A Sensitive and Fast Fiber Bragg Grating-Based Investigation of the Biomechanical Dynamics of in Vitro Spinal Cord Injuries

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Communication A Sensitive and Fast Fiber Bragg Grating-Based Investigation of the Biomechanical Dynamics of In Vitro Spinal Cord Injuries

Satyendra Kumar Mishra 1,2, Jean-Marc Mac-Thiong 2, Éric Wagnac 1,2, Yvan Petit 1,2 and Bora Ung 1,*

1 École de Technologie Supérieure, 1100 Notre-Dame Street West, Montreal, QC H3C 1K3, Canada; [email protected] (S.K.M.); [email protected] (É.W.); [email protected] (Y.P.) 2 Hôpital du Sacré-Cœur de Montréal, 5400 Gouin Boul. West, Montreal, QC H4J 1C5, Canada; [email protected] * Correspondence: [email protected]

Abstract: To better understand the real-time biomechanics of soft tissues under sudden mechanical loads such as traumatic spinal cord injury (SCI), it is important to improve in vitro models. During a traumatic SCI, the spinal cord suffers high-velocity compression. The evaluation of spinal canal occlusion with a sensor is required in order to investigate the degree of spinal compression and the fast biomechanical processes involved. Unfortunately, available techniques suffer with drawbacks such as the inability to measure transverse compression and impractically large response times. In this work, an optical pressure sensing scheme based on a fiber Bragg grating and a narrow-band filter was designed to detect and demonstrate the transverse compression inside a spinal cord surrogate in real-time. The response time of the proposed scheme was 20 microseconds; a five orders of magnitude enhancement over comparable schemes that depend on costly and slower optical spectral analyzers. We further showed that this improvement in speed comes with a negligible loss Citation: Mishra, S.K.; Mac-Thiong, in sensitivity. This study is another step towards better understanding the complex biomechanics J.-M.; Wagnac, É.; Petit, Y.; Ung, B. A involved during a traumatic SCI, using a method capable of probing the related internal strains with Sensitive and Fast Fiber Bragg high-spatiotemporal resolution. Grating-Based Investigation of the Biomechanical Dynamics of In Vitro Keywords: fiber Bragg grating; spinal cord; strain; optical spectrum analyzer; photodiode Spinal Cord Injuries. Sensors 2021, 21, 1671. https://doi.org/10.3390/ s21051671 1. Introduction Academic Editor: Damien Kinet Characterization of spinal cord surrogates is important as it allows the study of internal

Received: 30 December 2020 strain sustained from spinal cord injuries. As a consequence, a quantitative description of Accepted: 23 February 2021 their material properties, time-dependent stress-strain characteristics, and mechanisms of Published: 1 March 2021 failure is a considerable undertaking. By measuring strain, we can quantify their elasticity and health, among others [1]. A number of techniques have already been proposed for the Publisher’s Note: MDPI stays neutral mechanical characterization, such as indentation probes [2], tension testers [3], compression with regard to jurisdictional claims in techniques or rotatory shear techniques [4,5], and optical backscatter reflectometry [6]. All published maps and institutional affil- these techniques have common drawbacks, such as their inability to measure low-strain iations. values and their slow response time. In the last few decades, fiber Bragg gratings (FBGs) have being used extensively as sensors for the investigation of various parameters, such as temperature, pressure, displacement, humidity, strain, radiation, etc. [7–17]. FBGs consist of a periodic structure

Copyright: © 2021 by the authors. fabricated along the core of an optical fiber. In this periodic structure, the coupling of Licensee MDPI, Basel, Switzerland. energy between different co-propagating and counter-propagating optical modes of the This article is an open access article fiber takes place. The mode-coupling phenomenon is a strong function of the excitation distributed under the terms and wavelength. For a FBG written in a single-mode fiber, two identical counter-propagating conditions of the Creative Commons modes are coupled, and the energy is transferred from the forward-traveling mode to the Attribution (CC BY) license (https:// backward-traveling mode. The FBG, therefore, reflects certain wavelengths, thus acting as creativecommons.org/licenses/by/ an optical bandpass filter [18]. 4.0/).

