Computational modeling and simulation are commonly used during the development of cardiovas- cular implants to predict peak strains and strain amplitudes and to estimate the associated durability and fatigue life of these devices. However, simulation validation has historically relied on comparison with surrogate quantities like force and displacement due to barriers to direct strain measurement–most notably, the small spatial scale of these devices. We demonstrate the use of microscale two-dimensional digital image correlation (2D-DIC) to directly characterize full-ﬁeld surface strains on a nitinol device coupon under emulated physiological loading. Experiments are performed using a digital optical mi- croscope and a custom, temperature-controlled load frame. Following applicable recommendations from the International DIC Society, hardware and environmental heating studies, noise ﬂoor analyses, and in- and out-of-plane rigid body translation studies are ﬁrst performed to characterize the microscale DIC setup. Uniaxial tension experiments are also performed using a polymeric test specimen up to nominal stains of 5%. Sub-millimeter ﬁelds of view and sub-micron displacement accuracies (9 nm mean error) are achieved, and systematic (mean) and random (standard deviation) errors in strain are each esti- mated to be approximately 1,000 µ/epsilon1. The system is then demonstrated by acquiring measurements at the root of a 300 µm-wide nitinol device strut undergoing ﬁxed-free cantilever bending motion. Lüders- like transformation bands are observed originating from the tensile side of the strut that spread toward the neutral axis at an angle of approximately 55 °. Optical microscale 2D-DIC setups like that demon- strated herein will be useful in future studies for characterizing cardiovascular implant micromechanics, validating computational models, and guiding the development of next-generation material models for simulating superelastic nitinol. Keywords: Digital image correlation, Nitinol, Strain localization, Medical devices 1 1 Introduction Digital image correlation (DIC) has been described as “the most important advance in experimental me- chanics since the strain gage” [1]. The method is a non-contact approach for extracting displacement and strain measurements from a sequence of digital images by correlating grayscale pixel intensities [2–5]. Build- ing on advancements in computer vision and optical ﬂow, the method was developed for the study of solid mechanics in the early 1980s at the University of South Carolina [6–8]. Although initially limited to two- dimensional (2D) planar measurements of surface deformations at relatively large length scales, researchers have since extended the technique to the measurement of curved surfaces (stereo-DIC [9]), internal deforma- tions (volumetric DIC [10]), and micro- or even nano-scale mechanics using optical [11–17], scanning tunnel [18], scanning electron [19–23], and atomic force [24] microscopy. In brief, a standard subset-based 2D-DIC approach requires digital images with spatially varying grayscale intensity, ideally a non-repeating pattern of bright and dark patches referred to as a “speckle pattern”. The reference image is discretized into a col- lection of “subsets”, and possible subset deformations are described mathematically by a chosen set of shape functions. An optimization problem is then constructed to maximize the correlation in grayscale intensity values between subsets from the reference image and pixels in the deformed image, and displacement vectors are extracted. By using appropriate interpolation schemes, sub-pixel accuracies are routinely achieved [2]. Given its ability to characterize full-ﬁeld displacements and strains, DIC is attractive as a tool for validating computational solid mechanics models. Although strain gauges are also commonly used for this purpose, strain gauges require a direct bond to the surface of a specimen and therefore have the potential to inﬂuence measurements, whereas DIC is nominally a non-contact approach. Full-ﬁeld DIC measurements also overcome the inherent spatial averaging associated with strain gauges and thereby mitigate the loss of ﬁne-scale deformation details. Indeed, DIC has been used previously for validating ﬁnite element (FE) biomechanics models of femoral [25], hemipelvic [26], craniofacial [27], and dental [28] implants as well as replica [29] and cadaveric [30, 31] femurs. Digital image correlation has also been used to investigate the mechanics of polycrystalline nickel titanium (nitinol) starting in the mid 2000s [32, 33], with interest rapidly increasing since that time (e.g., [34–46]; Figure 1). However, direct strain measurement on ﬁnished nitinol cardiovascular devices using either strain gauges or full-ﬁeld DIC has been impractical to date due to limitations of scale, with typical strut cross-sectional dimensions measuring only a few hundred microns as illustrated in Figure 2. Small scale DIC measurements have been performed on raw nitinol materials like plates and wires using scanning electron microscopy [48, 49], but such investigations require advanced setups. Because of the diﬃculty in acquiring direct strain measurements on implantable cardiovascular devices,computationalmodelsusedforpredictingdevicedurabilityoftenrelyonsurrogateforce-displacement experiments for validation. However, If computational predictions of strain are to be used to inform a high- risk decision, validating against such surrogate measurements may be inadequate [50, 51]. Direct strain measurements are thus needed to enable more rigorous validation of computational models used to support the durability assessment of cardiovascular devices and to create opportunities for novel and higher-risk uses of evidence generated through computational modeling. Figure 1: Google Scholar search results for keywords “nitinol” and “digital image correlation” versus time (generated using the Pythonscript by V. Strobel [47]). Interest has grown rapidly since the early studies of Daly et al. [33] and Murasawa et al. [32] in 2007. 