Measurements of intracranial brain displacement in cadaveric specimens have been instrumental to the validation /uniFB01nite element (FE) models of brain injury. These data collections have used radio- graphic and sonomicrometric techniques, requiring the use of tissue-embedded tracking markers; how- ever, marker accuracy has never been adequately characterized. Marker tracking precision has been erroneously con/uniFB02ated with measurement accuracy, not accounting for changes in the natural response of surrounding tissues due to marker presence. Non-negligible inertia, high sti/uniFB00ness, and the aspect ra- tio of markers all contribute to this interference. This work investigated the dynamic coupling between published marker designs (NDTs, Sonomicrometry Crystals, and Tin) and a new elastomeric marker, and a block of tissue simulant subjected to a drop impact. The measured strains were compared to the base- line response of the simulant containing massless markers. The results found notable evidence of inter- ference in simulant strain amplitudes as well as considerable directional bias in the response of some markers. The elastomeric marker was found to have minimal interference in the deformation /uniFB01eld. Fu- ture FE model validation will need to account for the considerable interference and directional biases to the natural response of brain tissue in existing cadaveric datasets to maintain con/uniFB01dence in strain predictions. /one.pnum Introduction The bulk kinematic mechanisms behind brain trauma have been developed through investigations observ- ing brain motion in animal models. From these earliest animal models, it was shown that an impulsive ac- celeration of the head results in a di/uniFB00erential bulk motion of the brain within the skull (Pudenz and Shelden, /one.pnum/nine.pnum/four.pnum/six.pnum; Shelden et al., /one.pnum/nine.pnum/four.pnum/four.pnum) and that rotational acceleration of the head was highly correlated to di/uniFB00use brain injury (Holbourn, /one.pnum/nine.pnum/four.pnum/three.pnum; Ommaya and Gennarelli, /one.pnum/nine.pnum/seven.pnum/four.pnum). Further insights into the dynamic response of the brain to impulsive acceleration have been gained through intracranial measurements of brain tissue dis- placement and deformation in Post-Mortem Human Surrogates (PMHS). These intracranial measurements have been made using high-speed radiographic (Al-Bsharat et al., /one.pnum/nine.pnum/nine.pnum/nine.pnum; Guettler, /two.pnum/zero.pnum/one.pnum/seven.pnum; Hardy et al., /two.pnum/zero.pnum/zero.pnum/one.pnum, /two.pnum/zero.pnum/zero.pnum/seven.pnum) and sonomicrometry techniques (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum). Each of these techniques require the installation of embedded markers or targets within the brain tissue that were used to track tissue response in areas that are visually inaccessible using traditional optical methods. These data were used extensively in the validation of /uniFB01nite element (FE) head injury models (Ji et al., /two.pnum/zero.pnum/one.pnum/five.pnum; Kleiven and Hardy, /two.pnum/zero.pnum/zero.pnum/two.pnum; Takhounts et al., /two.pnum/zero.pnum/zero.pnum/eight.pnum; Zhao and Ji, /two.pnum/zero.pnum/two.pnum/zero.pnum; Zhou et al., /two.pnum/zero.pnum/one.pnum/nine.pnum); however, the accuracy of these methods as a result of the marker design choices has never been adequately characterized. Error quanti/uniFB01cation relating to the in- terference of these markers in the natural response of brain tissues to mechanical perturbation is critical to the validity of FE models and their injury predictions, as well as our broader understanding of brain trauma and injury. In the present study, we investigated the dynamic coupling between a variety of embedded marker designs used in prior PMHS brain displacement studies against the response of massless mark- ers in a drop-impacted tissue-simulating gel to quantify marker interference in the resulting deformation /uniFB01eld. The calibration and validation of FE models (Ghajari et al., /two.pnum/zero.pnum/one.pnum/seven.pnum; Giordano and Kleiven, /two.pnum/zero.pnum/one.pnum/four.pnum; Giudice et al., /two.pnum/zero.pnum/one.pnum/nine.pnum; Ji et al., /two.pnum/zero.pnum/one.pnum/four.pnum, /two.pnum/zero.pnum/one.pnum/five.pnum; Patton et al., /two.pnum/zero.pnum/one.pnum/three.pnum; Post and Hoshizaki, /two.pnum/zero.pnum/one.pnum/five.pnum; Post et al., /two.pnum/zero.pnum/one.pnum/nine.pnum; Takhounts et al., /two.pnum/zero.pnum/zero.pnum/eight.pnum; Zhao et al., /two.pnum/zero.pnum/one.pnum/seven.pnum; Zhao and Ji, /two.pnum/zero.pnum/two.pnum/zero.pnum; Zhou et al., /two.pnum/zero.pnum/one.pnum/nine.pnum) have relied heavily on the PMHS datasets 1 available in the literature (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum; Hardy et al., /two.pnum/zero.pnum/zero.pnum/one.pnum, /two.pnum/zero.pnum/zero.pnum/seven.pnum; Nahum et al., /one.pnum/nine.pnum/seven.pnum/seven.pnum). De- spite