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For experimental spinal cord injuries (SCIs), the initial stage of spinal cord compression remains undetected with current sensing techniques, which prevents a comprehensive understanding of the spinal cord behavior under various loading conditions. Experimen- tal replication of SCIs in vitro most often involves weight-drop contusion models. The contusion injury model is believed to be the most clinically relevant model of human SCIs [19]. Unfortunately, there is no method available for directly measuring the real-time biomechanics of contusion and mechanical behavior of the spinal cord [20]. This limitation strongly hinders our capability to study the relationships between the extent of the impact on the spinal cord, spinal cord loads/deformations, and functional outcomes. Several studies have reported technologies capable of recording the spinal canal occlusion by providing indirect measurements of spinal cord compression. For example, a water-filled flexible polymer tubing simulating the spinal cord was inserted into the spinal canal for in vitro fracture replication [21,22]. A physical surrogate of the human spinal cord was also developed using silicone rubber that can be made radio-opaque. The same radio-opaque physical surrogate was used to simulate spinal canal occlusion with the help of a high-speed fluoroscope [23,24]. Unfortunately, these techniques are not able to provide any information about the measurement of internal forces and strains sustained by the spinal cord during the trauma. Lucas et al. [25] proposed an imaging technique based on the fluoroscopic tracking of radio-opaque beads placed on the surface and within the spinal cord. However, fluoroscopic techniques are limited to a single plane of view (only in 2D), and visualization of the spinal cord is limited by the apparatus used to produce the SCI. Bhatnagar et al. [26] utilized MRI to quantify the internal deformation of the spinal cord, but this method cannot be used for the real-time assessment of impacts. The placement of the transducers on the spinal cord was restricted, and the long response time of the procedure precluded other methods of measurements [27]. Recently, we exploited the optical fiber bend loss method to evaluate the compression of a physical spinal cord surrogate based on light intensity modulation [28]. However, the latter method could not provide a precise localization of strain along the fiber (i.e., poor spatial resolution) and had a response limited to spinal cord compression rates larger than 40%. In this work, we demonstrate an optical pressure-sensing scheme based on FBG technology that provides a highly sensitive strain measurement with cm-scale axial resolution and fast response (on µs scale) inside a surrogate spinal cord that is relevant to real-time in vitro studies of traumatic SCIs.

2. Model and Theory 2.1. Physical Spinal Cord Surrogate The spinal cord surrogate was made of silicone elastomer foam (FlexFoam-iT III, Smooth-on, Macungie, PA, USA) and made by pouring the liquid primer form into a 3D- printed casting mold [29]. The dried foam acquired an ellipsoidal shape and the dimensions of 20 cm length, 11 mm major diameter, and 9 mm inner diameter (Figure1) that mimic the human thoracic spinal cord transverse section. During the casting and curing of the silicone spinal cord surrogate, a 0.6 mm diameter nylon wire ran longitudinally through the surrogate. After curing, this wire was pulled out and replaced by the optical ﬁber inscribed with an FBG. Figure1b depicts the transverse view of the mechanical and optical setup. Sensors 2021, 21, 1671 3 of 9 Sensors 2021, 21, x FOR PEER REVIEW 3 of 9

(a) (b)

Figure 1. ((aa)) Schematic Schematic representation representation of of the the long longitudinalitudinal mid-cross-section mid-cross-section of of the the instrumented instrumented spinal spinal cord cord surrogate surrogate with with thethe integrated integrated fiber ﬁber Bragg grating (FBG) sensor. (b) Transverse viewview ofof thethe mechanicalmechanical andand opticaloptical setup.setup.