2 Figure 2: Spatial scales relevant to implantable cardiovascular devices. The smallest strain gauges currently manufactured are millimeter-scale, whereas parameters of interest for fatigue assessment (e.g., peak strains and strain amplitudes) occur on spatial scales on the order of microns or smaller. In this study, we overcome the following primary challenges to the application of microscale DIC to the characterization of nitinol cardiovascular device mechanics: 1.setup complexity: Images are acquired using a standard digital optical microscope, and speckle patterns are applied using ﬁnely ground carbon powder. Speckling requires little preparation and can be repeated by simply brushing away the adhered powder and applying a new surface coating 2.need for temperature control : As temperature control is critical for characterizing nitinol device mechanics, experiments are performed using acustom, temperature-controlled air environmental cham- ber designed to accommodate the small working distances typically required for high-magniﬁcation optical microscopy. 3.limited depth of ﬁeld : An articulating base is used to carefully align specimens so that regions of interest are approximately perpendicular to the optical axis of the microscope objective during experiments. Measurements are acquired on laser-cut surfaces of the device that are made planar by high-quality electropolishing. Using this setup, we then verify our DIC method by following relevant recommendations from the Interna- tional DIC Society’s recent publication “A Good Practices Guide for Digital Image Correlation” [52] and from previous 2D-DIC work [53]. Veriﬁcation tests include camera and hardware heating studies, displace- ment and strain noise ﬂoor characterization, in-plane and out-of-plane rigid body translation studies, and uniaxial tension experiments. Finally, we demonstrate the method on a nitinol cardiovascular device coupon specimen with a strut width of approximately 300 µm. 2 Materials and Methods 2.1 Experimental setup Experiments are performed on a vibration isolation table (Benchmate 2200 series, Kinetic Systems) using a digital optical microscope (KH770, HIROX) and a custom temperature-controlled load frame (Figure 3a). An articulating base (AP-180, Thorlabs) is also used in some experiments (Figure 3a). The microscope is conﬁgured for reﬂected bright-ﬁeld illumination (coaxial) provided by a halogen light source. Digital images arecapturedbyatwomegapixelcharge-coupleddevice(CCD)sensorandarestoredas8-bitlosslessgrayscale 3 1 5 286 910a b 4 3 11 y x7z xFigure 3: a) Microscope and miniature temperature-controlled load frame used in the microscale 2D-DIC experiments. b) Enlarged view of the miniature load frame. 1: far-ﬁeld digital optical microscope, 2: miniature load frame, 3: articulating base, 4: vibration isolation table, 5: chamber cover plate, 6: heated breadboard, 7:precisiondigitalmicrometerwithnon-rotatingspindle, 8:miniatureloadcell, 9:thermistors for temperature control and monitoring, 10: fan used to circulate air in the chamber, 11: angle bracket, clamp, and nitinol device coupon specimen. TIFF ﬁles. Magniﬁcation is provided by an MXG-2500 REZ triple objective turret with a working distance of 10 mm. For all images considered here, the high-range lens is used at a medium zoom level corresponding to 500× magniﬁcation, yielding an eﬀective image spatial resolution of 0.37 µm/pixel. The miniature load frame (Figure 3b) consists of a temperature-controlled breadboard (PTC1, Thorlabs), a high-precision linear actuator with a non-rotating spindle (M-230.25, Physik Instrumente), a 200-gram load cell (LSB200, Futek), two thermistors (TSP-TH, Thorlabs, Inc.), a 12 VDC brushless fan, 3/8 inch thick acrylic sidewalls topped with adhesive foam padding, and a 1/16 inch thick acrylic chamber cover plate (Figure 3b). A 1.25 inch diameter hole through the chamber cover allows for passage of the objective into the heated air chamber (Figure 3a), thus facilitating image capture at the short working distances typically required for high-magniﬁcation microscopy. Temperature control is provided by a proportional–integral–derivative (PID) controller through software provided by Thorlabs, with the thermistor in contact with the specimen driving the control loop. When performing temperature-controlled experiments, the fan is powered on and used to mix the air throughout the air chamber to minimize temperature gradients. Spatial temperature gradients are also monitored by comparing the temperature diﬀerence between the primary and secondary thermistors (Figure 3b,9). Three specimens are used in the 2D-DIC veriﬁcation and demonstration experiments (Figure 4). Camera heating eﬀects, noise ﬂoor estimation, and in- and out-of-plane rigid body translation errors are characterized using a ﬂat, 1 cm ×1 cm×500 µm electropolished nitinol strip adhered to an aluminum right angle bracket using cyanoacrylate (Figure 4a). A hole in the angle bracket allows for the specimen to be mounted directly to the spindle of the digital actuator. Because nitinol cannot be easily subjected to uniform strain beyond 1% due to material instability and localization phenomena, strain error quantiﬁcation experiments are instead performed using a polymeric strip of Tygon tubing laminated between acrylic end pieces (Figure 4b). The specimen is thin to reduce out-of-plane motion generated by Poisson contraction in the through-plane axis during extension (e.g., as noted in [13]), thus reducing the need for refocusing during experiments. Demon- stration experiments are performed using a nitinol coupon specimen representing a single strut of a generic nitinol inferior vena cava (IVC) ﬁlter