Datasets obtained from cadaveric experimentation are broadly used in validating /uniFB01nite element mod- els of head injury. Due to the complexity of such measurements in soft tissues, experimentalists have relied on tissue-embedded radiographic or sonomicrometry tracking markers to resolve tissue motion caused by impulsive loads. Dynamic coupling of markers with the surrounding tissue has been a previ- ous concern, yet a thorough sensitivity investigation of marker in/uniFB02uences on tissue deformation has not been broadly discussed. Technological improvements to measurement precision have bolstered con/uniFB01- dence in acquired data, however precision is often con/uniFB02ated with accuracy; the inclusion of markers in the tissue may alter its natural response, resulting in a loss of accuracy associated with an altered displacement /uniFB01eld. To gain an understanding of how marker properties may in/uniFB02uence the measured re- sponse to impact, we prepared a set of nine marker designs using a Taguchi L/nine.pnum array to investigate marker design choice sensitivity. Each of these designs was cast into a block of tissue simulant and subjected to repeated drop tests. Vertical displacement was measured and compared to the response of the neat material, which contained massless tracking markers. Medium density and medium sti/uniFB00ness markers yielded the least deviation from the neat material response. The results provide some design guidelines indicating the importance of maintaining marker matrix density ratio below /one.pnum./seven.pnum/five.pnum and marker sti/uniFB00ness below /one.pnum./zero.pnum MPa. These properties may minimize marker interference in tissue deformation. Overall, em- bedded marker properties must be considered when measuring the dynamic response of tissue. /one.pnum Introduction Optical measurements of deformation are becoming more prevalent in experimental mechanics as full-/uniFB01eld strain measurements can be acquired with minimal sample contact (Palanca et al., /two.pnum/zero.pnum/one.pnum/six.pnum). Digital image correlation is a technique that involves tracking the motion of speckle patterns to determine displacement and deformation /uniFB01elds on a deforming body (Chu et al., /one.pnum/nine.pnum/eight.pnum/five.pnum; Schreier et al., /two.pnum/zero.pnum/zero.pnum/nine.pnum). These speckle patterns have primarily consisted of black paint on a white background for optimal contrast. However, some studies have used /uniFB02uorescence (Hu et al., /two.pnum/zero.pnum/one.pnum/eight.pnum), epoxy markers (Lauret et al., /two.pnum/zero.pnum/zero.pnum/nine.pnum), and cellular features (Meijer- ing et al., /two.pnum/zero.pnum/one.pnum/two.pnum) for tracking displacements of biological tissues. Where spatial resolution or experimental limitations dictate the need for a reduced marker or speckle number density, individual particle tracking algorithms can also be used to determine deformation and strain /uniFB01elds (Li et al., /two.pnum/zero.pnum/one.pnum/six.pnum). Due to the nature of these optical methods, this area of research is often concerned with surface deformations, as trackable patterns can only be applied to the surface of a body. This has led to the use of markers that are essen- tially massless. The massless marker is one whose inertia will not in/uniFB02uence the deformation process of the specimen subjected to dynamic loading. In specimens with internal, and consequently visually inaccessible, regions of interest, particle tracking techniques have been applied using radiographic markers embedded within the region (Karrholm et al., /two.pnum/zero.pnum/zero.pnum/six.pnum). Radiographic imaging has been used to evaluate displacement and deformation within optically opaque materials (Synnergren et al., /one.pnum/nine.pnum/nine.pnum/nine.pnum). Under radiographic imaging, markers require su/uniFB03cient den- sity to be radiopaque; however, the concern is that marker inertia is no longer negligible when tracking 1 deformation under dynamic loading events (Hardy et al., /two.pnum/zero.pnum/zero.pnum/seven.pnum; Whyte et al., /two.pnum/zero.pnum/one.pnum/nine.pnum). A recent study high- lighted that the post-impact migration of markers within brain tissue is a valid concern (Whyte et al., /two.pnum/zero.pnum/one.pnum/nine.pnum). While ensuring proper coupling of the markers to surrounding materials and negligible marker migration is important, the lack of marker migration is not necessarily a measure of ideal dynamic coupling. Prior designs of embedded markers were selected in an e/uniFB00ort to minimize di/uniFB00erences in inertia, either through optimizing marker density (Hardy et al., /two.pnum/zero.pnum/zero.pnum/seven.pnum; Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum) or minimizing the overall marker mass (Guettler, /two.pnum/zero.pnum/one.pnum/seven.pnum). Other approaches to marker tracking within brain tissues have included sti/uniFB00, low density sonomicrometry crystals to improve marker tracking precision (Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum). However, marker tracking precision does not guarantee the /uniFB01delity of dynamic marker coupling or the accuracy of a tissue deformation measurement, as the presence of the markers can signi/uniFB01cantly change the response of the surrounding tissues during dynamic events. It is important to quantify and ideally minimize the error associated with introducing markers into tissue as cadaveric data are used extensively in the validation of computational head injury models (Zhou et al., /two.pnum/zero.pnum/one.pnum/nine.pnum; Zhao and Ji, /two.pnum/zero.pnum/two.pnum/zero.pnum). While marker inertia is certainly an important property to consider, particularly for capturing realistic rigid body motion, it is not the only parameter of importance in a dynamic loading event. Any physical perturba- tion to a deformable body (e.g., brain tissue) will propagate as a series of perturbations, as per elastic wave theory (Meyers, /one.pnum/nine.pnum/nine.pnum/four.pnum). This is true regardless of the source of the impulsive load; both direct impacts and rigid body skull rotations generate perturbations in the tissue. To this point, the