Stress-free state in human carotid arteries cannot be revealed without layer separation

1 Residual stresses are considered as a significant factor influencing the stress-states in arteries. 2 These stresses are typically observed through opening angle of a radially cut artery segment, 3 often regarded as a primary descriptor of their stress-free state. However, the experimental 4 evidence regarding the stress-free states of different artery layers is scarce. In this study, two 5 experimental protocols, each employing different layer-separating sequences, were performed 6 on 17 human common carotid arteries; the differences between both protocols were found 7 statistically insignificant. While the media exhibited opening behaviour (reduced curvature), a 8 contrasting trend was observed for the adventitia curvature, indicating its closing behaviour. 9 In addition to the different bending effect, length changes of both layers after separation were 10 observed, namely shortening of the adventitia and elongation of the media. The results point 11 out that not all the residual stresses are released after a radial cut but a significant portion of 12 them is released only after the layer separation. Considering the different mechanical 13 properties of layers, this may significantly change the stress distribution in arterial wall and 14 should be considered in its biomechanical models. 15

16 Common carotid artery, layer specific residual deformation, vascular heterogeneity 17 1. Introduction 18 Biomechanical investigation of the presence of residual stresses (RSs) in arteries dates back 19 several decades (1–3). Arterial vessels, whether in situ or post-extraction, cannot be deemed 20 stress-free due to the existence of RSs in the vessel walls (4,5); they are manifested by the 21 typical opening of a circumferential strip of the artery wall documented in various 22 experimental studies (4,6). Although absolute values of RSs may be smaller in comparison to 23 the stresses experienced by arterial wall in vivo , their significance in shaping the resulting 24 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 3 stress distribution should not be overlooked. The strain stiffening response of arterial tissue 25 amplifies the impact of RSs, rendering the stress distribution more uniform throughout the 26 wall thickness (5–8). 27 Patient-specific computational models of pathological arteries have confirmed their capability 28 to predict arterial tissue rupture. For instance, Polzer et al. (9) demonstrated better rupture risk 29 prediction of abdominal aortic aneurysm (AAA) using a novel probabilistic rupture risk 30 index, outperforming the current treatment guidelines (10). A similar predictive approach 31 could be applied to assess the vulnerability of atheromas, particularly those located in life-32 threatening locations such as coronary or carotid arteries. The inclusion of RSs in 33 computational modelling is necessary, as the initial stress-free state is a prerequisite for any 34 computational model (11). However, multiple studies seem to overlook the effect of RSs and 35 strains in atherosclerotic carotid arteries (12–17) when evaluating their mechanical response 36 to in-vivo mechanical loading. Although efforts have been made to incorporate the RSs into 37 finite element (FE) models (11,18–22), proving the importance of RS in the resulting stress 38 distribution, the scarcity of experimental data demonstrating RSs in the simulated artery types 39 remains a challenge. 40 Most experiments focus on the entire artery wall without specific layer separation, thereby 41 neglecting the multi-layered heterogeneous structure of the arterial wall. An experimental and 42 computational study involving the complete human and porcine carotid artery bifurcation (5) 43 affirmed that the inclusion of RSs in the computational models leads to a more uniform stress 44 distribution and reduces maximal stress values on the inner wall surface. Greenwald et al. (4) 45 explored different opening angles in two layers of bovine carotid arteries, noting larger 46 opening angles in the inner layers compared to the outer ones. Holzapfel et al. (6) 47 experimentally examined layer-specific residual deformations in human aortas, specifically 48 exploring the opening angles of axial and circumferential strips from intima, media and 49 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 4 adventitia layers. The methodology was further refined in (23) and applied to human carotid 50 arteries in (24), where the adventitia (A) and media + intima (MI) layers were investigated 51 separately. They recorded significant curvature changes after having released residual 52 stretches in both axial and circumferential directions for both A and MI layers. 