relying on the same datasets for calibration, a comparison of two computational head injury models, resulted in peak Maximum Principal Strain (MPS) values that di/uniFB00ered by anywhere from /five.pnum/zero.pnum to /one.pnum/zero.pnum/zero.pnum %in their intracranial strain predictions, for the same input head kinematics (Beckwith et al., /two.pnum/zero.pnum/one.pnum/eight.pnum). These authors suggested that these variations in FE model intracranial strain predictions were the result of di/uniFB00erences in brain geometry and model boundary conditions. Zhao and Ji (Zhao and Ji, /two.pnum/zero.pnum/two.pnum/zero.pnum) noted that current FE model validation e/uniFB00orts rely on comparisons to brain tissue strain measurements with insu/uniFB03cient spatial resolution for an e/uniFB00ective validation under a variety of medium- and high-strain rate loading conditions. While spatial resolution is a limitation that must be overcome in future datasets, the di/uniFB00erence in strain predictions based on existing datasets may be evidence of a deeper limitation related to the accuracy of existing measurements of brain tissue motion and deformation. The precision of marker tracking methods have been quanti/uniFB01ed in prior work (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum); how- ever, the quoted precision of these techniques were not a true measure of the accuracy of these measure- ments in brain tissue under dynamic loading, as these estimates are based on static marker localization precision. Markers embedded in tissues have their own inertia, and as a result, their presence will nec- essarily change the response of brain tissue to impulsive mechanical perturbation. As such, much of the literature has con/uniFB02ated tracking precision with the accuracy of tissue deformation measurements, and a lack of marker migration within tissue as proof of the /uniFB01delity of dynamic marker coupling. While Whyte et al. (Whyte et al., /two.pnum/zero.pnum/one.pnum/nine.pnum) have shown that some markers do migrate within brain tissue, which is undesirable, this is not the only measure of accuracy relating to the dynamic coupling of an embedded marker within tissues. The mere presence of markers, having their own inertia and sti/uniFB00ness, will change the displacement and deformation /uniFB01elds of the surrounding tissues, and the true measure of the accuracy of the method is related to minimization and quanti/uniFB01cation of this interference (Dutrisac et al., nd). It is not su/uniFB03cient to precisely know the position of a marker, if that marker is in the wrong position due to its interference in the natural deformation /uniFB01eld. A recent study investigated the optimization of embedded markers within a tissue simulant, /uniFB01nding that a range of marker parameters (density, sti/uniFB00ness, and spacing) signi/uniFB01cantly altered the displacement /uniFB01eld in the surrounding matrix (Dutrisac et al., nd). The authors of that study sug- gested optimal density and sti/uniFB00ness ranges for such markers, which were the basis for a new radiopaque marker design used in the present work. In the present study, we investigated the accuracy of embedded markers, designs that have been used to track tissue deformation in prior PMHS studies, in measuring a dynamic /two.pnum-D strain /uniFB01eld within a block of tissue simulant. The markers, some of which had an elongated aspect ratio, were tested in di/uniFB00erent orientations to determine whether they produced an anisotropic, directionally biased, interference in the natural deformation /uniFB01eld of the tissue simulant. Comparisons were made to the deformation of a block of tissue simulant having a series of massless markers, which was taken as a baseline natural response of the matrix, as well as a proposed radiopaque marker designed for future PMHS studies. The primary objectives of this work were to determine the accuracy and directionality of the response of markers used to track PMHS brain response in prior studies, which may explain some of the disparity in strain responses predicted by FE models. This data, investigating the response variability of these markers, will be essential to the future calibration and validation of FE models of head injury used in protective equipment design and brain injury prevention e/uniFB00orts. /two.pnum Materials and Methods Three embedded marker types that have been used in prior PMHS investigations were considered in the present comparison. These three markers were the Neutral Density Targets (NDTs) used by Hardy et al. (Hardy et al., /two.pnum/zero.pnum/zero.pnum/one.pnum, /two.pnum/zero.pnum/zero.pnum/seven.pnum), the Sonomicrometry Crystals (SMC) used by Al-Shareef et al. (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum), and the tin granules used by Guettler (Guettler, /two.pnum/zero.pnum/one.pnum/seven.pnum). In addition to those established marker designs, we