designed by the authors. The coupon specimen was manufactured at Conﬂuent Medical Technologies (Fremont, CA) by laser cutting the geometry from 2.032 mm diameter SE508 (50.8% nickel) nitinol tubing, shape setting the strut proﬁle, and electropolishing the surface. Based on diﬀerential scanning calorimetry (DSC) measurements [54], the ﬁnished coupons have a martensite rever- 4 a b c Figure 4: Specimens used in the microscale 2D-DIC veriﬁcation and demonstration experiments. a) Elec- tropolished nitinol strip adhered to an aluminum right-angle bracket for noise ﬂoor characterization and rigid body motion veriﬁcation experiments. b) Polymer band specimen laminated between acrylic sheets at the ends for strain veriﬁcation experiments under approximately uniform uniaxial tension. c) Nitinol coupon specimen representative of a generic IVC ﬁlter designed by the authors. sion peak temperature M∗ p= 13°C, an R-phase reversion peak temperature R∗ p= 23°C, and an austenite ﬁnish temperature Af= 30°C. All specimens are speckled with a polydisperse carbon powder using the procedure shown in Figure 5. Note that the approach uses the native specimen surface as the background for the speckles in lieu of applying a base coat of paint. Similar techniques were previously performed for microscale DIC using silicone microparticles [15, 55]. Specimens are ﬁrst cleaned as needed by immersing them in a solution of acetone and deionized water (50/50 by volume) within a centrifuge tube and sonicating (M series, Branson) the tubes for 15 min. After removal and drying, specimens are reinserted into centrifuge tubes containing ﬁnely ground activated carbon powder (Figure 5a,i), shaken (Figure 5a,ii), and then separated from the powder using either a sieve screen or nonmarring plastic tweezers. Upon removal, speckles are invisible to the naked eye, although some discoloration is apparent (Figure 5a). Micrographs at 500× magniﬁcation reveal the presence of opaque carbon particles (Figure 5b,ii) adhering to the nitinol surface via electrostatic forces [15, 55]. Finally, large particles and particle aggregates are blown away using a bulb syringe (similarly to [55]). Although rigid particles like those used herein violate the assumption in DIC algorithms that speckle deformations exactly track the underlying specimen deformations, Barranger et al. [56] previously demonstrated errors associated with rigid particle speckle patterns are unbiased (random) and comparable to the image noise errors still present using ideal deformable particles, even for imposed Green–Lagrange strains as high as 80%. Inspection under microscopy also conﬁrms that particles electrostatically adhere to the specimen surface and faithfully follow underlying material deformations. Speckle patterns are quantitatively characterized using two metrics: mean speckle size [57] and mean intensity gradient [58]. Mean speckle size is estimated in ImageJ[59] by performing local contrast enhance- ment, converting images to binary by application of a pixel intensity threshold, applying a watershed ﬁlter to separate partially overlapping speckles, and ﬁnally using the ‘analyze particles’ tool to extract mean speckle diameters and areas. Mean intensity gradient (MIG) is calculated in Python/NumPy using the central- diﬀerence-based gradient function. Using this approach, the mean speckle diameter and area are found to be approximately approximately 5 pixels and 30 pixels2, respectively, for all specimens. Mean intensity gra- dients range from approximately 11 for the polymer band specimens to 17 for the nitinol strip and coupon specimens and are comparable to the MIGs previously reported for macroscale speckle patterns generated using aerosol paints (12 to 35; [58]). 5 a b ii i i iii iiFigure 5: a) Speckling approach used in our 2D-DIC experiments. Samples are (i) inserted into a centrifuge tube containing ﬁnely-ground carbon powder, (ii) shaken, and (iii) removed. Although speckles are not visible to the naked eye, samples appear slightly darker after speckling. b) Representative micrographs of samples (i) before and (ii) after speckling. 2.2 DIC processing Surfacedisplacementsandstrainsareextractedfromimagesequencesusingtheopen-sourcesubset-based2D- DIC software Ncorr–C++ [60].Ncorr–C++ uses the recently developed reliability-guided approach (RG-DIC [61])toincreasethespeedofcomputationandtodecreasetheriskforfailingtoﬁndamatchbetweenreference and deformed images (decorrelation). The procedure ﬁrst chooses a seed subset in the reference image and identiﬁes a match in the deformed image by optimizing the correlation criteria. After the deformation of the seed subset has been determined, neighboring subsets are next selected and initialized using the displacement results from the seed subset. The process is repeated for all subsequent computations by updating the reference displacement to that from the nearest subset neighbor. In so doing, fewer iterations are needed to optimize the correlation, greatly decreasing computation time and preventing the need for an exhaustive search over all image space. Ncorr–C++ additionally leverages the inverse compositional Gauss-Newton (IC- GN) approach [62] as the nonlinear optimizer for sub-pixel accuracy. Ncorr–C++ was previously validated [60] using the Society of Experimental Mechanics 2D-DIC Challenge Data [63] and veriﬁed by comparison with results from the commercial code VIC-2D [64]. For the DIC analyses performed herein, a region of interest (ROI) is ﬁrst deﬁned using a black-and- white TIFF image mask. The ROI is 446×297 µm2for the nitinol strip and polymer band specimens, and 241 ×303µm for the nitinol coupon. To reduce interpolation bias and aliasing [65, 66], Gaussian pre- ﬁltering of images is performed in Python/OpenCV [67] using a 3 ×3 kernel and a sigma value of 0.8. The ﬁltered images are analyzed in Ncorr–C++ using circular subsets with a radius of 31 pixels, a step size (‘scalefactor’ in Ncorr–C++) of 5 pixels, and a correlation coeﬃcient cutoﬀ of 2. After extracting dis- placements, Green–Lagrange strains are calculated in Ncorr–C++ by diﬀerentiating the displacement ﬁeld using the pointwise least squares strain window smoothing algorithm [68] and a strain subregion radius of 10 subsets. Displacement and strain results are ﬁnally exported as comma-separated values (CSV) ﬁles and read byPythonfor further visualization and post-processing. Details on the imaging, lighting, and sensors used in the DIC experiments and parameters used in the DIC processing are summarized in Table 1. 