53 However, a deeper experimental investigation of this phenomenon is essential to gather data 54 applicable as input for simulations of stresses in arteries with atheroma, as done, for instance, 55 by Pierce et al. (19) and Sigaeva et al. (20). Approaches based on stress homogenization 56 throughout the wall thickness, as seen in (25), may falter in highly non-homogeneous arteries 57 with atheromas. The review (26) focusing on atherosclerosis does mention RS yet exclusively 58 for the non-atherosclerotic tissue. 59 Hence, the objective of this study is to compare different experimental procedures ensuring 60 credible experimental data on RSs demonstrated by residual deformation in separate layers, 61 specifically in the circumferential direction, for healthy carotid arteries. Such insights can 62 prove invaluable for computational modelling of arteries afflicted with atheroma and 63 predictions of atheroma vulnerability. 64 2. Materials and Methods 65 For the purpose of this study, 17 common carotid arteries (CCAs) were harvested (between 66 1.4.2021 and 31.3.2024) during autopsies at Masaryk University, Department of Anatomy, 67 with the approval of the local Ethics committee. Informed written consent from the body 68 donors was obtained in Anatomy Bequest Program years prior to their death. The donor 69 cohort comprised 8 males and 7 females, with an average age of 80.7±7.5 years. The samples 70 were preserved frozen in a saline solution (0.9% NaCl) at -20°C since it was not possible to 71 test the samples immediately after extraction. Some studies suggest that freezing may change 72 the mechanical properties (27–30), however the change was observed in longitudinal direction 73 only or at higher strains (28,29), or was mostly statistically insignificant (30). Other studies 74 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 5 lean towards the conclusion that freezing at -20°C does not alter mechanical properties (31–75 34) and is actually better compared to mere refrigeration (30–32). On the testing day, they 76 underwent a gradual thawing process and were stabilized in the saline solution, maintaining 77 the temperature of 36.7±0.5°C. The samples did not outreach type IV lesion, as per the lesion 78 characterization according to (35), showing none or mild signs of atherosclerotic changes. 79 2.1. Sample preparation and experimental protocol 80 The loose connective tissue was meticulously removed from the outer adventitia surface. Due 81 to the limited sample length, varying between 10 and 30 mm, we were unable to obtain both 82 circumferential and axial strips; therefore, only circumferential rings were extracted. Two 83 distinct experimental protocols were implemented (see Fig. 1). 84 The experimental protocol 1 (replicated from (6)) started with cutting the “intact” artery 85 samples into 2 mm height circumferential rings, followed by equilibrating them in a 37°C 86 saline solution for 30 minutes. Subsequently, they were glued pointwise to a plastic cylinder 87 using cyanoacrylate adhesive, followed by a radial incision. This incision induced gradual 88 opening of the rings, manifesting thus a release of circumferential RS, tensile at the outer and 89 compressive at the inner artery surface. After 16 hours, the opened configuration was 90 documented, and the adventitia was separated from the MI layer. Another recording occurred 91 after additional 6 hours in the tempered bath. 92 In the experimental protocol 2, the A and MI layers were separated first. Attempts to isolate 93 the intima from the media without damage were hindered by the natural thinness of the 94 carotid intima. Moreover, the initial atherosclerotic stages related to patients’ age also blur the 95 intima-media interface. Similarly to other studies (24), the inner layer was denoted as the MI 96 layer. Then 2 mm circumferential strips were cut from both A and MI layers and glued 97 pointwise to a cylindrical plastic tube. Images [dataset ] were captured using a CCD camera 98 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 6 (resolution 1280x1024) perpendicular to the tested ring 30 minutes, 16 hours and 22 hours 99 after the radial incision, aligning with the intervals applied in (6) and maintaining time 100 consistency across both protocols. 101 The thickness of the unseparated ring and of both layers was measured by a dial indicator at 102 three locations for each specimen, the average value was considered for the subsequent 103 analysis. The layer separation was examined by histological analysis (Fig. 2C, D) (standard 104 haematoxylin and eosin stain) and quantified by the thickness ratio of the separated MI and A 105 layers. A total of 22 intact specimens were prepared for protocol 1, yielding 21 adventitia and 106 20 media specimens; for the second protocol, 27 media samples and 25 adventitia samples 107 were prepared. The specimen discard was due to occasional tissue damage and unsuccessful 108 layer separation. The adventitia layer, distinguishable from the media by colour and texture, 109 can be easily separated in a “turtleneck fashion” (24) (Fig. 2A). The media layer is stiffer and 110 maintains its cylindrical shape even post-separation, whereas the adventitia becomes flat 111 under gravity 112 (Fig. 2B). It was observed that upon repeated immersion in the saline solution, the adventitia 113 layer regains its cylindrical shape, demonstrating its high compliance. 