introduction of a simple constitutive material model into the equation of momentum conservation will result in a restatement of the familiar Newton’s second law as the wave equation, described by the expression, u=E r2u; (/one.pnum) where uis the second time derivative of position, r2is the Laplacian operator, Eandare the elastic modulus and density of the material, respectively. From this consideration, three design parameters may have an in/uniFB02uence on the time-dependent elastic response of the marker-tissue system: density, elastic modulus (i.e., sti/uniFB00ness), and spatial distribution. The di/uniFB00erences in both density and elastic moduli of the markers and their surrounding matrix will be important design factors in minimizing the interference of embedded markers in the deformation of surrounding tissue. Additionally, the spatial distributions of markers relate to the volume and mass fraction of the marker-type material in the surrounding matrix, causing local di/uniFB00erences in both the density and sti/uniFB00ness of the matrix. While density (Al-Bsharat et al., /one.pnum/nine.pnum/nine.pnum/nine.pnum; Hardy et al., /two.pnum/zero.pnum/zero.pnum/one.pnum, /two.pnum/zero.pnum/zero.pnum/seven.pnum) and marker mass (Guettler, /two.pnum/zero.pnum/one.pnum/seven.pnum) have been considered in prior designs of embedded markers, marker sti/uniFB00ness and the spacing between markers have not been broadly examined and deserve consideration. This study was designed to provide a systematic analysis of the in/uniFB02uence of marker density, sti/uniFB00ness, and pattern spacing on the deformation /uniFB01eld in a tissue simulating material. A Taguchi L/nine.pnum array (Shi et al., /two.pnum/zero.pnum/one.pnum/four.pnum) was used to develop nine unique marker designs using these three design variables. Each variable was tested at three values, corresponding to minimum, maximum, and mid-range quantities considered for a Post-Mortem Human Subject (PMHS) head impact study, a range developed after considering past PMHS studies (Hardy et al., /two.pnum/zero.pnum/zero.pnum/seven.pnum; Iwaskiw et al., /two.pnum/zero.pnum/one.pnum/eight.pnum; Al-Bsharat et al., /one.pnum/nine.pnum/nine.pnum/nine.pnum; Hardy et al., /two.pnum/zero.pnum/zero.pnum/one.pnum; Guettler, /two.pnum/zero.pnum/one.pnum/seven.pnum; Alshareef et al., /two.pnum/zero.pnum/one.pnum/eight.pnum, /two.pnum/zero.pnum/two.pnum/zero.pnum). To evaluate the new markers, the impact-induced displacement response of a tissue-simulating material containing massless markers was compared to that of the same simulant material containing the embedded markers. The objective of this investigation was to identify the in/uniFB02uence of mechanical properties of markers on the observed response of tissues, providing guidance for future marker design. /two.pnum Experimental Methods To gain an understanding of the sensitivity of a broader set of parameters that in/uniFB02uence tissue motion track- ing /uniFB01delity of embedded markers, we prepared a matrix of design parameters using a Taguchi L/nine.pnum array (Shi et al., /two.pnum/zero.pnum/one.pnum/four.pnum; Rao et al., /two.pnum/zero.pnum/zero.pnum/eight.pnum). The experimental markers were prepared according to speci/uniFB01ed variations in density and elastic modulus (E). The experimental markers were arranged in a grid pattern, with a speci/uniFB01c inter-marker spacing, cast along a single midplane of a tissue-simulant (Medical Gel #/four.pnum, Humimic Medical, Greenville, SC) block (Fig. /one.pnum). The inter-marker spacing variations replicate the range of spacing patterns achievable for ex vivo ,in situ insertion for a related PMHS study. The gel blocks and marker sets were /two.pnum dropped from a /uniFB01xed height onto an impact surface to generate displacement /uniFB01elds at strain rates similar to those achieved in PMHS impact testing (/one.pnum/zero.pnum1s1) (Hardy et al., /two.pnum/zero.pnum/zero.pnum/seven.pnum; Zhou et al., /two.pnum/zero.pnum/one.pnum/nine.pnum). The gel blocks were cast within a mould measuring /one.pnum/five.pnum/two.pnum mm /one.pnum/five.pnum/two.pnum mm/four.pnum/five.pnum mm. These block dimensions were chosen in order to maximize the test region given the limitations of the imaging and drop-testing systems available at the time of testing. A total of /one.pnum/zero.pnum blocks were prepared, one for each of the nine new marker designs and one for an ink-based marker (Table /one.pnum). The ink-based markers, which were essentially massless, were used to evaluate the response of the neat material. These massless markers did not have any X-ray attenuating properties and were observed optically during experimentation with a high-speed camera. /two.pnum./one.pnum Marker Preparation The nine unique new markers were blends of a powdered contrast agent and a variety of elastomeric binders, which were used to achieve the desired material properties. All markers were cast using the same precision machined aluminum mould, producing a sheet of elastomeric radiopaque material, from which /two.pnum mm diameter, /two.pnum mm long cylindrical markers protruded. All markers were given an aspect ratio of /one.pnum; the e/uniFB00ects of marker aspect ratio on the directionality of marker displacement was not investigated in the present work. Marker size and shape was chosen to provide clarity in imaging, and ease of manufac- turing and manipulation. Barium sulfate (BaSO 4) was used as the contrast agent, as it is readily available in powdered form and suspends well into binder materials. At the X-ray power levels used in diagnostic imaging (/two.pnum/five.pnum-/one.pnum/five.pnum/zero.pnum keV), BaSO 4has a high mass attenuation coe/uniFB03cient (/one.pnum/zero.pnum </</one.pnum/zero.pnum/zero.pnum cm2/g) (Seltzer, /one.pnum/nine.pnum/nine.pnum/five.pnum) for a material of its density (/four.pnum./five.pnum g/cm3), and as such is commonly used in diagnostic X-ray imaging. Three di/uniFB00erent elastomeric binders were used to develop high, medium, and low sti/uniFB00ness markers. The sti/uniFB00est binder material was a /one.pnum:/one.pnum blend of Sylgard /one.pnum/eight.pnum/four.pnum and /five.pnum/two.pnum/seven.pnum (Dow