6 Table 1: Parameters describing the microscale 2D-DIC setup reported as recommended in [69]. parameter value imaging systemHiRox KH7700 digital optical microscope sensor 2MP CCD, 8-bit image size 1600×1200 pixels lens HiRox MXG-2500 REZ, high range light source 60W metal halide lamp magniﬁcation 500× working distance 10 mm light conﬁguration bright-ﬁeld, coaxial DIC software Ncorr–C++ (open-source) [60] code validationSociety of Experimental Mechanics 2D-DIC Challenge Data [60] spatial scale 0.37µm / pixel speckle background electropolished nitinol surface speckle foreground ﬁnely ground activated carbon powder mean speckle size ≈30 pixels2 image ﬁltering low-pass (3×3 kernel Gaussian) subset shape and size circular, 31 pixel radius strain window 10 subsets (radius) step size 5 pixels subset advancement reliability guided (RG) [61] initial cross correlationzero-mean normalized cross correlation (ZNCC) [70] ﬁnal cross correlationzero-mean normalized sum of squared diﬀerence (ZNSSD) [70] nonlinear optimizerinverse compositional Gauss-Newton (IC-GN) [62] interpolation biquintic B-spline 7 2.3 2D-DIC veriﬁcation experiments To characterize errors associated with our speciﬁc experimental setup, we follow relevant recommendations from the iDICs good practices guide [52]. Note that the guide explicitly states it does not cover additional considerations for advanced setups such as those using microscopy. Thus, some of our methodology deviates from the iDICs recommendations. For example, although the iDICs guide recommends no changes be made to the camera setup once experiments begin, adjustment of the stand-oﬀ distance is sometimes required for microscale measurements (e.g., [11, 12, 16]) to mitigate defocusing errors that occur with even subtle out- of-plane motion due to the limited depth of ﬁeld at high magniﬁcations. Therefore, refocusing is performed as needed throughout the experiments described herein. 2.3.1 Camera and hardware heating study Previous studies [53, 71] have shown hardware self-heating to inﬂuence DIC measurements due to thermal expansion in the camera sensors and associated components (e.g., lenses and mirrors). As such, iDICs recom- mends waiting for all hardware to reach a steady-state temperature prior to acquiring images (Section 3.1.3 in [52]). Here, the inﬂuence of camera and hardware heating is quantiﬁed by tracking mean displacements and strains over time while imaging a static sample to estimate the required waiting time for the system to reach a thermal steady-state. Experiments are performed using the nitinol strip specimen from Figure 4a. The specimen is mounted to the micrometer spindle using an M4 set screw and nut. The experiment is initialized with the microscope turned oﬀ for two or more hours (i.e. “cold”). The load frame is positioned under the microscope and the microscope is powered on. Time-lapse image acquisition of the nominally static specimen then begins as soon as the specimen is brought into focus and rotated so that the specimen plane is approximately perpendicular to the optical axis of the microscope. Images are taken every two minutes for a three-hour period. Note that the heated breadboard and fan are not powered during this study. Following the experiment, images are processed in Ncorr–C++ and mean displacements and strains are calculated and plotted versus elapsed time. 2.3.2 Noise ﬂoor characterization To characterize the inﬂuence of random image noise on the DIC results (Section 3.3.1.3 in [52]), images are acquired of the nominally static nitinol strip specimen (Figure 4a) after allowing the camera and hardware to heat for the determined warm-up time (100 min). Two images are acquired in rapid succession of the nominally static specimen, once at room temperature and a second time with the heated breadboard and fan powered on and the PID control loop set to and stabilized at 37 °C. This second test is used to investigate the inﬂuence of environmental heating on the measurement noise ﬂoor. Images are processed in Ncorr–C++ to extract the systematic (mean) and random (standard deviation) errors in the displacement and strain ﬁelds. 2.3.3 Out-of-plane rigid body translation study Out-of-plane motion of specimens has previously been reported as a primary source of error for 2D-DIC measurements [ 9,53]. In the context of microscale DIC, out-of-plane errors have also been referred to as “refocus errors” [11] given that refocusing by adjusting the stand-oﬀ distance of the objective is frequently required to keep a specimen in focus during an experiment, and any error in matching the original stand-oﬀ distance will generate measurement errors. Because of the importance of out-of-plane motion errors for 2D-DIC, the iDICs guide recommends characterizing the magnitude of these errors in response to the range of out-of-plane motions that may occur during an experiment (Section 3.3.1.5 and Recommendation 3.15 in [52]). Here, we estimate out-of-plane errors by ﬁrst acquiring a reference image of a nominally static specimen in sharpfocus(Figure 4a). Imagesarethenacquiredwiththemotorizedobjectivemovedtothelower( ≈ −3µm) andupper(≈ +3µm)boundsofthedepthofﬁeldwhereblurringoftheimagesbecomesqualitativelyobvious. Images are again processed in Ncorr–C++ to extract the systematic (mean) and random (standard deviation) errors in the displacement and strain ﬁelds. 