2.2.2.2. FBG FBG Fiber Fiber Sensor Sensor Theory Theory AA silica-based silica-based 125 125 micron micron diameter diameter opti opticalcal FBG FBG pressure pressure sensor sensor (Technica (Technica LLC, LLC, Charleston,Charleston, SC, SC, USA) USA) retains retains the the intrinsic intrinsic prop propertieserties of ofBragg Bragg gratings gratings while while offering offering the smallthe small size sizeand andmechanical mechanical compliance compliance for insertion for insertion into a into spinal a spinal cord cordsurrogate. surrogate. The pro- The curedprocured FBG FBG was waswritten written in a inGe-doped a Ge-doped single-mode single-mode fiber fiber at a length at a length of about of about 3.5 mm 3.5 mmand exhibitedand exhibited 90% peak 90% reflectivity peak reflectivity at the 1550 at the nm 1550 center nm wavelength. center wavelength. The silica The glass silica cladding glass iscladding coated with is coated a polyimide with a polyimide polymer to polymer protect to it protectagainstit humidity against humidity and scratches and scratches that can leadthat canto crack lead formation to crack formation and impairments and impairments to the fiber’s to the mechanical fiber’s mechanical stability. stability. TheThe sensing sensing principle principle of of the FBG is based on the BraggBragg reflection.reflection. The change in wavelengthwavelength is causedcaused byby the the axial axial strain strain change change∆ εΔ𝜀and and the the temperature temperature variation variation∆T. TheΔ𝑇. Therelation relation between between temperature, temperature, wavelength, wavelength, and and strain strain is written is written as [25 as] [25] 𝛥𝜆 ∆λ = (1− 𝑝 )𝛥𝜀 + (𝜅 + 𝜉) 𝛥𝑇 (1) 𝜆= (1 − p )∆ε + (κ + ξ) ∆T (1) λ e where λ is the initial center wavelength of the FBG, 𝛥𝜆 is the shift in the Bragg wave- where λ is the initial center wavelength of the FBG, ∆λ is the shift in the Bragg wavelength, length, pe, κ, and ξ are the effective photo-elastic coefficient (for silica 4.22 × 10−13 (d/cm2)−1), × −13 2 −1 thepe, κthermal, and ξ are expansion the effective coefficient photo-elastic (8.52 ×coefficient 10−6·K−1 at(for room silica temperature), 4.22 10 and(d/cm the thermo-) ), the × −6· −1 opticthermal coefficient expansion (1.090 coefficient × 10−5/°C), (8.52 respectively,10 K atof room fused-silica temperature), fiber. The and strain the thermo-optic inside the coefficient (1.090 × 10−5/◦C), respectively, of fused-silica fiber. The strain inside the FBG is FBG is defined as defined as ∆𝛥L 𝐿 ∆ε𝛥𝜀= = (2)(2) L𝐿 ∆ L wherewhere L isis the the longitudinal longitudinal strain strain applied applied on on the the FBG FBG of of length length “ “LL”.”. Note Note that that in most cases of practical interest, the FBG is subjected to strains for which ε = ε , where these cases of practical interest, the FBG is subjected to strains for which εεx = y, where these strains are in x and y directions. It is also assumed that a standard Poissonx relationy relates strainsthe transverse are in x strainsand y directions. to the longitudinal It is also as strain,sumed i.e., thatε =a standardε = −νε Poisson[30]. relation relates εεx ==−y νεz the transverseIf in Equation strains (1) to wethe considerlongitudinal∆T strain,= 0 (constant i.e., x temperature),yz [30]. then the equation simplifiesIf in Equation to (1) we consider ΔT = 0 (constant temperature), then the equation sim- ∆λ plifies to = (1 − p )∆ε. (3) λ e 𝛥𝜆 Note that the photo-elastic coefficient= of(1−𝑝 the fiber)𝛥𝜀. core (p ) can be expressed as (3) 𝜆 e 2 Note that the photo-elastic coefficientne f f of the fiber core (pe) can be expressed as p = [p − v(p + p )] e 12 11 12 (4) 𝑛2 𝑝 = [𝑝 −𝑣(𝑝 +𝑝 )] (4) 2