Inc., E = /eight.pnum/three.pnum/zero.pnum kPa), the intermediate sti/uniFB00ness binder was a /one.pnum:/five.pnum blend of Sylgard /one.pnum/eight.pnum/four.pnum and /five.pnum/two.pnum/seven.pnum (E = /one.pnum/three.pnum/zero.pnum kPa)(Palchesko et al., /two.pnum/zero.pnum/one.pnum/two.pnum). The least sti/uniFB00 binder was the same thermoplastic gel used in the tissue-simulant blocks (Gel #/four.pnum, Humimic Medical) with an estimated E/nine.pnum kPa. This value for elastic modulus was calculated (Larson, /two.pnum/zero.pnum/one.pnum/seven.pnum) from the manufacturer supplied durometer of /one.pnum/one.pnum./eight.pnum (Shore /zero.pnum/zero.pnum) using the expression, E= 0:0037e0:0718s; (/two.pnum) whereEis elastic modulus (MPa) and sis durometer (Shore /zero.pnum/zero.pnum). The estimated elastic modulus is consis- tent with similar conversions found in past tissue studies (Li et al., /two.pnum/zero.pnum/one.pnum/five.pnum). Once placed in the mould, uncured marker preparations were degassed at 29mmHg to remove small air bubbles. Markers with Sylgard-based binders were cured at room temperature, while the thermoplastic gel markers were brought to their melt temperature during casting and allowed to cool at room tempera- ture. Variations in density were achieved by adjusting the mass ratio of elastomer binder to contrast agent. Given the random orientation of the BaSO 4particles in the elastomer matrices, the elastic moduli of the re- sulting composites were calculated with the Reuss mixture model (Meyers and Chawla, /two.pnum/zero.pnum/zero.pnum/nine.pnum). The mixture model indicates an average increase in moduli of /three.pnum/zero.pnum %for the composite material. Despite this increase, sti/uniFB00ness design parameter steps remained valid as they increased /one.pnum/zero.pnum-fold over each other, maintaining a wide parameter space. The levels of density that were investigated were /one.pnum./zero.pnum/five.pnum, /one.pnum./four.pnum/five.pnum, and /one.pnum./eight.pnum/five.pnum g/cm3, com- pared to a density of /zero.pnum./eight.pnum/five.pnum g/cm3for the neat gel block material. Given the volume of these markers of /six.pnum./three.pnum103cm3, corresponding marker masses were /six.pnum./six.pnum mg, /nine.pnum./one.pnum mg, and /one.pnum/one.pnum./six.pnum mg, respectively. The levels of sti/uniFB00ness that were investigated were /one.pnum/two.pnum, /one.pnum/seven.pnum/zero.pnum, and /one.pnum/one.pnum/zero.pnum/zero.pnum kPa, compared to a sti/uniFB00ness of /nine.pnum kPa in the gel block material, which is comparable to the sti/uniFB00ness of brain tissue (Budday et al., /two.pnum/zero.pnum/one.pnum/five.pnum). A summary of the marker designs, their mechanical properties, and preparation variations are provided in Table /one.pnum. To produce the thermoplastic gel test blocks, two identical reusable square moulds prepared from a /one.pnum:/one.pnum blend of Sylgard /one.pnum/eight.pnum/four.pnum and /five.pnum/two.pnum/seven.pnum were cast using a mould constructed of medium density /uniFB01breboard (MDF). These elastomeric moulds were preferred for sample preparation due to the heat resistance of the ther- moset material. For each block, new tissue-simulating gel was melted completely by heating to /one.pnum/six.pnum/zero.pnumC. The liquid gel was degassed in a vacuum oven to 29mmHg to remove entrapped air, then poured into moulds, stopping at the half-way mark in order to create the marker plane. Once the half-/uniFB01lled blocks were set, a printed grid pattern, corresponding to the spacing level of interest for each design, was transferred to the marker plane with ink. Markers were placed on top of the pattern. The massless markers were created by drawing approximately /two.pnum./five.pnum mm diameter circles with an alcohol-based permanent marker at a pattern spacing of /one.pnum/zero.pnum mm. The negligible density of these markers permitted them to be slightly larger than the /three.pnum 40 mm Marker PlaneFigure /one.pnum: Top and front photographic views of the neat material block (massless markers) mounted inside the drop housing. Marker plane indicated with dashed line. Central region used for analysis is within dashed circle. /four.pnum Table /one.pnum: Summary of Taguchi L/nine.pnum marker designs used in the present study. Marker Design Density (g=cm3) Spacing ( cm) Sti/uniFB00ness ( kPa ) Binder Material /one.pnum /one.pnum./zero.pnum/five.pnum /one.pnum./zero.pnum /one.pnum/two.pnum Humimic #/four.pnum /two.pnum /one.pnum./zero.pnum/five.pnum /one.pnum./five.pnum /one.pnum/seven.pnum/zero.pnum Sylgard /one.pnum:/five.pnum blend /three.pnum /one.pnum./zero.pnum/five.pnum /two.pnum./zero.pnum /one.pnum/one.pnum/zero.pnum/zero.pnum Sylgard /one.pnum:/one.pnum blend /four.pnum /one.pnum./four.pnum/five.pnum /one.pnum./zero.pnum /one.pnum/seven.pnum/zero.pnum Sylgard /one.pnum:/five.pnum blend /five.pnum /one.pnum./four.pnum/five.pnum /one.pnum./five.pnum /one.pnum/one.pnum/zero.pnum/zero.pnum Sylgard /one.pnum:/one.pnum blend /six.pnum /one.pnum./four.pnum/five.pnum /two.pnum./zero.pnum /one.pnum/two.pnum Humimic #/four.pnum /seven.pnum /one.pnum./eight.pnum/five.pnum /one.pnum./zero.pnum /one.pnum/one.pnum/zero.pnum/zero.pnum Sylgard /one.pnum:/one.pnum blend /eight.pnum /one.pnum./eight.pnum/five.pnum /one.pnum./five.pnum /one.pnum/two.pnum Humimic #/four.pnum /nine.pnum /one.pnum./eight.pnum/five.pnum /two.pnum./zero.pnum /one.pnum/seven.pnum/zero.pnum Sylgard /one.pnum:/five.pnum blend Massless /zero.pnum /one.pnum./zero.pnum /zero.pnum n/a embedded markers, allowing them to be seen more clearly in optical imagery. To avoid deformation of the marker plane due to material melting or creep during the casting of the second half of the encasing thermoplastic block, this preparation was placed in a freezer at a temperature of -/one.pnum/eight.pnumC for a minimum of /three.pnum/zero.pnum minutes before the remainder of the mould was /uniFB01lled. Completed blocks were left to set at room tem- perature and inspected for seams, voids, or material inhomogeneity due to the casting process. Following inspection, each specimen was wrapped in plastic and shelved to avoid indentation, creep, or compres- sion. The Sylgard