will investigate a novel elastomeric marker that was designed speci/uniFB01cally for PMHS brain tis- sue studies, which will be referred to as the Carleton Elastomeric Marker (CEM) (Dutrisac et al., nd). This elastomeric marker was optimized using the results of a parametric study on embedded marker proper- ties (Dutrisac et al., nd). Once prepared, each marker type was cast into the central plane of a block of tissue-simulant, Humimic #/four.pnum. This tissue-simulant had a density of /zero.pnum./eight.pnum/five.pnum g/cm3and an elastic modulus of approximately /nine.pnum kPa, based on the manufacturer supplied durometer of /one.pnum/one.pnum./eight.pnum (Shore OO) (Larson, /two.pnum/zero.pnum/one.pnum/seven.pnum; Mix and Giacomin, /two.pnum/zero.pnum/one.pnum/one.pnum), which is the same order of magnitude as the elastic modulus of brain tissue (Budday et al., /two.pnum/zero.pnum/one.pnum/five.pnum). Schematics of the block and marker designs are shown in Fig. /one.pnum and Fig. /two.pnum, respectively. /two.pnum Marker Pattern 152 mm 152 mm45 mm2 31 4Marker PlaneFigure /one.pnum: A schematic of the tissue simulant block, marker arrangement, and elements used in the strain calculation. (a) (b) (c) (g) (h) (i) (d) (e) (f) Figure /two.pnum: A schematic of the markers used in the present work: (a) Massless marker; (b) Carleton Elas- tomeric Marker; (c) Tin Marker; (d) SMC - no wire; (e) SMC - vertical wire; (f) SMC - horizontal wire; (g) NDT - horizontal orientation; (h) NDT - vertical orientation; (i) NDT - transverse orientation. Note that all markers were drawn to scale. /three.pnum Table /one.pnum: Summary of marker mechanical and geometric properties Marker Density (g/cm3) Elastic Modulus (MPa) Geometry Aspect Ratio Massless - - - - NDT /one.pnum./five.pnum /two.pnum/zero.pnum/zero.pnum Cylinder /two.pnum./five.pnum SMC /one.pnum./one.pnum /one.pnum/zero.pnum Bulb and wire /one.pnum Tin /seven.pnum./three.pnum /four.pnum/one.pnum,/six.pnum/zero.pnum/zero.pnum Sphere /one.pnum CEM /one.pnum./six.pnum /zero.pnum./zero.pnum/one.pnum/two.pnum Cylinder /one.pnum /two.pnum./one.pnum Marker and block preparation Each set of embedded markers was prepared according to descriptions found in the literature, with an e/uniFB00ort to maintain their size, density, and sti/uniFB00ness characteristics based on the available materials. The NDT markers were each composed of a thin-walled polyethylene tube /five.pnum mm in length with a /one.pnum./five.pnum mm diameter. The low-density polyethylene is less sti/uniFB00 than the polystyrene ( E=/three.pnum./five.pnum GPa) described by Hardy et al. (Hardy et al., /two.pnum/zero.pnum/zero.pnum/seven.pnum), however it is still several orders of magnitude sti/uniFB00er than the matrix material. A /one.pnum./five.pnum mm long, /one.pnum./five.pnum mm diameter piece of /nine.pnum/seven.pnum%-Sn-/three.pnum%-Cu solder wire was cut and inserted into each tube. Tubes were sealed using cyanoacrylate adhesive. The SMC markers were replicated using an amine epoxy (/three.pnumM DP /four.pnum/two.pnum/zero.pnum, Dow Inc.) and a twisted pair signal cable (/three.pnum/four.pnum AWG, PTFE Jacket, Daburn Electronics). These components are identical to those used in the o/uniFB00-the-shelf sonomicrometry crystals used by Al-Shareef et al. (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum). Pre-cut /three.pnum/zero.pnum/zero.pnum mm lengths of twisted pair cable were dipped in uncured epoxy, building up a bulbous capsule at the tip. This process was repeated until bulbs of approximately /one.pnum./five.pnum to /two.pnum mm diameter were achieved and dipped wires were left to fully cure. The SMCs without a signal wire were created in the same fashion, however the excess wire was cut once the capsule was fully cured. The tin granules used by Guettler (Guettler, /two.pnum/zero.pnum/one.pnum/seven.pnum) were formed from a /nine.pnum/seven.pnum %-Sn-/three.pnum%-Cu solder wire. Pre-cut /three.pnum mm lengths of solder wire cut and heated using a /uniFB01ne point soldering tip until lique/uniFB01ed. Once lique/uniFB01ed, the surface tension of the molten material pulled it into a spherical granular form which was left to cool. While these granules were not pure tin, given the relatively small amount of alloying material, the density remained consistent with pure tin (/seven.pnum./three.pnum g/mL). Carleton Elastomeric markers were a blend of thermoplastic gel (Humimic #/four.pnum) and a powdered contrast agent (BaSO 4). A mixture of /six.pnum/zero.pnum wt %BaSO 4was used for the present investigation. Gel material was melted at /one.pnum/six.pnum/zero.pnumC and mixed with BaSO 4powder. The mixture was pressed into a precision machined brass mould. The mould was left to set at room temperature for /two.pnum/four.pnum hours. Once set, a sheet of /two.pnum mm-diameter and /two.pnum mm-long cylindrical markers was removed from the mould. Massless markers were made from alcohol-based ink (Sharpie) drawn approximately /two.pnum mm in diameter. A summary of marker properties can be found in Table /two.pnum./one.pnum. It should be noted that while the wire-free SMCs had an aspect ratio of /one.pnum, the wired version could be considered as a non-unity aspect ratio. Insertion of markers into tissue-simulant blocks would damage the surrounding material and obscure the required optical clarity. Instead, markers were prepared in advance and cast into the simulant blocks. A mould constructed from a /one.pnum:/one.pnum blend of Sylgard /one.pnum/eight.pnum/four.pnum and /five.pnum/two.pnum/seven.pnum was used to produce the tissue simulant blocks; this material provided necessary heat resistance for the melted material while remaining /uniFB02exible for demoulding. Blocks measured /one.pnum/five.pnum/two.pnum mm /one.pnum/five.pnum/two.pnum mm /four.pnum/five.pnum mm (Fig. /one.pnum). Thermoplastic tissue-simulant gel (Humimic #/four.pnum) was slowly melted in a ceramic crucible and agitated to remove large air bubbles. Once fully lique/uniFB01ed, the gel was poured into the mould, /uniFB01lling it half way, agitated again to remove entrapped air and was left to set. The surface of the half /uniFB01lled mould was used as the marker plane. A template was placed on top of the surface and registration marks were drawn to ensure even placement of markers. Markers were placed in a /five.pnum /five.pnum grid, with /two.pnum/zero.pnum mm spacing. The surface was lightly heated to allow local melting, allowing placed markers to stay in place during the pattern assembly. Once all markers were placed, additional melted tissue simulant gel was poured into the mould, /uniFB01lling it completely. The mould was agitated again to remove larger air bubbles, and the remaining air bubbles were removed manually. The wires attached to SMC markers were coated with a release agent (Ease Release /two.pnum/zero.pnum/zero.pnum) to prevent the tissue simulant from bonding to them, as bonding between the wire and surrounding matrix would not have been consistent with their use in PMHS testing. SMC and NDT markers were tested in various orientations due to their non-unity aspect ratios. For each of these markers, vertical and horizontal orientations were achieved by rotating the same test block /nine.pnum/zero.pnumwithin the drop-housing. The wire-free SMC markers were cast separately from the wired version. Similarly, for the NDTs in the transverse orientation, a separate tissue simulant block was produced. /four.pnum Rigid Frame Drop Carriage Acrylic Housing Tissue Simulant Block Sylgard Encasement Observation Area Anvil Figure /three.pnum: A schematic of the drop assembly used in the investigation. /two.pnum./two.pnum Drop testing and data capture The impact response of the tissue simulant blocks was tested by subjecting each to a series of /three.pnum indepen- dent vertical drops from a height of /eight.pnum/four.pnum./zero.pnum /zero.pnum./three.pnum cm onto a rigid anvil using a custom drop-tower (Fig. /three.pnum). To protect against boundary damage, blocks were placed within the Sylgard mould used in the casting pro- cess. The block and mould assembly was sandwiched between plates of acrylic. These plates restricted out of plane motion and buckling of the specimen blocks. The total thickness of the blocks and acrylic plates was maintained precisely at /four.pnum/seven.pnum mm to ensure a reproducible clamping strength and the consistency of the boundary conditions. Each specimen assembly was assessed for damage and slippage within the housing between repeated drop tests. The impact and deformation of the tissue simulant blocks were captured using a high-speed video camera (NAC HX-/three.pnum) at a frame rate of /seven.pnum,/five.pnum/zero.pnum/zero.pnum fps for a period of /two.pnum/zero.pnum/zero.pnum ms with a /two.pnum/five.pnum %pretrigger. To achieve su/uniFB03cient image contrast, a white, translucent paper membrane was applied to the specimen housing and back-lit using a /two.pnum/zero.pnum/zero.pnum/zero.pnum lumen LED lighting /uniFB01xture (Cinema Work Light, MossLED Inc.). /two.pnum./three.pnum Analysis The videos of the impact events were processed for to measure marker displacement and calculate strain using a custom particle tracking code that has been validated in prior work (Dutrisac, /two.pnum/zero.pnum/two.pnum/zero.pnum). A set of non- deforming /uniFB01ducial markers on the drop carriage assembly was tracked, enabling us to precisely determine the moment of impact as well as to subtract rigid body motion from the analysis. Standardizing the defor- mation across the sample set, these /uniFB01ducial markers were also used to develop a relative pixel-to-millimetre scale for each specimen. For the Massless, CEM, and SMC specimens, the scale was /four.pnum./two.pnum/five.pnum /zero.pnum./zero.pnum/one.pnum px/mm, while for NDT and tin specimens, the scale was /four.pnum./six.pnum/nine.pnum /zero.pnum./zero.pnum/one.pnum px/mm. /five.pnum For consistency, the comparisons were made through an analysis of the motion of the central markers to avoid lateral boundary in/uniFB02uences. The pre-impact position of these markers was used as a baseline to determine post-impact displacement with the block. The positions of the nine central markers, forming a /three.pnum/three.pnum grid, were tracked through the video frames using the particle tracking code. The displacements of these markers were used to calculate the elemental strain in the central region based on a de/uniFB01nition of /four.pnum triangular elements, as illustrated in Fig. /one.pnum. The method is similar to that proposed in previous work related to brain-tissue strain (Zhou et al., /two.pnum/zero.pnum/one.pnum/nine.pnum). The strain was determined using a /two.pnumD polynomial /uniFB01t to the triangular element described by the nodal markers (Pan, /two.pnum/zero.pnum/zero.pnum/seven.pnum), u[x;y] =a0+a1x+a2y; (/one.pnum) v[x;y] =b0+b1x+b2y; (/two.pnum) whereuandvare the displacement vectors of each node at position ( x,y) and (a0,a1,a2,b0,b1,b2) are coe/uniFB03cients used in the strain tensor. Once /uniFB01tted, the polynomial coe/uniFB03cients are solved using marker displacement data and Green-Lagrangian strain is calculated using the expressions, xx=@u @x+1 2h@u @x2+@v @x2i ; yy=@v @y+1 2 @u @y2 + @v @y2 ; (/three.pnum) xy=1 2 @u @y+@v @x +1 2h @u @x@u @y+@v @x@v @yi ; wherexx,yy, andxyare the respective directional and shear strains. The Maximum Principal Strain (MPS) can then be determined from the equation, MPS =xx+yy 2+sxxyy 22 +xy 22 ; (/four.pnum) whereMPS represents the maximum principal strain. The averaged MPS response across the /four.pnum triangular elements were then used to determine the strain response at the centre of the tissue simulant block. The averaged MPS response was determined and reported for each drop event and was used to draw comparisons of marker in/uniFB02uence on the tissue simulant deformation across the samples. /three.pnum Results The strain response data are shown separately for each embedded marker type and orientation. The base- line response of the tissue simulant from each drop, which was tracked using massless markers, is shown in Fig. /four.pnum. Each solid curve in this /uniFB01gure represents the average strain values determined from a single drop test, while the dashed curve represents the average response of all drop tests recorded. The massless marker system exhibited multiple identi/uniFB01able strain maxima and minima in the /uniFB01rst /four.pnum/zero.pnum ms following im- pact, the timing and shape of which were consistent across the three tests conducted. The variability of the strain measurement within the /uniFB01rst two peaks were particularly minimal, but diverged to a greater ex- tent after /two.pnum/five.pnum ms. These results demonstrate the high level of reproducibility between the drop tests. The average response curve in Fig. /four.pnum will be used as a comparison basis against the other embedded markers tested to determine their interference in the natural deformation response of the tissue simulant. Devi- ations from this average massless marker response will be interpreted as evidence of embedded marker interference. The strain responses measured with the NDTs (Hardy et al., /two.pnum/zero.pnum/zero.pnum/one.pnum, /two.pnum/zero.pnum/zero.pnum/seven.pnum) are shown separately for NDTs mounted in a horizontal (Fig. /five.pnuma), vertical (Fig. /five.pnumb), and transverse (Fig. /five.pnumc) orientation and were compared to the baseline response of the tissue simulant matrix. The strain response of the matrix with embedded NDTs had the same general shape as its baseline response, although the amplitudes of the peak strains varied appreciably, particularly in the vertical and transverse orientations. The NDTs consistently damped the initial strain peak in the matrix, underestimating it, and then rebounded in a manner that extended the tensile strain in the matrix at the second peak. Subsequent peaks were inconsistent with the matrix response both temporally and in terms of strain magnitudes. The overall interference of the NDTs in the natural response of the tissue simulant matrix was strongly directionally dependent. /six.pnum Massless Marker -10-5 020 Maximum Principal Strain (%) 15 510 Time (ms) 10 20 30 40 Average Massless Figure /four.pnum: The maximum principal strain response measured from the baseline massless markers for three separate drop impacts. An averaged response of the massless markers is shown as a dashed line. The SMCs (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum) were investigated in several con/uniFB01gurations, one of which did not include wiring and two that included wiring in two di/uniFB00erent orientations. In PMHS experiments, these crys- tals were wired to a diagnostic setup (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum), so