8 2.3.4 In-plane rigid body translation study In-plane rigid body translation tests have been used since the earliest DIC studies (e.g., [6]) to characterize displacement accuracy and are recommended by the iDICs guide for this same purpose (Section 3.3.1.5 [52]). Errors computed from in-plane translation tests represent a combination of the errors from spatially varying lens distortion, illumination, and camera sensor noise. We characterize the displacement accuracy of our DIC system by translating the nitinol strip specimen (Figure 4a) along one axis using the M-230.25 precision actuator that has a nominal sensor resolution of 5 nm and a minimum increment resolution of 50 nm. To avoid backlash, the actuator is ﬁrst advanced a few millimeters in the target direction of travel before acquiring a reference image. Total displacements of 1, 2, 5, 10, 20, and 50 micron are then prescribed, with an image taken after each displacement increment. Images are processed in Ncorr–C++ to extract displacements and strains. Systematic (mean) errors in dis- placement are calculated by computing the mean diﬀerence between the measured and nominal displacement over each subset, and random errors are calculated by computing the standard deviation of the displacement ﬁeld (nominally zero). Systematic (mean) and random (standard deviation) errors in the nominally zero strain ﬁeld are also calculated from the subset values. 2.3.5 Uniaxial tension test In addition to the tests recommended by the iDICs guide, we also perform a uniaxial tension test as in [11, 53] to characterize the accuracy of strain measurements with our DIC setup. For these experiments, the articulated base is removed, and the load frame is placed upon the motorized stage of the KH7700 microscope. The polymer specimen (Figure 4b) is fastened in the air chamber between a #8 eye bolt (ﬁxed end) and a 4 mm miniature clevis mount (actuated end). To prevent sagging, a small pre-strain is applied to the specimen, and the reference length Lis recorded along with a reference image. Deformed lengths l needed to prescribe uniaxial Green–Lagrange strains /epsilon1G=1 2/parenleftBig l2 L2−1/parenrightBig of 1%, 2%, 3%, 4%, and 5% are then calculated and prescribed by moving the actuator, and deformed images are acquired at each nominal strain level. To keep the original region of interest approximately centered in the ﬁeld of view, the load frame is repositioned after each increment in strain using the motorized stage. Images are processed in Ncorr–C++ to extract strains. Systematic (mean) errors in strain are calculated by computing the mean diﬀerence between the measured and nominal strains at each subset, and random errors are calculated by computing the standard deviation of the measured strain ﬁeld. 2.4 Nitinol device coupon demonstration experiments Use of the veriﬁed microscale 2D-DIC system is demonstrated on a nitinol medical device coupon under emulated physiological loading. Speciﬁcally, the single-strut nitinol IVC ﬁlter coupon specimen (Figure 4c) is subjected to ﬁxed-free cantilever bending motion by clamping the coupon hub and pressing on the distal end of the strut using a ﬂat micrometer tip (Figure 4c, right). The miniature force transducer is placed inline between the micrometer and the specimen for these experiments (Figure 3b). Because the mechanics of nitinol are temperature-dependent, experiments are performed at body temperature (37 °C) using the previously described temperature control loop. The primary (controlling) thermistor is positioned so that it is in contact with the coupon hub throughout the experiment, and the secondary thermistor is positioned free-standing in the air a few millimeters away to characterize the in-chamber temperature gradient. For these experiments, the ROI is the sidewall of the strut at the strut root (Figure 5b) where the highest strains occur during bending. Because the nitinol coupon is laser cut from round tubing, the strut sidewalls are not parallel to one another or to the load frame base (Figure 4c). Thus, to allow for alignment of the ROI to the camera viewing plane, the miniature load frame is mounted on the articulating platform for these experiments (Figure 3a,3). The platform is tilted and the microscope objective adjusted until as much of the coupon sidewall is in focus as possible. After aligning and focusing the microscope, a reference image is acquired of the strut sidewall in the undeformed conﬁguration. The coupon is then subjected to quasi-static loading as the strut tip is displaced in increments of 0.163 mm up to a maximum displacement of 2.61 mm and then unloaded by the same increments, with images and forces recorded at each displacement level. The micrometer is translated at a relatively slow rate of approximately 0.05 mm per second to minimize 9 temperature changes in the nitinol associated with the latent heat of crystallographic phase transformation between cubic (B2) austenite and monoclinic (B19’) martensite. 