moulds were kept and later used to house each block within a drop apparatus for impact testing. /two.pnum./two.pnum Drop Testing To evaluate the dynamic response of the markers within the gel block, each specimen was mounted in a custom housing which was subsequently subjected to three drops onto a rigid steel anvil. A small custom drop tower was constructed for this purpose (Fig. /two.pnum). The custom housing was used to protect against boundary damage in order to facilitate multiple tests. Each block was inserted back into one of the two identical Sylgard moulds (encasements) used in the casting process. This assembly was then sandwiched between two /six.pnum./four.pnum-mm-thick acrylic plates and fastened at the corners with bolts (Fig. /one.pnum). The acrylic housing ensured that the blocks would not buckle out of plane or slide during impact. In order to provide consistent boundary conditions for each drop test, the distance between the acrylic sheets was maintained at /four.pnum/one.pnum mm, resulting in a controlled, pre-strained condition. The drop carriage on the drop tower was hoisted manually and /uniFB01xed in place by an electromechanical latch at the maximum achievable system height of /seven.pnum/six.pnum./five.pnum cm and the specimens were dropped onto a rigid steel anvil. Following each drop, the samples and housing were inspected for damage and reset to the drop position. An electronic triggering system was used to coordinate the drop with the image capture system, allowing the recording of block motion from /five.pnum/zero.pnum ms before and /one.pnum/three.pnum/zero.pnum ms after impact. The purpose of the drop impact was simply to generate a reproducible dynamic loading event in the range of /one.pnum/zero.pnum1s1, which is consistent with many PMHS studies (Hardy et al., /two.pnum/zero.pnum/zero.pnum/seven.pnum; Zhou et al., /two.pnum/zero.pnum/one.pnum/nine.pnum), but was not meant to replicate any speci/uniFB01c impact event. Each marker assembly was dropped three times to ensure reproducibility of the results. /two.pnum./three.pnum Data Collection Impact image sequences were captured using the HSXR system at Carleton University at a rate of /seven.pnum,/five.pnum/zero.pnum/zero.pnum fps. The resultant scale between camera and experiment was /three.pnum./four.pnum /zero.pnum./one.pnum/seven.pnum px/mm. The neat material block was tested using the same drop procedure, however as its markers do not attenuate X-rays, particle motion was acquired using a high-speed optical camera at the same capture rate. Refractive and re/uniFB02ective distortion of the optical signal through the gel was mitigated with the use of the acrylic housing; after inspection of the source video, this phenomenon had a negligible e/uniFB00ect on the tracked motion of markers. Images were processed to improve contrast and a correction to the lens distortion was applied. A custom particle tracking code (Dutrisac, /two.pnum/zero.pnum/two.pnum/zero.pnum) was written in MATLAB to extract the displacement of markers and housing features from collected image sequences. To avoid con/uniFB02ation of internal deformation with rigid body impact motion, portions of the external hous- ing were tracked across the time series and used to determine both the moment of impact and rebound /five.pnum Latch Rigid frame Drop carriage Specimen block Sylgard encasement Observation area AnvilAcrylic housingFigure /two.pnum: Front and right-section schematic views of the drop tower used in the study. Impact observation zone is denoted with a dashed line. Maximum drop height: /seven.pnum/six.pnum./five.pnum cm. /six.pnum dynamics of each sample. For each drop, the rebound rate was linear over the /two.pnum/five.pnum/zero.pnum frame (/three.pnum/three.pnum ms) period of interest, at /zero.pnum./one.pnum/one.pnum /zero.pnum./zero.pnum/one.pnum mm/frame. While the internal deformation occurred within the moving frame of reference, this rebounding rate was common across all test iterations, permitting the comparison of deformation responses. The cohesion of the marker motion tended to dissipate into the second period of the oscillation (t >/two.pnum/five.pnum ms), reducing repeatability at later times. For this study, the /uniFB01rst and second peaks of the /uniFB01rst period response were used as the basis of comparison across all specimens, as the data was both cohesive and relevant to tissue-based impact studies(Hardy et al., /two.pnum/zero.pnum/zero.pnum/seven.pnum, /two.pnum/zero.pnum/zero.pnum/one.pnum). The /uniFB01rst peak represents the compressive phase fol- lowing impact, and the second peak represents the relaxation and release of stored elastic energy following compression. For the sensitivity analysis, normalized output values were necessary (Shi et al., /two.pnum/zero.pnum/one.pnum/four.pnum). These output values ( ) are de/uniFB01ned as, = t n n100; (/three.pnum) where nand tare the measured values of the displacements for the neat material and marker-embedded material, respectively. The output value provides a measure of deviation, as caused by the presence of a marker particle. These output values ( ) were subsequently used in the Taguchi signal-to-noise function to make comparisons across the experimental group (Shi et al., /two.pnum/zero.pnum/one.pnum/four.pnum). /two.pnum./four.pnum Analysis The Taguchi approach to experimentation was used to reduce the number of specimen iterations required to determine parameter sensitivity(Shi et al., /two.pnum/zero.pnum/one.pnum/four.pnum; Rao et al., /two.pnum/zero.pnum/zero.pnum/eight.pnum). The Taguchi orthogonal array provides a method of combining variable adjustments across individual experimental trials, as shown in the marker design parameters in Table /one.pnum. This method has seen broad uptake in many /uniFB01elds, including the biomedical and clinical research /uniFB01elds to reduce the burden of experimental cost and supply limitations (Rao et al., /two.pnum/zero.pnum/zero.pnum/eight.pnum). In order to separate the valuable data from the noise in/uniFB02uence, the analysis uses signal-to-noise ratios (SNr ) as a measure of experimental output due to varying design parameters. SNr calculations can focus on a nominal value, a lowest-is-best, or a largest-is-best output. In the case of this study, the largest-is-best evaluation was used, meaning that a large SNr corresponds to a good match between the neat material and the experimental material response. In this case, SNr is given by, SNr =10 log10" 1 n nX i=1 2 i!