the in/uniFB02uence of the wiring on the tissue simulant matrix deformation is of considerable importance. The performance of the SMCs them- selves, without wiring or barbs, are provided in Fig. /six.pnuma. The strain response with these crystals was similar to that of the NDTs, where the /uniFB01rst strain peak was notably damped by the presence of the crystals, but then the subsequent strain peak had extended the tensile strain in the matrix. With the addition of the wiring, the response became considerably anisotropic, having a directionally dependent response. With the wire oriented in the vertical direction (Fig. /six.pnumb), the same damped response of the /uniFB01rst peak and ex- tension of the second peak was observed as it had been for the crystal without a wire (Fig /six.pnuma). One major change in the response of the matrix deformation with a crystal having a vertically-oriented wire was seen beyond /two.pnum/zero.pnum ms, where the presence of the wire damped the further motion of the matrix. For the SMC, hav- ing wires oriented in the horizontal direction (Fig. /six.pnumc), the response of the matrix was completely altered, changing the frequency of the strain response and damping many of the strain peaks. The strain responses measured with tin markers (Guettler, /two.pnum/zero.pnum/one.pnum/seven.pnum) are shown in Fig. /seven.pnum. These tin markers resulted in a deformation response of the tissue-simulant matrix with the highest degree of magnitude variability. The same general trends of a damped /uniFB01rst strain peak and over-extended tensile deformation at the second peak. The /uniFB01nal marker that was tested was the Carleton Elastomeric Marker (Dutrisac, /two.pnum/zero.pnum/two.pnum/zero.pnum), the results for which are shown in Fig. /eight.pnum. The tissue simulant matrix response with this embedded marker was extremely similar to the natural response of the matrix, exhibiting a similar level of scatter around the baseline average strain values. The measured strain response in the tissue simulant matched the shapes and magnitudes of the peak strain values of the neat materials for the entire observation window. The only clear di/uniFB00erence in the response of the matrix using this embedded marker was a time shift of the tertiary strain peaks that appeared /two.pnum/two.pnum ms following the impact. This marker resulted in the lowest variability in its measured strain response among the markers investigated. /four.pnum Discussion As a /uniFB01rst order comparison of the interference of the various embedded markers in the deformation of the tissue simulant, the /uniFB01rst and second peaks strain values (occurring at approximately /five.pnum ms and /one.pnum/five.pnum ms, respectively) are shown in a series of bar charts Fig. /nine.pnuma and Fig. /nine.pnumb, respectively. This comparison illustrates the variability of the deformation measured in comparison to the neat matrix, as well as the directionality of this interference. None of the markers used in prior PMHS studies lay consistently within the strain bounds of the response of the neat matrix tracked using massless markers. The only marker that provided a similar response, with identical bounds of performance were the Carleton Embedded Markers, which were designed based on the guidance a parametric study of optimal material properties (Dutrisac et al., /seven.pnum 40 NDT (Horizontal Orientation) -10-5 020 Maximum Principal Strain (%) 15 510 Time (ms) 10 20 30 Average Massless (a) NDT (Transverse Orientation) -10-5 020 Maximum Principal Strain (%) 15 510 Time (ms) 10 20 30 40 Average Massless (c)NDT (Vertical Orientation) -10-5 020 Maximum Principal Strain (%) 15 510 Time (ms) 10 20 30 40 Average Massless (b)Figure /five.pnum: The maximum principal strain response measured from the motion of the NDT markers used by Hardy et al. (Hardy et al., /two.pnum/zero.pnum/zero.pnum/one.pnum, /two.pnum/zero.pnum/zero.pnum/seven.pnum) for three separate drop impacts in (a) a horizontal orientation; (b) a vertical orientation; and (c) a transverse orientation. The averaged response of the massless markers from Fig. /four.pnum is included as a dashed line for comparison. nd). The parametric study of optimal material properties found that the ideal range of marker sti/uniFB00ness in- volved an elastic modulus of less than /one.pnum MPa and a suggested marker-to-tissue density ratio of below /eight.pnum Sonomicrometry Crystal (Horizontal Wire) -10-5 020 Maximum Principal Strain (%) 15 510 Time (ms) 10 20 30 40 Average Massless (c)(b)Sonomicrometry Crystal (Vertical Wire) -10-5 020 Maximum Principal Strain (%) 15 510 Time (ms) 10 20 30 40 Average Massless Sonomicrometry Crystal (No Wire) -10-5 020 Maximum Principal Strain (%) 15 510 Time (ms) 10 20 30 40 Average Massless (a)Figure /six.pnum: The maximum principal strain response measured from the motion of the sonomicrometry crys- tals used by Al-Shareef et