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where p11 and p12 denote the photo-elastic tensor components (typical values for fused silica: p11 = 0.113 and p12 = 0.252), v is Poisson’s ratio (typically for fused silica: v = 0.17), and where p11 and p12 denote the photo-elastic tensor components (typical values for fused silica: neff is the effective index of the core-guided optical mode. Typical values of the coefficients p11 = 0.113 and p12 = 0.252), v is Poisson’s ratio (typically for fused silica: v = 0.17), and neff inis thesilica-core effective optical index fibers of the yield core-guided pe = 0.21, opticalresulting mode. in a strain Typical sensitivity values of ( theΔλB coefficients/ε)~1.2 pm/με in and strain limits of +/− 2500 με. silica-core optical fibers yield pe = 0.21, resulting in a strain sensitivity (∆λB/ε)~1.2 pm/µε and strain limits of +/− 2500 µε. 3. Results 3.1.3. Results Characterization of FBG Sensor with OSA 3.1. CharacterizationFirst, optical characterization of FBG Sensor withof the OSA FBG sensor was performed using an optical spec- trumFirst, analyzer optical (OSA). characterization A schematic diagram of the FBG of the sensor setup was is shown performed in Figure using 2. We an opticalused a broadbandspectrum analyzer near-infrared (OSA). source A schematic (EDFA, 1520–15 diagram60 of nm), the optical setup iscirculator, shown in FBG, Figure and2 .OSA. We Weused connected a broadband the FBG near-infrared sensor to the source laser (EDFA, source 1520–1560 through the nm), circulator, optical circulator,while the other FBG, armand OSA.of the Wecirculator connected was the connected FBG sensor to the to theOSA laser for sourcedetection. through The broadband the circulator, light while was coupledthe other to arm the ofFBG the fiber circulator sensor was via connected the optica tol circulator, the OSA forwhich detection. also collects The broadband the back- reflectedlight was signal coupled from to thethe FBG sensor fiber that sensor is then via themeasured optical by circulator, the OSA. which Stretching also collects the fiber the causesback-reflected a minute signal change from in the the sensor grating that period is then that measured shifts the by center the OSA. Bragg Stretching wavelength the fiber in thecauses reflection a minute spectrum. change Therefore, in the grating before period recording that shifts any data, the center we fixed Bragg the wavelength instrumented in spinalthe reflection cord (with spectrum. the FBG Therefore, sensor) beforewith glue recording on a glass any data,slide. weThe fixed weight the instrumentedpressure was appliedspinal cord in the (with normal the FBGdirection sensor) in the with middle glue on of athe glass spinal slide. cord The for weight 4 min pressureand then wasthe measurementapplied in the was normal recorded. direction Next, in thewe changed middle of the the weight spinal (3.34, cord for7.97, 4 min9.78, andand then24.98 the g) andmeasurement recorded the was data. recorded. The diameter Next, we of changed the different the weight weights (3.34, applied 7.97,9.78, was andkept 24.98 constant g) and at 1recorded cm. Without the data. applying The diameter any weight, of the the different full-width weights half-maximum applied was kept(FWHM) constant bandwidth at 1 cm. wasWithout calculated applying from any the weight, recorded the reflectanc full-widthe spectrum half-maximum as 0.56 (FWHM) nm, and bandwidththe peak wave- was lengthcalculated was from1549.88 the nm. recorded reflectance spectrum as 0.56 nm, and the peak wavelength was 1549.88 nm.