# ; (/four.pnum) where is the measured output for each experiment, SNr is the signal-to-noise ratio, and nis the number of repeated trials. TheSNr for each experiment is used to evaluate the design variable in/uniFB02uence for each of the output responses. The mean SNr for each parameter at each level is computed as SNr PL=1 kX SNr i; (/five.pnum) whereLis the parameter level, Prepresents the speci/uniFB01c parameter, and kis the number of trials in which that combination appears. The index, i, corresponds to the speci/uniFB01c trials containing the PLcombina- tion. For example, the mean SNr for the sti/uniFB00ness parameter at its lowest level would be the mean for experiments /one.pnum, /six.pnum, and /eight.pnum, as can be seen when consulting Table /one.pnum. To evaluate the magnitude of parameter in/uniFB02uence, analysis of variance (ANOVA) is required (Shi et al., /two.pnum/zero.pnum/one.pnum/four.pnum; Oktem et al., /two.pnum/zero.pnum/zero.pnum/seven.pnum). ANOVA relates the contribution of the variance for each design parameter to the total experimental variance. The total variance ( SSt) for each experiment is equal to the sum of the design parameter variances (P3 i=1SSi) and the external variance, or noise ( SSe) (Oktem et al., /two.pnum/zero.pnum/zero.pnum/seven.pnum). Whereas the SNr provides information on which design parameter levels may be desirable, the magnitude provides information on the overall sensitivity of that parameter. SSt=SSe+nX i=1SSi (/six.pnum) /seven.pnum SSP=kX j=1(PSNr L)2 k G2 n; (/seven.pnum) whereGis the grand total from each of the nexperiments and kis the number of experiments of each design parameter Pat each level, L. /three.pnum Results The resultant /uniFB01rst and second internal peak vertical displacements for blocks embedded with the experi- mental marker designs were used to identify how the individual design parameters (density, sti/uniFB00ness, and spacing) contributed to the deviation in the response as compared to the displacements measured in the neat material (ink markers). /three.pnum./one.pnum Marker Displacement Within each block, markers were indexed from left to right, top to bottom. The vertical and horizontal displacement for each marker was computed for the entire time series. An example of the horizontal and vertical motion paths for markers, shown in Fig. /three.pnum reveals that the most repeatable /one.pnum-D displacements were seen in the central region of each block; marker motion closer to the boundary was less repeatable, likely due to minor variations in sample position between repeated tests. Within the central region (/one.pnum./five.pnum cm ra- dius), the in/uniFB02uence of horizontal motion resulted in an average resultant displacement of less than /one.pnum pixel as compared to the vertical direction alone. Given this, both horizontal and transverse displacements were neglected from the analysis. Although this resulted in only a small portion of the markers being tracked, the in/uniFB02uence of neighbouring markers remained relevant, as their existence in the matrix material inevitably al- tered the observed response. An investigation of marker migration revealed that between impacts, markers did not migrate relative to each other, though blocks did shift slightly within the impact assembly, creating negligible changes to starting positions (Fig. /four.pnum). For each block, the mean vertical marker displacement for all markers in the central region, observed over three repeated drop tests, was computed, providing a single representative curve for each marker design. All specimens were tested in the same manner, each displaying a high degree of repeatability as con/uniFB01rmed with the computation of a /nine.pnum/five.pnum %con/uniFB01dence interval (CI) for each trace. The CI was computed with a two- tailed t-test, identifying the repeatability of the response. As shown in Fig. /five.pnum, the vertical position of central markers was extracted and aligned at the moment of impact. The mean signal was computed, along with the CI. For the duration of interest, only minor variations in the motion pro/uniFB01le occur, providing a clear picture of the impact response and its repeatability. The /uniFB01rst and second peak vertical displacements for each of the experimental markers are seen in Table /two.pnum, along with the associated range of the /nine.pnum/five.pnum %CI, and the Taguchi SNr as per Equations /three.pnum and /four.pnum. The SNr value functions as a largest-is-best representation for each response. Each response was generated from a number of input displacement traces, belonging to /three.pnum to /one.pnum/two.pnum markers depending on the grid spacing used in the design. Markers in the centre region were used as to lessen the e/uniFB00ect of erratic motion observed at the boundary. The vertical motion pro/uniFB01les of these markers are shown together with the neat material pro/uniFB01le in Fig. /six.pnum. A comparison of the displacement response of the neat material block with marker-embedded blocks is shown in Figure /seven.pnum, via the output value, (Equation /three.pnum). Here, it can be seen that Design /two.pnum deviates least from the neat material at the /uniFB01rst (compressive) peak, while Designs /four.pnum, /five.pnum, and /six.pnum were the next closest to neat material response. At the second (tensile) peak, responses di/uniFB00er more substantially, which can be expected due to increased stochastic nature of the responses, re/uniFB02ected in the broader con/uniFB01dence intervals at later times (Table /two.pnum). /three.pnum./two.pnum Sensitivity While it is evident that there was some variation in the marker motion between the various marker designs, the in/uniFB02uence of individual design parameters can be shown more clearly by examining the mean SNr for each design variable at each of its di/uniFB00erent intensity levels (L/one.pnum, L/two.pnum, or L/three.pnum), as per Equation /five.pnum. The purpose of this process was to assess how the variations in the properties (density, sti/uniFB00ness, and spacing) relate /eight.pnum 550 750 650 850 950(a)(b) Drop 3Drop 2Drop 1 Horizontal Position (px)Vertical Position (px) 550 450 350 250 150Figure /three.pnum: Example: Horizontal and vertical motion trace, Design /seven.pnum, for 0t20ms. For clarity, only odd-numbered marker paths are shown. (a) Central region, with repeatable /one.pnum-D response. (b) Boundary response is less repeatable, with increased horizontal component. /nine.pnum 30 mmDrop 3Drop 2Drop 1Figure /four.pnum: Overlay of drops /one.pnum to /three.pnum pre-impact, Design /seven.pnum. For clarity, only odd-numbered markers are high- lighted. Negligible shift in position signi/uniFB01es no migration of markers in block. /one.pnum/zero.pnum Table /two.pnum: Experimental outcomes from drop test and respective SNr . Experiment First Peak Second Peak (mm)C.I.(mm)SNr(dB) (mm)C.I.(mm)SNr(dB) Neat /one.pnum/one.pnum./eight.pnum /zero.pnum./two.pnum  /one.pnum/eight.pnum./six.pnum /zero.pnum./nine.pnum  /one.pnum /one.pnum/zero.pnum./six.pnum /zero.pnum./three.pnum /one.pnum/nine.pnum./six.pnum /two.pnum/zero.pnum./three.pnum /zero.pnum./four.pnum /two.pnum/one.pnum./one.pnum /two.pnum /one.pnum/one.pnum./five.pnum /zero.pnum./four.pnum /three.pnum/one.pnum./one.pnum /one.pnum/six.pnum./nine.pnum /zero.pnum./nine.pnum /two.pnum/zero.pnum./six.pnum /three.pnum /eight.pnum./one.pnum /zero.pnum./four.pnum /one.pnum/zero.pnum./zero.pnum /two.pnum/two.pnum./eight.pnum /zero.pnum./eight.pnum /one.pnum/three.pnum./zero.pnum /four.pnum /one.pnum/two.pnum./two.pnum /zero.pnum./three.pnum /three.pnum/zero.pnum./one.pnum /one.pnum/eight.pnum./seven.pnum /zero.pnum./six.pnum /four.pnum/five.pnum./five.pnum /five.pnum /one.pnum/two.pnum./two.pnum /zero.pnum./three.pnum /two.pnum/nine.pnum./zero.pnum /one.pnum/zero.pnum./five.pnum /zero.pnum./five.pnum /seven.pnum./two.pnum /six.pnum /one.pnum/one.pnum./two.pnum /zero.pnum./one.pnum /two.pnum/five.pnum./four.pnum /two.pnum/zero.pnum./seven.pnum /one.pnum./zero.pnum /one.pnum/nine.pnum./three.pnum /seven.pnum /one.pnum/zero.pnum./two.pnum /zero.pnum./two.pnum /one.pnum/seven.pnum./three.pnum /one.pnum/seven.pnum./zero.pnum /zero.pnum./two.pnum /two.pnum/zero.pnum./nine.pnum /eight.pnum /nine.pnum./six.pnum /zero.pnum./two.pnum /one.pnum/four.pnum./eight.pnum /one.pnum/seven.pnum./nine.pnum /zero.pnum./three.pnum /two.pnum/seven.pnum./seven.pnum /nine.pnum /one.pnum/zero.pnum./three.pnum /zero.pnum./two.pnum /one.pnum/eight.pnum./zero.pnum /two.pnum/zero.pnum./four.pnum /zero.pnum./four.pnum /two.pnum/zero.pnum./seven.pnum to deviations in the material response. For each design variable, the spread of the means of SNr values highlights how sensitive the output metric is to changes in the variable intensity (Table /one.pnum). These results 0 10 20 5 15 Time (ms) -680-660-640-620-600-580-560-540Vertical Pixel Position (y) (px) Pixel Position of Markers in Image Drop 1 Drop 2 Drop 3 Drop 1 Drop 2 Drop 3 Time (ms)-15-10-5 0510 15 20 Vertical Displacement ( ) (mm) Displacement of Markers Relative to Start Position Drop 1 Drop 2 Drop 3 Time (ms) -15-10-5 0510 15 20 Mean Vertical Displacement ( ) (mm) Mean Displacement with 95% C.I. 95% C.I. Mean Min. Max.(a) (b) (d) (c)Compression Tension t=t0 N =4 y 1y 2 y 3y 4y (t) 1 2y (t) 3y (t) 4y (t) (t) = y (t) - y (t ) m m m 0m = 1 m = 4 0 10 20 5 15 0 10 20 5 15 m = 1 4 (t)= m (t)1 3N C.I.= (t)±T (3N) 0.5 T=f([0.025 0.975],d ) f d = N-1 f Figure /five.pnum: Example: Design /seven.pnum vertical displacement, extracted by selection of central markers (a) for pixel position tracking. Pixel positions (b), were converted from pixels to millimetres and normalized to their moment-of-impact positions, creating a displacement curve (c). Displacements were used to generate mean displacement and CI curve (d), where the peak /uniFB01rst and second displacements were evaluated. Mo- ment of impact occurs at t = /zero.pnum ms, with the /uniFB01rst and second peaks occurring at approximately /four.pnum ms and /one.pnum/three.pnum ms, respectively. /one.pnum/one.pnum Time (ms) 25 15 10 5 0 -5 -10 -1520 0 20 15 10 5Vertical Displacement (mm) Design 1 Design 2 Design 3 Design 4 Design 5 Design 6 Design 7 Design 8 Design 9 Neat23 14 6 9 5 8 7Figure /six.pnum: Mean vertical response of central markers within each test block. Curves are aligned at the moment of impact. /one.pnum/two.pnum Table /three.pnum: Mean SNr at Peak /one.pnum MeanSNr Parameter L/one.pnum L/two.pnum L/three.pnum Spread Density /two.pnum/zero.pnum./two.pnum /two.pnum/eight.pnum./two.pnum /one.pnum/six.pnum./seven.pnum /one.pnum/one.pnum./four.pnum Spacing /two.pnum/two.pnum./three.pnum /two.pnum/four.pnum./nine.pnum /one.pnum/seven.pnum./eight.pnum /seven.pnum./one.pnum Sti/uniFB00ness /two.pnum/zero.pnum./zero.pnum /two.pnum/six.pnum./four.pnum /one.pnum/eight.pnum./eight.pnum /seven.pnum./six.pnum are shown in Tables /three.pnum and /four.pnum for displacement peak /one.pnum and peak /two.pnum, respectively. The results demonstrate that the parameters with the highest in/uniFB02uence in the displacement at the /uniFB01rst and second peak were di/uniFB00erent. In Table /three.pnum, representing the response of the markers in the /uniFB01rst displacement peak, the greatest range of motion was associated with changes in marker density. In Table /four.pnum, responses in the second displacement peak were associated with the greatest spread in sti/uniFB00ness and were not strongly correlated to marker density. The comparison of mean SNr provides insight into how each design variable contributes to the deviation of the output, however it does not evaluate the strength of the contribution. Using the ANOVA described in Equations /six.pnum and /seven.pnum, the sensitivity of both the input design variables and the external noise were evaluated. These results are shown in Table /five.pnum as representative percentages of the total sensitivity. The sensitivity values reinforce what was learned from the SNr comparisons, suggesting that early on in the deforma- tion process, marker density (/four.pnum/six.pnum %) played a signi/uniFB01cant role in ensuring the /uniFB01delity of the deformation /uniFB01eld being measured. Marker sti/uniFB00ness (/two.pnum/two.pnum %) and spacing (/one.pnum/eight.pnum %) were less signi/uniFB01cant than density, but still in/uniFB02u- ence the deformation process and must be considered. As the deformation progresses, the matrix defor- mation became extremely sensitive to marker sti/uniFB00ness and spacing sensitivity (/three.pnum/nine.pnum %, /two.pnum/eight.pnum%, respectively), while density was substantially less in/uniFB02uential (/six.pnum %). External noise also contributed, which is related to uncontrollable factors (Rao et al., /two.pnum/zero.pnum/zero.pnum/eight.pnum), which increased from the /uniFB01rst to second peak (/one.pnum/four.pnum %, /two.pnum/seven.pnum%). -50-40-30-20-10010 20 30 First Peak Second PeakOutput Value ( ) 1 2 3 4 5 6 7 8 9 Figure /seven.pnum: Output value, , as computed with Equation /three.pnum, for each design at /uniFB01rst and second peak values. /one.pnum/three.pnum Table /four.pnum: Mean SNr at Peak /two.pnum MeanSNr Parameter L/one.pnum L/two.pnum L/three.pnum Spread Density /one.pnum/eight.pnum./two.pnum /two.pnum/four.pnum./zero.pnum /two.pnum/three.pnum./one.pnum /five.pnum./seven.pnum Spacing /two.pnum/nine.pnum./two.pnum /one.pnum/eight.pnum./five.pnum /one.pnum/seven.pnum./six.pnum /one.pnum/one.pnum./five.pnum Sti/uniFB00ness /two.pnum/two.pnum./seven.pnum /two.pnum/eight.pnum./nine.pnum /one.pnum/three.pnum./seven.pnum /one.pnum/five.pnum./two.pnum Table /five.pnum: Parameter sensitivity ( %) from ANOVA Parameter Peak /one.pnum Peak /two.pnum Density /four.pnum/six.pnum /six.pnum Spacing /one.pnum/eight.pnum /two.pnum/eight.pnum Sti/uniFB00ness /two.pnum/two.pnum /three.pnum/nine.pnum External Noise /one.pnum/four.pnum /two.pnum/seven.pnum /four.pnum Discussion The results of this study can be examined in two distinct ways. First, a marker "performance" can be es- tablished by evaluating which markers yielded the least deviation from the neat material response at their /uniFB01rst and second displacement peaks. Second, using the results from the sensitivity study and ANOVA, a range of optimal design parameters can be described, helping to minimize the interference of markers in the deformation of the matrix material for future work. Fig. /eight.pnum provides a closer look at the variability of di/uniFB00erent marker groupings in the medium and high sti/uniFB00ness range (Fig. /eight.pnuma and /eight.pnumb) as well as in the medium and high density range (Fig. /eight.pnumc and /eight.pnumd). With these group- ings, although there were confounding factors, it is clear that a medium sti/uniFB00ness material was preferable to a high sti/uniFB00ness marker material. In this context, medium sti/uniFB00ness and hard sti/uniFB00ness markers had elastic moduli that were /two.pnum and /three.pnum orders of magnitude higher than the matrix, respectively. Similarly, high density marker materials resulted in a consistently lower displacement response of the matrix, and large variabil- ity on the second peak. The medium density markers did not greatly in/uniFB02uence the /uniFB01rst peak displacement of the matrix gel, but the in/uniFB02uence in second peak response was dominated by marker sti/uniFB00ness, as seen from high-sti/uniFB00ness Design /five.pnum ( E=/one.pnum/one.pnum/zero.pnum/zero.pnum kPa). In the context of the present work, medium and high density markers were de/uniFB01ned as markers with density ratios of /one.pnum./seven.pnum and /two.pnum./two.pnum, respectively. The trends were less clear when examining the e/uniFB00ects of marker spacing. For Design /four.pnum ( E=/one.pnum/seven.pnum/zero.pnum kPa, =/one.pnum./four.pnum/five.pnum g/cm3), a marker spacing of /one.pnum/zero.pnum mm, or /five.pnum marker diameters, appears to be suitable, given its per- formance, yet Design /one.pnum ( E=/one.pnum/two.pnum kPa,=/one.pnum./zero.pnum/five.pnum g/cm3), with the same spacing, yielded a poor match to the neat material response. It may be possible that the speci/uniFB01c blend of parameters in Design /four.pnum outweighed the in/uniFB02uence of the minimal spacing distance, which is observable in the response of Design /one.pnum. Examining the response of the block containing Design /six.pnum ( E=/one.pnum/two.pnum kPa,=/one.pnum./four.pnum/five.pnum g/cm3), whose spacing was at a the maximum, /one.pnum/zero.pnum marker diameters (/two.pnum/zero.pnum mm), the response was not a perfect match to the neat material, but it is among the less deviating responses. Considering both the /uniFB01rst and second peaks, along with the sensitivity analysis (Table /five.pnum), it is clear that both density (/four.pnum/six.pnum %) and sti/uniFB00ness (/three.pnum/nine.pnum %) must be equally considered when designing embedded markers. However, precisely matching the matrix density and sti/uniFB00ness is not critical to reducing the in/uniFB02uence of the markers on the deformation /uniFB01eld; a marker density below /one.pnum/seven.pnum/five.pnum %of that of the matrix and a marker sti/uniFB00ness below /one.pnum./zero.pnum MPa appears to be bene/uniFB01cial. Design /four.pnum falls within this optimal range and was the best performing marker in this study. In contrast, high density designs (/seven.pnum, /eight.pnum, /nine.pnum) and high sti/uniFB00ness designs (/three.pnum, /five.pnum, /seven.pnum) were among the worst performers when /uniFB01rst and second peak displacements were considered together (Fig. /eight.pnumb and /eight.pnumd, respectively). Though consideration of pattern spacing is valuable, this design parameter results in a lower overall in/uniFB02uence on the matrix (/two.pnum/eight.pnum %at the second peak). This balance of properties is re/uniFB02ective of the variables known to a/uniFB00ect the dynamics of matrix deformation and strain equilibration based on Equation /one.pnum. Adjustments to total marker mass via size and density will in/uniFB02uence inertia, while density and sti/uniFB00ness, coupled with spacing of markers, will a/uniFB00ect the material sound speed(Meyers, /one.pnum/nine.pnum/nine.pnum/four.pnum). As such, no speci/uniFB01c formula for marker