3 Results 3.1 2D-DIC veriﬁcation experiments Results of the veriﬁcation tests are summarized in Table 2. Table 2: Estimated errors in displacement and strain from microscale 2D-DIC veriﬁcation experiments. rigid body, rigid body, static static, 37 °C out-of-plane in-plane uniaxial strain errorsyst. rand. syst. rand. syst. rand. syst. rand. syst. rand. (mean) (std)(mean) (std)(mean) (std)(mean) (std)(mean) (std) µm-0.032 0.007 -2e-5 1.1e-4 0.176 0.188 0.009 0.109 N/A N/A µ/epsilon1 4256 -43 264*1130 716 758 402 -912 1162 syst: systematic error; rand: random error; std: standard deviation; N/A: not applicable *average absolute value of mean strains generated by out-of-plane translation i) toward and ii) away from the specimen 3.1.1 Camera and hardware heating study Images acquired from an initially cool (i.e., room-temperature) system reveal a settling period during which displacements and false strains in the DIC results increase in magnitude (Figure 6). Interrogation of raw images and extracted displacements reveals evidence of in-plane spatial drift, with ﬁnal displacement mag- nitudes of about 3–4 µm in both the x- andy-directions at the end of the three-hour study (Figure 6, left). The observed mean /epsilon1xxand/epsilon1yystrains ﬁrst increase slightly ( 0< t < 2min), then decrease sharply until reaching a minimum of approximately -3,000 µ/epsilon1att= 100min (Figure 6, right). From t= 100min on, the/epsilon1xxand/epsilon1yystrains remain approximately constant, indicating that a steady state has been reached. In contrast, the mean shear strain /epsilon1xyremains approximately unchanged throughout the experiment (Figure 6, right). Image focus also deteriorates during the initial settling-in period between 0<t< 100min. Figure 6: Spatial drift (left) and false strains (right) versus elapsed time from the three-hour camera and hardware heating study. An approximately steady state is reached after 100 min in all ﬁelds except the y-displacement (v ). All strains are Green–Lagrange. 3.1.2 Noise ﬂoor characterization Images of nominally static samples taken after the 100 min hardware warm-up period are used to estimate the systematic and random errors in displacement and strain summarized in Table 2. Images taken at room 10 temperature and with environmental heating to 37 °C yield very similar displacement and strain noise levels (Table2; Figure 7). Under these nominally static conditions, the one-standard deviation strain noise ﬂoor is comparable in the /epsilon1xxand/epsilon1yystrains, both with and without environmental heating, and is estimated to be approximately 250 µ/epsilon1(Table2; Figure 7). Figure 7: Systematic (mean) and random (standard deviation) strain errors extracted from two subsequent images of a static sample. Random errors are represented by one standard deviation. 3.1.3 Out-of-plane rigid body translation study Out-of-plane translations to the upper and lower bounds of the depth of ﬁeld generate relatively large errors in both displacement and strain compared to those observed with a static sample in sharp focus (Table 2; Figure8). Mean strain errors are positive ( ≈+2000µ/epsilon1) when the objective is moved away from the specimen (z+) and negative ( ≈ −1500µ/epsilon1) when the objective is moved toward the specimen ( z−) (Figure 8, left). The estimated strain noise ﬂoor is approximately 2.7 ×higher than that observed in the absence of intentionally applied out-of-plane motion (Table 2; Figure 8, right). Figure 8: Systematic (mean) and random (standard deviation) strain errors generated by out-of-plane trans- lations of the objective lens toward ( z−) and away from (z +) a nominally static specimen initially in sharp focus. Translations are large enough to appreciably deform the image. Random errors are represented by one standard deviation. 3.1.4 In-plane rigid body translation study Excellent agreement is observed between nominal actuator displacements and those measured using 2D- DIC (Table 2; Figure 9). The mean displacement error is approximately 9 nm (Table 2). Random errors in displacement are relatively small for small displacements (e.g., standard deviation σ= 34nm at 1µm 11 displacement) and increase with increasing displacement (standard deviation σ= 411nm at 50µm displace- ment; Figure 9). Systematic and random errors in strain are greater than those obtained from the noise ﬂoor characterization study but less than those observed during the out-of-plane translation experiments (Table 2). Figure 9: Results from in-plane rigid body displacements of a planar nitinol specimen for displacement error characterization. Error bars represent one standard deviation of the displacements extracted from the ROI. 3.1.5 Uniaxial tension test Excellent agreement is also observed between nominal uniaxial strains and those measured using 2D-DIC in experiments using the polymer band specimen (Table 2; Figure 10). The mean strain error is approximately -912µ/epsilon1. Systematic errors in strain are lower at small strains (e.g., -159 µ/epsilon1error at 10,000 µ/epsilon1) than at larger strain levels (e.g., -2154 µ/epsilon1error at 50,000 µ/epsilon1; Figure 10). Random errors also increase over the explored strain range (from 750 µ/epsilon1error at 10,000 µ/epsilon1to 2052µ/epsilon1error at 50,000 µ/epsilon1; Figure 10). : Figure 10: Results from uniaxial tension experiments with a polymer band specimen between nominal strains of 10,000µ/epsilon1(1%) and 50,000 µ/epsilon1(5%). Error bars represent one standard deviation of the calculated strain values over the DIC region of interest. All strains are Green–Lagrange. 12 3.2 Nitinol device coupon demonstration experiments Fixed-free cantilever bending experiments on the nitinol coupon specimens (Figure 11a) reveal nonlinear force-displacement behavior (Figure 11b) and hysteresis between the loading and unloading paths for tip displacements greater than approximately 0.8 mm (points 4–15; Figure11b). Full-ﬁeld strain measurements acquired on sidewall of the strut root show typical continuous strain contours for beam bending up to tip displacements of approximately 1.3 mm (frames 1–5; Figure 11c). Above tip displacements of 1.3 mm, Lüders-like transformation bands initiate and spread from the tensile side toward the neutral axis (frames 6–9; Figure11c). Transformation bands persist upon unloading until the tip displacement decreases below 1.3 mm (frames 10–14; Figure 11c). Localization bands then begin to recede (frame 14) until they are no longer visible below tip displacements of approximately 0.65 mm (frames 16–18; Figure 11c). After mapping the full-ﬁeld strain results for maximal tip displacement (frames 9and 10) to the reference conﬁguration, the angle between the transformation bands and the strut axis is measured to be approximately α= 54.9 ±3° (Figure 11d). 