Figure 2. Experimental setup for the characterization of the fiber Bragg grating FBG sensor. Figure 2. Experimental setup for the characterization of the fiber Bragg grating FBG sensor. Figure3 depicts the reflectivity curve for different weight loads over the spinal cord attached with the FBG. We observed that as we increased the weight over the spinal cord, Figure 3 depicts the reflectivity curve for different weight loads over the spinal cord the reflectivity spectrum redshifted (Figure3), as expected from theory and owing to attached with the FBG. We observed that as we increased the weight over the spinal cord, strain-induced local modification in the grating period of the FBG. From the results, it is theclear reflectivity that as we spectrum increased redshifted the pressure, (Figure the resonance 3), as expected wavelength from redshiftedtheory and(Figure owing4 a)to, strain-inducedwith a corresponding local modification change in thein the local grating strain period (as calculated of the FBG. with From Equation the results, (3)), andit is clearexhibited that as a 7% we relativeincreased error the in pressure, the linear the curve resonance fit displayed wavelength in the redshifted plot. Since (Figure the optical 4a), withbandwidth a corresponding was relatively change large in (0.56 the local nm), strain it limited (as calculated the accuracy with in determiningEquation (3)), the and value ex- hibitedof the wavelength a 7% relative corresponding error in the linear to the curv peake power.fit displayed Figure in4b the shows plot. the Since change the optical in the bandwidthlocal strain was with relatively respect to large the shift (0.56 in nm), the resonanceit limited the wavelength. accuracy in determining the value of the wavelength corresponding to the peak power. Figure 4b shows the change in the local strain with respect to the shift in the resonance wavelength.

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Figure 3. Reflection spectra (normalized with input power) of the sensor for different transverse FigureFigure 3. 3. ReflectionReﬂection spectra spectra (normalized (normalized with with input input powe power)r) of the of thesensor sensor for fordifferent different transverse transverse pressures on the spinal cord surrogate using the optical spectrum analyzer. pressurespressures on on the the spinal spinal cord cord surrogate surrogate using using the the optical optical spectrum spectrum analyzer. analyzer.