114 Fig. 1: Two distinct experimental protocols were employed in this study to investigate the 115 residual deformations of carotid wall layers and to compare different RS releasing 116 procedures. The A (blue) and MI (yellow) layers were recorded within 22 hours after being 117 radially cut. Black circles represent plastic cylinders used for specimen fixation. 118 Given the temperature-dependent nature of arterial mechanical responses (36,37), specimens 119 were kept in the 37°C saline solution throughout testing for both experimental protocols, 120 preventing tissue dehydration. 121 Fig. 2: The adventitia and media separation in a "turtleneck fashion” (A). The adventitia 122 layer turned inside-out for removal of the remaining media (B). Histological examination of 123 adventitia (C) and whole artery wall (D) showed some remaining portions of the media on the 124 adventitia. 125 126 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 7 2.2. Image processing 127 Each acquired specimen image underwent analysis using an in house semi-automatic program 128 in Python to obtain essential geometric parameters. The opening angle Φ [°] was defined by 129 two lines pointed from the middle of the inner boundary to both ending points (equidistant). 130 The definitions of the opening angle vary among studies, but they can be recalculated (8) for 131 comparison, assuming the circular shape. However, local curvature represents a better RS 132 quantifier independent of the strip length and asymmetry of the specimens (24); this is 133 important especially for non-homogeneous atherosclerotic CCA walls. For this purpose, the 134 inner and outer artery borders were manually traced, ensuring enough points (approx. 20 for 135 each) for their accurate description. Subsequently, B-splines were utilized to approximate 136 these traced borders and divided by 40 equidistant points. The sum of lengths between these 137 points was considered as the approximate specimen length. Image scale was obtained using 138 the known diameter of the plastic cylindric tube. Local curvature [mm -1] was calculated at 139 each of the points using equation (1): 140 /g3404 /g3051 /g4594/g3052 /g4594/g4594/g2879/g3052 /g4594/g3051 /g4594/g4594 /g4672/g3051 /g4594/g3118/g2878/g3052 /g4594/g3118/g4673 /g3119 /g3118 ( 1 ) 141 where /g1876 /g4593 , /g1877 /g4593 and /g1876 /g4593/g4593 , /g1877 /g4593/g4593 are the first and second derivatives of the B-spline, respectively. 142 Subsequently, a local radius of curvature [mm] was calculated as follows: 143 /g1844/g3404 /g2869 ( 2 ) 144 which was then averaged across all the calculated points within each segment boundary. 145 Therefore, we evaluated local curvatures of the B-spline of the respective line (38 points for 146 each B-spline); the averaged value represents then a global characteristic. 147 In summary, the six parameters of interest for both detached layers included their thickness, 148 inner and outer curvature, inner and outer length, and opening angle. 149 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 8 2.3. Statistical analysis 150 Statistical analyses were conducted using the Minitab software. The Anderson-Darling 151 normality test was employed for each dataset to ascertain a normal distribution of the data. If 152 the normal distribution was confirmed, the data was presented as mean ± standard deviation; 153 otherwise, the median and interquartile range were used. To assess differences in thickness, 154 curvature and the opening angle of layers between both experimental protocols, a 2-sample t-155 test was applied when normal distribution was confirmed; otherwise, the Mann-Whitney test 156 was employed. For variables measured within the same sample (e.g. length before and after 157 the release of RS), the paired t-test was used for normally distributed data, and the Wilcoxon 158 signed-rank test served as the nonparametric alternative. 159 Furthermore, Spearman's correlation coefficient ρ was used for identification of a potential 160 relationship between the opening angle and sample thickness. In all cases, statistical 161 significance was considered if p < 0.05. 162 3. Results 163 Thickness 164 Histological examination indicated that achieving a perfect separation of the adventitia layer 165 was challenging as some portions of the media consistently adhered to the adventitia layer 166 (Fig. 2C). Despite meticulous efforts, achieving a flawless separation was deemed 167 unattainable even under the supervision of an experienced surgeon from St. Anne’s 168 University Hospital. As the media consists of multiple very thin elastin membranes, they 169 enable different separation planes and are prone to tearing (Fig. 2D). Despite the efforts to 170 clean the media from the adventitia post-separation, the thickness variations of the adventitia 171 layer persisted across specimens pointing out the inability of cleaning the retained media 172 completely. A 2-sample t-test indicated no significant difference in thickness of the specific 173 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 9 layers (MI and A) between both protocols 1 and 2. The mean thickness values for MI, A and 174 the intact artery wall (I) were 0.60±0.14 mm, 0.36±0.11 mm and 0.92±0.15 mm, respectively. 