design is presented, rather a recommendation to help narrow down the design space. Both image-based and ultrasound-based particle tracking systems have been used in PMHS impact studies /one.pnum/four.pnum Time (ms) 25 15 10 5 0 -5 -10 -1520 0 20 15 10 5Vertical Displacement (mm) Medium Stiffness Designs (a)Time (ms) 25 15 10 5 0 -5 -10 -1520 0 20 15 10 5Vertical Displacement (mm) High Stiffness Designs (b) Time (ms) 25 15 10 5 0 -5 -10 -1520 0 20 15 10 5Vertical Displacement (mm) Medium Density Designs 6 54Design 4 Design 5 Design 6 Neat (c)Time (ms) 25 15 10 5 0 -5 -10 -1520 0 20 15 10 5Vertical Displacement (mm) High Density Designs (d)Design 2 Design 4 Design 9 Neat 92 43 75Design 3 Design 5 Design 7 Neat 9 8 7Design 7 Design 8 Design 9 NeatFigure /eight.pnum: The displacement response of the massless marker (neat material) to various marker groupings with (a) medium sti/uniFB00ness (/one.pnum/seven.pnum/zero.pnum kPa), (b) high sti/uniFB00ness (/one.pnum/one.pnum/zero.pnum/zero.pnum kPa), (c) medium density (/one.pnum./four.pnum/five.pnum g/cm3), and (d) high density (/one.pnum./eight.pnum/five.pnum g/cm3). Note the density and sti/uniFB00ness of the matrix material were /zero.pnum./eight.pnum/five.pnum g/cm3and /nine.pnum kPa, respectively. with a high degree of precision. Although these systems are well suited to identify how tracking parti- cles move following an impact, the particles themselves introduce their own uncertainty. These results con/uniFB01rm that the insertion of any marker that is used to track deformation will change the deformation of the surrounding matrix material. The measurements comparing marker displacements to neat mate- rial demonstrate that the /uniFB01delity of the local deformation patterns were a/uniFB00ected by the presence of the markers, leading to errors that were related to the comparative material properties of the markers and matrix material. This has signi/uniFB01cant implications to the use of marker tracking data within brain tissues of cadaveric specimens and our understanding of their accuracy, which should not be confounded with marker tracking precision. Locating a marker with high precision is of the utmost importance; however, if the marker is in the wrong location due to its in/uniFB02uence on tissue deformation, the measurement is pre- cise but not an accurate representation of the natural physical response of the tissue. The results of the present work demonstrate the importance of proper marker design to improve measurement accuracy. Although it was not veri/uniFB01ed in the present work, we expect that large marker aspect ratios and anisotropic con/uniFB01nement of the markers through tethers may result in directional variability of marker disruption of the deformation /uniFB01eld and associated errors. /five.pnum Conclusion The inclusion of any tracking marker into a deformable matrix will alter the response of that matrix to im- pulsive loading, making it a challenge to measure the deformation. The parametric design and subsequent sensitivity analysis embedded tracking markers has revealed that density, sti/uniFB00ness, and marker spacing each play a role in altering the natural response the matrix. The least in/uniFB02uential marker had a density /one.pnum/five.pnum and sti/uniFB00ness in the middle of the design space ( =/one.pnum./four.pnum/five.pnum g/cm3, E=/one.pnum/seven.pnum/zero.pnum kPa), with a minimal spacing dis- tance (/one.pnum/zero.pnum mm). Other low-in/uniFB02uence markers included those with with low sti/uniFB00ness and density, but had broader spacing distances of /one.pnum/five.pnum-/two.pnum/zero.pnum mm. This group deviated least during the /uniFB01rst, compressive, phase of displacement. Within this group, all properties except high density and high sti/uniFB00ness were represented, clearly indicating that carefully selected combinations of parameters, and not individual qualities, result in a reduction deviation from the neat material response. It appears that low to medium density, up to /one.pnum/seven.pnum/five.pnum%of the matrix material density, and low to medium sti/uniFB00ness, below /one.pnum./zero.pnum MPa, make the best markers and minimize the in/uniFB02uence on matrix deformation. Markers outside of this range tend to cause greater deviations from the neat material response. Although less signi/uniFB01cant, marker spacing between /seven.pnum and /one.pnum/zero.pnum marker diameters may help to reduce volume fraction matrix sti/uniFB00ening e/uniFB00ects, improving the similarity to the neat material response. The uncertainty on displacement measurements and subsequently calculated strain values is a function of marker design, placement, and time-after-impact. This work provides a clearer understanding of the errors associated with the measured displacement of tissues through the use of embedded markers, as well as providing a basis for the future design of such markers. The results of this work illustrate the importance of properly quantifying the errors associated with strain /uniFB01elds and FE model validation calculated on the basis of markers previously used in prior PMHS studies. While this study is speci/uniFB01c to the dynamic loading and coupling of tracking particles in soft tissue, these /uniFB01ndings highlight the importance of evaluating gauge interference for other loading types and measure- ment con/uniFB01gurations. Under quasi-static loading or low-rate cyclic loading, dynamic coupling may not be a concern. However, the inclusion of particles may, for example, sti/uniFB00en or weaken a matrix, altering the natural mechanical properties, leading to a loss of accuracy in the measurement. Care should be taken un- der these circumstances to develop measurement systems that minimally, or predictively, in/uniFB02uence those natural responses. /six.pnum Acknowledgements Funding for this work was provided by the Canadian Institutes of Health Research and the Natural Sciences and Engineering Research Council of Canada through the Collaborative Health Research Program (CPG- /one.pnum/five.pnum/one.pnum/nine.pnum/six.pnum/seven.pnum). The cineradiography equipment was funded through 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 program.