al. (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum) for three separate drop impacts with (a) crystals having no wire; (b) crystals having vertical wires; and (c) crystals having horizontal wires. The averaged response of the massless markers from Fig. /four.pnum is included as a dashed line for comparison. /one.pnum./seven.pnum (Dutrisac et al., nd). Embedded markers outside of these ranges were found to deviate considerably from the response of non-inertial markers. Those /uniFB01ndings were consistent with the observations made in this dataset. /nine.pnum Tin Marker -10-5 020 Maximum Principal Strain (%) 15 510 Time (ms) 10 20 30 40 Average Massless Figure /seven.pnum: The maximum principal strain response measured from the motion of the tin granule markers used by Guettler (Guettler, /two.pnum/zero.pnum/one.pnum/seven.pnum) for three separate drop impacts. The averaged response of the massless markers from Fig. /four.pnum is included as a dashed line for comparison. Carleton Elastomeric Marker -10-5 020 Maximum Principal Strain (%) 15 510 Time (ms) 10 20 30 40 Average Massless Figure /eight.pnum: The maximum principal strain response measured from the motion of the Carleton Elastomeric Markers designed based on the marker design sensitivity study by Dutrisac et al. (Dutrisac et al., nd) for three separate drop impacts. The averaged response of the massless markers from Fig. /four.pnum is included as a dashed line for comparison. /one.pnum/zero.pnum Massless NDT - Vert. NDT - Horiz. NDT - Trans. SonoCrystal - No Wire SonoCrystal - Vert. Wire SonoCrystal - Horiz. Wire Tin Marker Carleton Elastomeric Marker 4 2614 0(b) Second Peak Comparison Average Response of Massless Marker Maximum Principal Strain (%) 12 10 8Massless NDT - Vert. NDT - Horiz. NDT - Trans. SonoCrystal - No Wire SonoCrystal - Vert. Wire SonoCrystal - Horiz. Wire Tin Marker -2 -1 -3 -4 0(a) First Peak Comparison Average Response of Massless Marker Maximum Principal Strain (%) Carleton Elastomeric Marker Figure /nine.pnum: A bar chart comparison of the measured strains using the various embedded markers for the (a) /uniFB01rst strain peak and (b) second strain peak. The dashed line represents the average value taken from the massless marker data shown in Fig /four.pnum. /one.pnum/one.pnum The NDTs had a density of /one.pnum./five.pnum g/cm3, an elastic modulus of approximately /two.pnum/zero.pnum/zero.pnum MPa (based on the polyethy- lene exterior), and an length-to-diameter aspect ratio of /two.pnum./five.pnum (Hardy et al., /two.pnum/zero.pnum/zero.pnum/one.pnum, /two.pnum/zero.pnum/zero.pnum/seven.pnum). While the NDTs were within the optimal density range, the high sti/uniFB00ness of these markers resulted in signi/uniFB01cant interference in the deformation pattern of the tissue simulant (Fig. /five.pnum). Furthermore, the variability of the strain response in the three orientations tested was due to a combination of their aspect ratio and the anisotropy in the sti/uniFB00ness of the NDTs along the di/uniFB00erent axes. The block used in the horizontal and vertical orientations was the same block of simulant rotated /nine.pnum/zero.pnum degrees, so these di/uniFB00erences were not related to manufactur- ing variability. As a result, the strain response measured using this marker was highly dependent on its orientation, a variability that must be considered in the analysis and implementation of this dataset into future FE model validation. The SMCs (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum) had a density of /one.pnum./one.pnum/three.pnum g/cm3, an elastic modulus of approximately /one.pnum/zero.pnum MPa, an aspect ratio of unity, and the addition of wiring. While the density of these markers was also within the recommended range, their sti/uniFB00ness was higher than the recommended marker sti/uniFB00ness bound (Dutrisac et al., nd). This high sti/uniFB00ness explains the interference of these markers in the deforma- tion of the tissue simulant seen in Fig. /six.pnuma, which was similar to the interference of the NDTs. While the aspect ratio of the markers themselves was /one.pnum for this investigation, these crystals have previously been used in a barbed con/uniFB01guration (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum) which may result in a directionally-dependent interference in tissue deformation, although this has not been quanti/uniFB01ed in the present work. That being said, the present work did investigate the in/uniFB02uence of the wires attaching to these crystals, which are re- quired for their operation (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum). The wires were able to slide easily within paths made for them, but despite this ease of motion, the presence of horizontal wires completely changed the deformation pattern in the tissue simulant (Figs. /six.pnuma and /six.pnumb). Once again, the same test assembly was used in both orientations to ensure that the results were not due to