175 Opening angle 176 The opening angles for both experimental protocols are shown in Fig. 3, displaying values for 177 detached layers as well as intact artery walls (for protocol 1). Predominantly positive values 178 were observed for the media and even slightly higher for the intact wall. Conversely, negative 179 values predominated for the adventitia, indicating strip closure rather than opening (Fig. 7C or 180 H). Absolute values of both opening and closing angles increased in time for both layers and 181 experimental protocols, which were compared for the separate layers in the final states. For 182 both layers, the statistical analysis revealed no significant difference between the two 183 protocols, therefore they were merged; the median of MI opening angle was 42.17° (13.38, 184 97.27), and the mean opening angle of A was -5.19±30.11°. For the intact wall, i.e. protocol 1 185 after 16 hours, the opening angle was 53.05±35.84°. 186 Fig. 3: Opening angle [°] for both MI and A layers as well as intact ring I (in experimental 187 protocol 1). 188 Curvature 189 Curvature of the inner boundary is summarized in Fig. 4. The trends are opposite to those of 190 the opening angles because of their inverse relation. Similarly to the opening angles, 191 comparison of the final values (after 22 hours) revealed no statistically significant differences 192 for both MI and A layers between the two experimental protocols, thus their values were 193 merged. The curvature was 0.243±0.105 mm -1 for the MI layer, 0.343±0.071 mm -1 for the A 194 layer, and 0.237±0.080 mm -1 for the intact wall (protocol 1 only). Similar results were 195 observed for the outer boundary with curvature values of 0.237±0.145 mm -1, 0.280±0.058 196 mm-1 and 0.181±0.056 mm-1 for the MI and A layers and the intact artery wall, respectively. 197 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 10 Fig. 4: Curvature [mm -1] for both experimental protocols (protocol 1 is on grey 198 background) – inner boundary (top), outer boundary (bottom). 199 Impact of imperfect separation 200 Visual inspection, histology analysis and thickness measurement revealed varying amounts of 201 media remaining on the adventitia layer (see Fig. 2C). The MI/A thickness ratio 202 approximately quantifies this portion, with lower values indicating the adventitia layer more 203 polluted with residual media. A positive correlation (ρ = 0.625; p < 0.005) was found between 204 the adventitia curvature and the thickness ratio (see Fig. 5), suggesting that lower curvatures 205 (i.e. positive opening angles) of adventitia are linked to a higher portion of residual media. 206 Conversely, for a lower amount of residual media, opening angles were mostly negative 207 according to their negative correlation with the thickness ratio (ρ = -0.432, p < 0.005). For the 208 MI layer, trends were opposite to those found for adventitia, negative for the curvature 209 (ρ = -0.419, p = 0.011) and positive for the opening angle. However, this last correlation was 210 not statistically significant ( ρ = 0.273, p = 0.069), although the p-value was close to the 211 significance level of 0.05. 212 Fig. 5: Correlation between thickness ratio and the opening angle (left) and inner curvature 213 (right). The higher the thickness ratio, the lower portion of media remains on the adventitia 214 layer. 215 Length of specimens 216 Time development of the length of specimens in the circumferential direction at their inner 217 and outer boundaries is presented in Fig. 6. Comparisons of inner and outer boundary lengths 218 did not reveal significant differences between experimental protocols 1 and 2 thus, analogous 219 to curvature and opening angle, the data was merged. The mean length of the inner boundary 220 in the final stage was 18.404±2.703 mm for media, 19.654±2.280 mm for adventitia and 221 18.471±2.754 mm for the intact wall (protocol 1 only). For the outer boundary, the mean 222 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 11 values were 21.845±2.387 mm, 24.205±2.983 mm and 23.869±2.695 mm for media, 223 adventitia, and intact wall, respectively. 224 Fig. 6: Length [mm] of the specimens for both experimental protocols (protocol 1 is on grey 225 background) – inner boundary (top), outer boundary (bottom). 