0% strain1% 2% 3% 4% 5% -1% -2% -3%1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 50.7°58.3° 53.6° 56.9°micrometerload cell clamp imaging window a cb 123456789 10 11 12 1314 15 16 17 18 d300μm Figure 11: Representative full-ﬁeld strain measurements for a nitinol device coupon heated in air to 37 °C. The geometry of the coupon is that of a single strut of a generic IVC ﬁlter designed by the authors (Figure 4). a) Schematic showing ﬁxed-free cantilever bending boundary conditions applied to the coupon specimens. b) Force versus tip displacement curve during loading and unloading. c) Full-ﬁeld strain results mapped to thedeformed conﬁguration and overlaid on deformed images for loading ( 1–9) and unloading ( 10–18). d) Enlarged view of the full-ﬁeld strain results mapped to the reference conﬁguration with measured trans- formation band angles. For the specimen shown, the transformation band front angles αare 54.9° ±3°. All strains are Green–Lagrange. 13 4 Discussion Building upon previous 2D-DIC studies using bright-ﬁeld microscopy (e.g., [11, 13,16]), we demonstrate the use of a standard digital optical microscope and a low-cost miniature load frame to acquire full-ﬁeld surface measurements over sub-millimeter ﬁelds of view with sub-micron displacement accuracy. Furthermore, we use a simple speckling technique that requires little time and preparation and that can be used repeatedly on the same specimen if desired (e.g., by removing speckles with a soft brush between experiments). A temperature-controlled chamber accommodating the small working distances typically required by high- magniﬁcation optical microscopy is also demonstrated and used to heat nitinol device coupon specimens to physiologically relevant conditions (i.e., 37 °C). Such temperature control is essential for characterizing the mechanics of temperature-sensitive nitinol medical devices. Together, these characteristics make the setup relatively well-suited for characterizing the micromechanics of nitinol cardiovascular devices. Where applicable, we follow recommended good practices from iDICs [52] to characterize our 2D-DIC setup and estimate measurement errors in displacement and strain. Camera and hardware heating studies reveal a required warm-up time of approximately 100 min to reach steady-state operation (Figure 6), similar to previous macroscale studies (e.g., approximately 1.5 hr in [53]). Random (standard deviation) errors estimated from image pairs taken of a static sample are also comparable to those reported in previous studies (e.g., ≈0.02 pixels here and in [11, 16]). Systematic errors from in-plane translation experiments are comparable to those reported previously (e.g., mean displacement error is 9 nm or about 0.02 pixels here and in [12, 13]), although random errors are larger (≈0.06 pixels for small translations and up to 1.1 pixels for the largest translation; Figure 9), likely due to increasing i) variability in specimen illumination, ii) out-of-plane motion generated by alignment errors between the microscope objective and the specimen, and iii) lens aberration errors with increasing displacement. Strain errors generated by intentional out-of-plane rigid-body translation are similar to those reported by Lei et al. [16] (~2,000 µ/epsilon1), another optical microscale DIC study also performed at 500× magniﬁcation. In addition to tests recommended by iDICs, we characterize strain errors using uniaxial tension experi- ments as performed in some previous DIC studies (e.g., [11, 13,53]). Systematic and random strain errors estimated based on these experiments are each approximately 1,000 µ/epsilon1(Figure10; Table 2). Bias error magnitudes increase slightly with increasing mean strain, possibly due to subtle misalignment of stage and camera axes that generates some oﬀ-axis or out-of-plane motion when re-centering the region of interest to the ﬁeld of view. End eﬀects near the clamped portions of the polymer specimen may also increase the strain locally and thereby decrease the true strain generated in the observed region of interest. In general, strain errors are higher than those typically obtained with macroscale DIC setups (e.g., ≈50µ/epsilon1in [53]), but are comparable to those reported for previous microscale measurements (e.g., 500 µ/epsilon1in [13]). The impor- tance of these errors, however, depends on the intended use for the DIC measurements and the associated signal-to-noise ratio for an application [29]. That is, the DIC measurement errors are generally acceptable for an experiment as long as the strains of interest are much greater than the noise ﬂoor. Thus, the DIC setup developed herein could reasonably be used for applications where strains of interest are greater than 1,000µ/epsilon1(0.1%) by a factor of two or three. To demonstrate the veriﬁed microscale DIC system, we acquire full-ﬁeld measurements of a single strut of a generic nitinol medical device undergoing ﬁxed-free cantilever bending motion at 37 °C (Figure 11). Inhomogeneous deformations are observed in the form of Lüders-like transformation bands that initiate from the tensile side and spread toward the neutral axis of the strut (Figure 11c). This strain localization phenomenon has been observed previously for superelastic nitinol strips and tubes subjected to uniaxial ex- tension [37, 72,73] and four-point bending [36, 37]. As explained by Hill [74] and later applied to superelastic deformations of nitinol by Shaw et al. [ 72] and Reedlunn et al. [37], the ideal in-plane band front angle αfor necking of a thin strip in uniaxial tension is described by cos (2α) =−1−ν 1+ν, whereνis the Poisson’s ration of the material. Assuming no volume change during plastic (here pseudoplastic) deformation