any variability in sample construction, yet the directional in/uniFB02uence of the wires on the deformation of the brain simulant was pronounced. The tin markers had a density of /seven.pnum./three.pnum g/cm3, an elastic modulus of approximately /four.pnum/one.pnum./six.pnum GPa, and an aspect ratio of unity (Guettler, /two.pnum/zero.pnum/one.pnum/seven.pnum). While they were extremely small to reduce their inertia, this did not prevent their in/uniFB02uence on the dynamic deformation of the tissue simulant (Fig. /seven.pnum). This in/uniFB02uence appeared to be the result of a competition between the damping response of their high density and the in/uniFB02uence of their sti/uniFB00ness on the deformation of the tissue simulant, which was consistent with prior observations (Dutrisac et al., nd). The competition between the role of density and sti/uniFB00ness in interfering with the deformation of the tissue simulant was likely a factor in the higher strain variability in this dataset, compared to that of other markers. The Carleton Elastomeric Markers had a density of /one.pnum./six.pnum g/cm3, an elastic modulus of approximately /one.pnum/two.pnum kPa, and an aspect ratio of unity. These markers are at the edge of the acceptable density range, but within the recommended sti/uniFB00ness range (Dutrisac et al., nd). The interference between these markers and the matrix tissue simulant was minimal (Fig. /eight.pnum). These markers o/uniFB00ered the best performance of the marker designs investigated with strain /uniFB01eld bounds that perfectly matched those of the baseline test system and were designed for future use in PMHS experiments. These results reinforce the concept that the accuracy of dynamic deformation measurements is not only guided by the precision of a measurement, but the interference of the technique on the measurement. The introduction of an inertially signi/uniFB01cant target within a material will a/uniFB00ect the deformation of the matrix it is embedded within. Ensuring lack of marker migration is only one consideration in the dynamic coupling of a material. Under quasi-static conditions, proper coupling of a gauge to a material will ensure that the two materials experience the same strains. In dynamic conditions, a large disparity in the marker and matrix sti/uniFB00nesses will result in an associated strain disparity that will change the dynamic response of the matrix. Future PMHS studies observing dynamic tissue deformation should focus on the use of freely suspended, neutral density, and neutral sti/uniFB00ness markers (e.g., Carleton Elastomeric Marker) with an aspect ratio of unity to ensure uniform and minimal interference tracking of tissue deformation. Given the similarity of the material properties of brain tissue and the tissue simulant used in this research, we expect that these results would accurately inform the marker response within PMHS brain tissue. From an FE model validation perspective, the results demonstrate that the existing PMHS datasets have inher- ent directionally-dependent biases that must be accounted for in future validation work. The embedded markers that have thus far been used in PMHS brain motion studies were likely to have interfered with the dynamic tissue response of the PMHS brains. This interference resulted in measurement inaccuracies and uncertainties that have yet to be considered or fully quanti/uniFB01ed, but are more signi/uniFB01cant than the tracking precision of any individual method. Due to the anisotropic interaction between the markers and the tis- /one.pnum/two.pnum sues, care must be taken to properly account for these biases inherent in the existing three-dimensional datasets to recover an adequate representation of the natural deformation response of brain tissues. While the di/uniFB00erences in strain predictions made with various FE models are notable (Beckwith et al., /two.pnum/zero.pnum/one.pnum/eight.pnum), per- haps these di/uniFB00erences may be at least partially explained by these issues of accuracy and directional bias of the interference of embedded markers on the tissue deformation captured in the existing datasets (Fig. /nine.pnum). Properly accounting for the true anisotropic accuracies of existing PMHS data will be necessary to maintain con/uniFB01dence in the validation of FE model strain predictions. /five.pnum Acknowledgments The authors thank Sheng Xu and Jennifer Rovt for their insights and useful feedback on the experiment and its interpretation, and MacKenzie Brannen for assistance with specimen preparation. This work was funded by the CIHR and NSERC through the Collaborative Health Research Program (CPG-/one.pnum/five.pnum/one.pnum/nine.pnum/six.pnum/seven.pnum). The high-speed camera was purchased with funds from the Canada Foundation for Innovation and Ontario Research Fund (Project /three.pnum/two.pnum/nine.pnum/three.pnum/three.pnum). SD received funding through the Ontario Graduate Scholarship.