226 227 In addition, comparison between the length of the initial uncut ring and the length of the final 228 state (after RS release) was conducted for each specimen using a paired t-test (for MI and A 229 layers in protocol 2 and for I in protocol 1). The test revealed significant differences in 230 lengths for all cases (MI, A, and I) at the inner boundary, while at the outer boundary, only A 231 and I exhibited statistically significant differences. The inner boundary of the MI layer 232 elongated by 6.12%, while the outer boundary remained unchanged. For the A layer, both the 233 inner and outer boundaries shortened by 3.80% and 3.81%, respectively. The inner boundary 234 of I elongated by 6.18%, whereas the outer boundary shortened by 4.18%. While the strain 235 distribution in the media showed mostly a bending nature, in the adventitia, both bending and 236 stretching were evident. 237 4. Discussion 238 Knowledge on the mechanical behaviour of arterial wall is essential for its computational 239 modelling, where RSs are generally accepted to play a significant role, and their inclusion in 240 computational models is often recommended. However, experimental evidence, especially in 241 specific carotid artery layers and atheromatous arteries, remains sparsely explored and 242 contradictory. Existing studies are based either on endarterectomy carotid samples (38), 243 which exhibit small opening angles, or on coronary arteries (21), characterized by large 244 opening angles. However, specimens from endarterectomy show much higher degree of 245 atherosclerosis and incorporate atheroma instead of adventitia (and partially media), thus the 246

in (39) correspond rather to our MI layer. The same models and approaches were used 247 for mouse samples in (40), recommending (together with (41)) the use of circumferential RS 248 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 12 when analysing healthy and diseased arterial tissue. However, images of a closed segment 249 published in (41) show some buckling effects causing unrealistic penetration of the fibrous 250 cap (FC) or even lipid core into the lumen area. These effects were not discussed, although 251 they indicate large negative stresses in the FC instead of positive stresses expected at FC 252 rupture. This contradiction requires further experimental and computational investigation of 253 this phenomenon. 254 In this study, two experimental protocols evaluating RS were compared. The first 255 experimental protocol, echoing the methodology employed in (6), involves layer separation 256 16 hours after the radial cut, as opposed to the second experimental protocol introduced in this 257 study, which opts for cutting the rings after the separation of layers. When the radial cut is 258 made first and the separation of layers follows, the initial RS release happens while the layers 259 are still joined together and influence each other. However, no statistically significant 260 difference was found between final stages of both experimental protocols (after 22 hours) for 261 any of the investigated parameters (thickness; opening angle; inner and outer curvature; inner 262 and outer length) for both A and MI layer. Differences are in the attainable results: while the 263 first method mediates insights into the intact wall, the second unfolds layer-specific 264 deformation, which is of dominantly bending character in the intact wall as well as in the MI 265 layer. However, the A shows much lower bending stiffness (it is proportional to the third 266 power of the layer thickness) and much lower average opening angle values (or change of 267 curvature). , Consequently, the adventitia deformation is dominated by contraction with a 268 nearly constant average value of 3.8 % throughout the thickness and considering this effect on 269 the RS distribution may be more important than the opening angle (or change of curvature) of 270 the A layer. 271 When comparing adventitia and media, both layers show statistically significant differences 272 for all the six parameters. The thickness was found to be 0.60±0.14 mm for the MI and 273 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 13 0.36±0.11 mm for the adventitia. These results corroborate that adventitia is much thinner 274 than the MI layer. Nevertheless, our histology analysis revealed that the adventitia separation 275 was not perfect (Fig. 2C) although the thicknesses are comparable with the values (0.7±0.13 276 mm and 0.47±0.07 mm, respectively) published in (24). As our MI/A thickness ratio was even 277 higher than in that study, it suggests neither their separation was perfect. 