((aa)) ((bb)) Figure 4. (a) Variation of peak wavelength and strain with respect to applied pressure. (b) Sensor relationship between FigureFigure 4. 4. ((aa)) Variation Variation of peak wavelengthwavelength andand strainstrain with with respect respect to to applied applied pressure. pressure. (b ()b Sensor) Sensor relationship relationship between between the the strain as a function of the peak wavelength shift. thestrain strain as aas function a function of theof the peak peak wavelength wavelength shift. shift. 3.2. Calibration of Compression Sensing Capability of Spinal Cord 3.2.3.2. Calibration Calibration of of Compression Compression Se Sensingnsing Capability Capability of of Spinal Spinal Cord Cord FigureFigure 55 depictsdepicts thethe setupsetup usedused forfor evaluatievaluatingng thethe compressioncompression sensingsensing capabilitiescapabilities of theFigure proposed5 depicts sensing the scheme, setup used where for we evaluating can see the the cylindrical compression steel sensing impactor capabilities that was ofof the the proposed proposed sensing sensing scheme, scheme, where where we we can can see see the the cylindrical cylindrical steel steel impactor impactor that that was was usedused to to compress compress the the spinal spinal cord cord surrogate, surrogate, mounted mounted on on a a three three axis-stage axis-stage with with microm- microm- eterused positioners. to compress In the Figure spinal 6, cord we surrogate,plotted the mounted change in on the a three optical axis-stage power withas a micrometerfunction of eterpositioners. positioners. In In Figure Figure6, we6, we plotted plotted the the change change in in the the optical optical power power asas aa functionfunction of transversetransverse compressioncompression appliedapplied toto thethe spinalspinal cordcord surrogate.surrogate. OpticalOptical powerpower waswas calcu-calcu- latedtransverse as a percentage compression of appliedits initial to value, the spinal measured cord surrogate. at the beginning Optical powerof the first was load calculated cycle latedas a percentageas a percentage of its of initial its initial value, value, measured measured at the at beginning the beginning of the of first the loadfirst cycleload cycle (with (with no load applied). The procedure was performed five times in order to ensure repeat- (withno load no load applied). applied). The procedureThe procedure was performedwas performed five timesfive times in order in order to ensure to ensure repeatability. repeatability. In Figure 6, we plotted the microstrain induced by the transverse compression (as ability.In Figure In 6Figure, we plotted 6, we plotted the microstrain the microstr inducedain induced by the transverse by the transverse compression compression (as deduced (as deduced from the optical power change) and observed, as expected, an increase in the deducedfrom the from optical the power optical change) power andchange) observed, and observed, as expected, as expected, an increase an inincrease the measured in the measured strain with the compression rate. Notably, it was shown that even though the measuredstrain with strain the compressionwith the compression rate. Notably, rate. it Notably, was shown it was that shown even though that even the though FBG sensor the FBG sensor was buried 1 mm below the surface of the spinal cord surrogate, the optical FBGwas sensor buried was 1 mm buried below 1 the mm surface below of the the surface spinal cordof the surrogate, spinal cord the opticalsurrogate, sensing the optical scheme sensing scheme exhibited a quasi-immediate response to compression rates over 0%. On sensingexhibited scheme a quasi-immediate exhibited a quasi-immediate response to compression response to rates compression over 0%. Onrates further over increase0%. On further increase of the transverse loading, the sensor showed a good response, and in par- furtherof the transverseincrease of the loading, transverse the sensor loading, showed the sensor a good showed response, a good and response, in particular, and in inside particular, inside the range of 20–60% compression, a quasi-linear relationship was observed ticular,the range inside of 20–60%the range compression, of 20–60% compression, a quasi-linear a relationshipquasi-linear relationship was observed was between observed the between the measured microstrains with respect to the applied transverse compression. betweenmeasured the microstrains measured microstrains with respect towith the appliedrespect to transverse the applied compression. transverse We compression. note that the WeWelatter notenote results thatthat the representthe latterlatter results aresults significant representrepresent improvement aa sisignificantgnificant in the improvementimprovement detection limit inin thethe over detectiondetection the previous limitlimit overovermethod the the previous employingprevious method method fiber bend employing employing losses [29 fiber fiber], where bend bend a losses losses minimum [29], [29], 40%where where compression a a minimum minimum was 40% 40% required com- com- pressionpressionfor the onset was was required ofrequired the optical for for the the sensor onset onset response. of of the the optical optical sensor sensor response. response.

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Figure 5. 5. InstrumentedInstrumented spinal spinal cord cord surrogate surrogate under under testing. testing. Figure 5. Instrumented spinal cord surrogate under testing. Figure 5. Instrumented spinal cord surrogate under testing.