such that ν=1 2, the predicted in-plane front angle is α= 54.74°. Although experiments here consider cantilever bending rather than uniaxial tension, the observed transformation band angles of 54.9° ±3°(Figure11) closely agree with the band angle predicted by theory as well as with those reported in previous investigations of nitinol by Shaw et al. [72] and Murasawa et al. [32] ( ≈55°) and by Reedlunn et al. [37] (44.5 °to 70.5°for tubes in bending). Microscale full-ﬁeld measurements like those demonstrated herein have not been reported previously for 14 ﬁnished cardiovascular medical devices. Such measurements will empower device engineers to more directly validate and improve the computational models they use for device development. Full-ﬁeld measurements will also guide the development and validation of models capable of reproducing inhomogeneous deformations [72, 75, 76] like the strain localization bands observed here (Figure 11). Measurements of medical devices undergoing emulated physiological loading may also be useful for detecting cyclic crystallographic phase transformation, which has recently been demonstrated to be an indicator for low-cycle fatigue failure [45, 46]. While more advanced methods such as high-energy X-ray diﬀraction can provide a more direct measure of the phase transformation (e.g., [77]) in bulk samples such as medical devices, the 2D-DIC method described here provides access to similar information with a substantially simpler experimental setup. Some limitations of the microscale 2D-DIC approach described here should be noted. First, magniﬁcation and depth of ﬁeld are inherently limited by the physics of optical microscopy. Both higher magniﬁcation and greater depth of ﬁeld are possible using more advanced techniques such as scanning electron or atomic force microscopy. However, as noted by others (e.g., [13, 15]), the advantages of these approaches come with the additional cost, setup and acquisition time, and complications such as sensitivity to electrical noise and spatial drift. Measurements acquired using a single camera and single perspective optical microscope are also limited by being strictly two-dimensional and are, thus, subject to out-of-plane errors with even subtle changes in working distance during an experiment. Because of these limitations of 2D-DIC, the iDICs good practices guide states “[s]tereo-DIC is strongly recommended over 2D-DIC for all tests if possible, even tests in which a nominally planar test piece undergoes nominally planar deformation” (Section 2.1.5 in [52]). However, stereo-DIC has its own challenges at the microscale, for example, physical limitations to the minimum distance at which separate camera sensors can be positioned. Stereomicroscopy is also similarly restricted to small depths of ﬁeld, making the technique again impractical unless specimens are approximately planar. Indeed, commenting on the relative strengths and weaknesses of 2D versus stereo- DIC, Pan et al. [2] predict that 2D-DIC will remain an “eﬀective and irreplaceable tool” for measurement at the microscale for the foreseeable future. 5 Summary and Conclusions •2D-DIC measurements are demonstrated over sub-millimeter ﬁelds of view with sub-micron displace- mentaccuracyusinganunmodiﬁeddigitalopticalmicroscopeandasimple, inexpensive, andfastspeck- ling technique. A low-cost temperature- and displacement-controlled load frame is also demonstrated that accommodates the short working distances required by high-magniﬁcation optical microscopy. •Following general recommendations from the iDICs good practices guide [52], we performed multiple tests to characterize and estimate the displacement and strain errors associated with our DIC setup. Based on the veriﬁcation experiments, systematic and random errors in strain are each estimated to be approximately 1,000 µ/epsilon1. The method is thus useful for applications where strains of interest are greater than 1,000 µ/epsilon1(0.1%) by a factor of two or three. •Full-ﬁeld strain measurements are acquired on the sidewall of a ﬁnished laser-cut nitinol medical device coupon with a strut width of approximately 300 µm. Microscale Lüders-like transformation bands are observed in the nitinol strut at larger deformations. •Future use of microscale DIC in the medical device industry is motivated by the need to i) validate computational models used in the development and durability assessment of cardiovascular devices, ii) characterize the mechanics of these devices and detect cyclic phase transformations when present, and iii) guide the development of next-generation constitutive models for superelasticity and inhomo- geneous deformations (e.g., strain localization). The emergence of free and open-source DIC softwares (e.g.,Ncorr[60],DICe[78],Multi-DIC [79],pyDIC[80]) will further drive the adoption of DIC for these applications. 15 6 Acknowledgments We thank Daniel Porter (FDA) for reviewing the manuscript. We also thank Andrew Baumann, Mau- reen Dreher, Shiril Sivan, Daniel Porter (FDA), Tom Duerig (Conﬂuent Medical Technologies), and Robert Campbell (Pennsylvania State University) for helpful discussions. This study was performed under an active Research Collaborative Agreement between FDA and Conﬂuent Medical Technologies and was funded by the U.S. FDA Center for Devices and Radiological Health (CDRH) Critical Path program. The research was supported in part by an appointment to the Research Participation Program at the U.S. FDA administered by the Oak Ridge Institute for Science and Education through an interagency agreement between the U.S. Department of Energy and FDA. The ﬁndings and conclusions in this article have not been formally dis- seminated by the U.S. FDA and should not be construed to represent any agency determination or policy. The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health and Human Services. 16