278 The tendency of adventitia to negative angles (closing rather than opening, see Fig. 7 C, H) is 279 not yet thoroughly described in literature. For instance, Teng et al. (39), although focused 280 mainly on mechanical characterization (strength and stress-strain response) of both layers, 281 mentioned the opening effect for the whole wall, as well as for the separated layers. However, 282 their provided photo documentation is ambiguous, one figure shows an opened adventitia 283 segment while another shows its zero opening. As they reported equal thickness of MI and A, 284 their results correspond to ours with the lowest MI/A thickness ratio of approximately 1 (i.e. a 285 significant portion of residual media on the adventitia), which gave also nearly zero angles in 286 our study. It is also unclear whether their figures were taken in the solution or in the air, thus 287 possibly influencing the results. Kural et al. (42) focused mainly on biaxial tensile tests but 288 briefly mentioned RS characterized by the opening angle. A positive mean opening angle of 289 63° was reported for intact carotid artery walls while for separated layers some retraction or 290 expansion was mentioned without being specified or further discussed. Esmaeili Monir et al. 291 (18) focused on finite element modelling but showed one CCA sample with separated 292 adventitia, media and intima. Here, a negative opening angle of -13° was recorded for 293 adventitia which confirms our results. 294 Fig. 7: Example of typical opening of segments glued pointwise at the outer surface to a 295 plastic cylinder. A, B: Intact wall – ring and after 16 hours; C, D: Adventitia and MI – 6 296 hours after separation, respectively; E, F: MI – ring and after 22 hours; G, H: Adventitia – 297 ring and after 22 hours. 298 299 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 14 Sommer et al. (24) presented a decrease of curvature (opening tendency) in both MI and A 300 layers of CCA immediately after their separation while some tendency to its re-increase with 301 time occurred. They stated a slight increase of adventitia curvature (mean values) within 6 302 hours after separation, supporting thus partially the results of our study, in which we also 303 accepted their approach applying the average curvature as RS quantifier. Although the final 304 curvature was slightly higher than that of the intact wall, it was still much lower than the 305 curvature of the uncut ring and represented thus an opening behaviour of adventitia. However, 306 the specimens were glued on the inner surface to a plastic cylinder with diameter comparable 307 to their inner diameter, thus a larger closing of the ring (negative opening angle) was 308 precluded, and no statistical analysis was presented either. Statistical test of our results 309 comparing the curvature of the inner adventitia boundary (in the stable state of experimental 310 protocol 2) with the uncut adventitia ring confirmed the closing behaviour of adventitia 311 indicating a significant release of RS. The same test done for the outer adventitia boundary 312 has not reached statistical significance, because the remaining connective tissue makes the 313 boundary blurry. Moreover, it induces some friction and constrains thus mutual movement of 314 the free ends. This behaviour was noted when the free ends were mutually pushed together, 315 distorting thus the circularity of the ring; the friction prevented the segment from further 316 closing even though such tendency was apparent. 317 When comparing the length of the uncut adventitia ring and the length of the stable state cut 318 specimen, the adventitia strips shortened significantly. This behaviour was also supported by 319 the results from the intact wall specimens; here the statistical test revealed a difference 320 between the inner and outer boundaries. The inner boundary (intima) elongated by 6.18%, 321 whereas the outer boundary (adventitia) shortened by 4.18%. When comparing also the results 322 from the separated MI layer, which elongates on the inner boundary but keeps the same length 323 of the outer boundary, the following conclusions can be drawn: the intima on the inner surface 324 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 15 tends to elongate and, conversely, the adventitia layer shows shortening behaviour. The 325 experimental evidence on the length changes is scarce in literature; (18) reported elongation 326 by 2.6% for media, 10.5% for adventitia and shortening by 9.3% for the intima layer for one 327 CCA specimen. It is in contradiction to our results; however, it seems these values were read 328 shortly after the radial cut; thus, they cannot represent the stable-state values reached much 329 later. Additionally, these layer-specific length values were compared with the lengths of 330 different intact specimen taken from the same CCA which may cause a deviation in the 331 results. Sommer et al. (24) reported an axial shortening of the adventitia which was also 332 observed in our experiments but could not be investigated and quantified due to small 333 dimension of the specimens; in contrast, shortening in the circumferential direction is not 334 discussed there. Holzapfel et al. (6) found that adventitia shortens significantly in both 335 circumferential and axial directions after the release of RS, and the intima showed elongation, 336 which corroborates our results although the media was found to shorten in the circumferential 337 direction. Nevertheless, that study dealt with abdominal aortas differing significantly in 338 composition and portion of the media layer from the muscular CCA, which may explain these 339 differences. 