Figure 6. Relative power loss and microstrain plotted as a function of spinal cord transverse com- pressionFigure 6. 6. forRelativeRelative static loading.power power loss loss and andmicrostrain microstrain plotted plotted as a function as a function of spinalof cord spinal transverse cord transversecom- com- pressionFigure 6. for Relative static loading.power loss and microstrain plotted as a function of spinal cord transverse com- pressionpression for static static loading. loading. 3.3. Fast Transverse Compression Measurement Using a Narrow-Band-Pass Filter and Power 3.3. Fast Transverse Compression Measurement Using a Narrow-Band-Pass Filter and Power 3.3.Meter3.3. Fast Transverse Transverse Compression Compression Measurement Measurement Using Using a Narrow-Band-Pass a Narrow-Band-Pass Filter and Filter Power and PowerMeter Meter MeterFurther, we interfaced the circulator with a power meter via a narrow-band-pass filter thatFurther,Further, reduced we we interfacedthe interfaced bandwidth the the circulator of circulator the reflection with with a power spectrum, a power meter meterand via thereforea vianarrow-band-pass a narrow-band-pass allowed for fil- a filter ter thatFurther, reduced we theinterfaced bandwidth the circulator of the reflection with a power spectrum, meter and via thereforea narrow-band-pass allowed for fil- a thatmoreter that reduced accurate reduced themeasurement the bandwidth bandwidth of ofthe of the wavelengththe reflection reflection shift spectrum,spectrum, 𝛥𝜆. The andand FWHM therefore therefore of the allowed allowedensuing for re- for a a more more accurate measurement of the wavelength shift 𝛥𝜆. The FWHM of the ensuing re- accurateflectionmore accurate spectrum measurement measurement was measured of the of the wavelength at wavelength0.11 nm (i shift.e., shift one-fifth∆ λ𝛥𝜆.. The The of FWHM FWHMthe previously of the ensuing ensuingunfiltered re- reflection flection spectrum was measured at 0.11 nm (i.e., one-fifth of the previously unfiltered spectrumspectra). Figure was 7 measured shows the schematic at 0.11 nm diagram (i.e., one-fifth of the modified of the setup previously where, notably, unfiltered we spectra). spectra).flection spectrumFigure 7 shows was measured the schematic at 0.11 diagram nm (i .e.,of the one-fifth modified of thesetup previously where, notably, unfiltered we replacedspectra). theFigure OSA 7 withshows a powerthe schematic meter. diagram of the modified setup where, notably, we Figurereplaced7 showsthe OSA the with schematic a power meter. diagram of the modified setup where, notably, we replaced thereplaced OSA the with OSA a power with a meter.power meter.

Figure 7. Experimental setup of the strain FBG sensor based on a ﬁxed narrow-band optical ﬁlter

and a fast photodiode (i.e., power meter). Sensors 2021, 21, x FOR PEER REVIEW 7 of 9

Sensors 2021, 21, 1671 7 of 9 Figure 7. Experimental setup of the strain FBG sensor based on a fixed narrow-band optical filter and a fast photodiode (i.e., power meter).

AsAs is is well well known, known, the the response response time time of ofa typical a typical OSA OSA is slow is slow (around (around 2 s). 2 In s). order In order to recordto record fast fast events events such such as asa SCI, a SCI, we we replaced replaced the the OSA OSA with with a afast fast Si Si photodiode-based photodiode-based opticaloptical power power meter meter connected connected to to a adigital digital inte interfacerface for for data data acquisition acquisition with with a a response response timetime of of 20 20 μµs.s. The The response response time time thereby thereby improved improved by by five five orders orders of of magnitude magnitude compared compared toto the the conventional conventional OSA-based OSA-based method. method. FigureFigure 8a8a shows the variationvariation ofof powerpower with with respect respect to to the the applied applied pressure pressure as as well well as asthe the linear linear curve curve fit fit that that exhibited exhibited a 3%a 3% relative relative error. error. As As indicated indicated previously, previously, the the applied appliedpressure pressure induces induces transverse transverse compression compression in the in FBGthe FBG section, section, which which in turn in turn redshifts redshifts the thecenter center wavelength wavelength of the of reflectionthe reflection spectrum. spectrum. As the As reflection the reflection spectrum spectrum passes throughpasses throughthe narrow-band the narrow-band filter, the filter, decrease the decrease in peak in intensity peak intensity directly directly depends depends on the appliedon the appliedpressure, pressure, as shown as shown on Figure on 8Figurea. A transverse 8a. A transverse compression compression variation variation curve, curve, when when fitted fittedlinearly, linearly, shows shows a relative a relative error oferror 8.9%. of Since8.9%. theSince change the change in Bragg in wavelengthBragg wavelength is directly is directlyproportional proportional to the change to the change in strain in (transversestrain (transverse compression), compression), we can we thus can calculate thus calcu- the latetransverse the transverse compression compression of the FBG of the fiber FBG (assuming fiber (assuming a constant a co temperature).nstant temperature).

