. The most accurate MF measurement can beperformed by collecting phase data immediately after the RF ex-citation pulse. This is the major technical limitation for all con-ventional MRI methods employing long evolution times. The high-frequency components are effectively filtered out by long TEsin the FLASH method. In voxels exhibiting a linewidth of γΔB(2π)−1 >> 1/TE, the FLASH signal would be completely suppressed.Furthermore, once significant intravoxel averaging occurs, the fieldmap derived from the overall phase measurement ceases to be ac-curate even before the signals decay. In addition, the high frequen-cies are suppressed by echo shifting and assigned to wrong locations

Fig. 5. Photographs of (A) intact and (B) damaged PS batteries. {x-z} slices through io-FLASH (C and D) and io-SPRITE (E and F) maps. (H2O - containingregions; ROI [region of interest]: 41 × 41 mm2; TP range: 0.1–0.33 ms; NTP = 1; n = 37, Nint = 37 × 4).

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as a result of misregistration (32). By contrast, SPRITE suffersonly from a minimal T2* weighting since its MF sensitizing periodis much shorter (0.1 ms). Since SPRITE imaging is distortion-free,the main limitation for SPRITE-based ioMRI applications arisesfrom T2* times, short compared to TP. A sensitivity limit can beestablished as TP ∼ 5T2*. Assuming TP < 50 μs, the detectablerange of frequencies Δν1/2 = (πT2*)

−1 is ∼30 kHz, i.e., 75 ppm in9.4 T. A background gradient generating this linewidth over a 1-mmvoxel (700 mT m−1) is much greater than gradients produced bytypical MRI systems (20–100 mT m−1).A relationship between SOC and susceptibility provides a

mechanism of ioMRI contrast suitable for accurate battery di-agnostics. In order to remove MF components independent ofSOC, the fully charged iPhone-5 battery served as a referencesample. The reference MF map was subtracted from maps of thebattery at different SOC. The histograms of MF perturbationvariation (δΔB0) due to SOC are shown in Fig. 6. This experimentdemonstrates that despite the presence of large field distortions inthese cells, the subtler changes in SOC distributions can easily bedetected with the SPRITE approach.The cathode chemistry is responsible for the extent of the MF

variations with SOC. Charging the PS cell (500 mA h) resulted inup to a 4-ppm change in the MF (SI Appendix, Fig. S3). A strongereffect was attributed to the overall higher content of magnetic

elements, in particular Co. This consideration is in line withelectron-dispersive X-ray spectroscopy (EDX) analysis (SI Ap-pendix, Figs. S4 and S5).In summary, we demonstrated a distortion-free ioMRI battery

diagnostics method based on centric-scan SPRITE. Examples ofpractical relevance of the presented work are battery failures inpopular smart phones (e.g., Samsung Galaxy Note 7). The majorbenefit of SPRITE is the ability to accurately visualize the magneticfield around devices containing strongly magnetic components,common ingredients of the battery manufacturing process. In ad-dition to the superior image quality, a high temporal resolution canbe achieved, which is suitable for in situ battery characterizationand commercial quality control applications. The method is highlysensitive to mechanical defects and can distinguish fine changes inthe electrode’s chemical states and composition.

Materials and MethodsMaterials, MRI hardware and experiment parameters, software, imageprocessing, and EDX equipment are described in SI Appendix, Note S2.

ACKNOWLEDGMENTS. We acknowledge US National Science FoundationAward CBET 1804723 and Mercedes-Benz Research & Development NorthAmerica for funding.We acknowledgeMohaddeseMohammadi and TrinanjanaMandal for EDX microanalysis.

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