(a) (b)

FigureFigure 8. 8. (a(a) )Variation Variation of of power power loss loss and and transverse transverse compression compression with with respect respect to to applied applied pressure. pressure. (b (b) )Sensor Sensor relationship relationship betweenbetween the the transverse transverse compression compression as as a a function function of of the the relative relative power power loss. loss.

FigureFigure 8b8b shows thethe variationvariation of of the the transverse transverse compression compression sustained sustained by by the the surrogate surro- gatespinal spinal cord cord with with respect respect to to changes changes in in optical optical power power lossloss thatthat indicates a a quasi-linear quasi-linear relation.relation. The The latter latter curve curve allows allows us us to to define deﬁne and and evaluate evaluate the the sensor’s sensor’s sensitivity sensitivity in in terms terms ofof transverse transverse compression compression as as a a function function of of re relativelative power power loss, loss, at at 10.3% 10.3% (which (which in in decibel decibel unitsunits translates translates into into 0.9% 0.9% transverse transverse compre compression/dBssion/dB optical optical power power loss), loss), a a fairly fairly sensitive sensitive valuevalue to to be be expected expected for for FBG-based FBG-based strain strain sensors. sensors.

4.4. Discussion Discussion ConsideringConsidering that that during during a a SCI SCI involving involving a a burst-type burst-type fracture, fracture, bone bone fragments fragments can can be be propelledpropelled through through the the spinal spinal cord cord at at speeds speeds of of 4.5 4.5 m/s m/s [31], [31], the the injury injury timescale timescale is is around around 22 ms. ms. In In this this paper, paper, we we proposed proposed and and demonstrated demonstrated a a fiber fiber optic optic FBG FBG strain strain sensor sensor with with a a fastfast response response time time of of around around 20 20 μµs, thus allowingallowing thethe fullfull andand accurateaccurate temporal temporal investiga- investi- gationtion of of strain strain dynamics dynamics occurring occurring in in a a spinal spinal cord cord surrogate surrogate for for the thein in vitro vitroreplication replication of ofSCIs. SCIs. All All the the while, while, the the proposed proposed scheme scheme maintains maintains the the compact compact size, size, unobtrusiveness, unobtrusiveness, and andmechanical mechanical compliance compliance that that are hallmarkare hallmark features features of optical of optical fiber fiber sensors. sensors. The proposedThe pro- posedmethod method moves moves away away from from the slowthe slow and and costly costly OSA, OSA, traditionally traditionally used used for for performing perform- spectral measurements of the FBG sensor response; instead, this method uses a static and ing spectral measurements of the FBG sensor response; instead, this method uses a static cost-effective narrow-band filter to obtain power loss measurements that are correlated to and cost-effective narrow-band filter to obtain power loss measurements that are corre- the spectral shift in the FBG’s peak reflectivity (and ultimately the internal strain values). lated to the spectral shift in the FBG’s peak reflectivity (and ultimately the internal strain The latter method’s speed enhancement of over five orders magnitude, gained by replacing spectral interrogation with power measurements, was obtained with a small loss in sensor accuracy in the process. We note that the latter accuracies can be further improved by

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adding more sample measurements in the calibration curves. Owing to the high sensitivity of the FBG-based optical sensor and the fast (microsecond scale) response of the proposed power sensing scheme, we believe that this method provides a new tool to further investigate the real-time strain and compression dynamics that occur during SCI events, using artiﬁcial or cadaveric spinal cord samples instrumented with the FBG optical ﬁber sensors.

Author Contributions: Conceptualization and methodology of the experiment was performed by S.K.M., J.-M.M.-T., É.W., Y.P., and B.U. Experimental demonstration and data acquisition was done by S.K.M. The original draft was written by S.K.M. and B.U. All authors participated in data analysis, writing—review and editing. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Fonds de recherche du Québec–Santé (FRQS), by the Medtronic research Chair in spinal trauma at Université de Montréal, and the Natural Sciences and Engineering Research Council of Canada (NSERC). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: This study does not report any additional public data. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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