340 The length modification was examined only as the uncut ring vs. the cut stable state (in 341 protocol 1 for the intact wall and protocol 2 for the A and MI) allowing us a direct 342 comparison of each sample and thus eliminating the interpatient variation. Surprisingly, when 343 comparing the outer length of MI and the inner length of the A layer (for both separated rings 344 before radial cut), the adventitia is always shorter (p-value for paired t-test <0.05) with values 345 of 22.38±2.57 mm and 20.52±3.03 for MI and A, respectively. Although the layer separation 346 of MI and A in the “turtleneck” fashion should not influence the bending RS, the 347 tensile/compressive RS are influenced. This means the shortening effect of the A layer 348 reaching nearly 10% strain may be even more significant. 349 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 16 The circumferential shortening of the adventitia documented in our study may also cause the 350 curvatures of the intact specimen to be smaller than those of media, meaning the intact wall 351 shows bigger opening angle than any of its components. The shortening tendency of the 352 adventitia pulls the ends of the intact specimen further away from each other, resulting in a 353 larger opening compared with the MI layer. This difference contradicts both hypotheses of 354 constant strain and constant stress in the artery wall (throughout its thickness) and may 355 change completely the RS distribution calculated in biomechanical modelling of artery wall. 356 This impact should be verified in a future study. 357 5. Limitations 358 Acquisition of human tissue is quite challenging, so the sample number is limited. To increase 359 the number of specimens, we were able to obtain multiple specimens from one sample. 360 However, consideration of these specimens may induce a bias due to the natural inter-patient 361 variability. Therefore, all the statistical analyses were recalculated on smaller data sets 362 containing only one specimen per patient to avoid this bias, which allowed the use of paired t-363 test for direct specimen to specimen comparison (Wilcoxon signed-rank test as the 364 nonparametric alternative). The results corroborate the conclusions obtained from the full 365 datasets; no statistically significant difference was found between two different experimental 366 protocols (p<0.05) for both MI and A layers when comparing all the parameters of interest: 367 thickness, opening angle, inner and outer curvature, inner and outer length; the choice of 368 experimental protocol does not have significant effect. Additionally, the length change after 369 radial cut was confirmed on the reduced data as well. The comparison of length of inner 370 boundary of A with outer boundary length of MI was confirmed on the reduced data set as 371 well; the adventitia was 7.1 % shorter. 372 The study is also limited by using circumferential specimens only, thus further measurements 373 of axial residual stresses could enhance the description of the 3D residual stress distribution. 374 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 17 6. Conclusion 375 The experimental evaluation of the opening angles, curvatures and length changes of 376 circumferential segments of human common carotid arteries and their layers revealed 377 surprisingly increasing curvatures (negative opening angles) for separated adventitia layers. 378 The inner MI layers showed an expectable decrease of curvature (i.e. positive opening 379 angles), as well as the segments of intact (unseparated) artery wall, both dominated evidently 380 by their bending. Together with significant shortening of adventitia after layer separation, 381 these effects may completely change the distribution of stresses throughout the wall thickness. 382 Neither of the hypotheses of constant strain or stress throughout the wall thickness, nor the 383 residual stresses calculated based on opening angle of the artery wall segment are capable to 384 describe the distribution of residual stresses correctly. 385

386 This publication was supported by the Czech Science Foundation, research project No. 21-387 21935S, as well as by the project "Mechanical Engineering of Biological and Bio-inspired 388 Systems", funded as project No. CZ.02.01.01/00/22_008/0004634 by Programme Johannes 389 Amos Commenius, call Excellent Research and Brno Ph.D. Talent Scholarship – Funded by 390 the Brno City Municipality. 391

392 1. Fung YC. On the Foundations of Biomechanics. Journal of Applied Mechanics. 1983 Dec 393 1;50(4b):1003–9. 394 2. Fung Y. Biodynamics: Circulation. New York: Springer-Verlag; 1984. (Biomechanics). 395 3. Chuong CJ, Fung YC. On residual stresses in arteries. J Biomech Eng. 1986 396 May;108(2):189–92. 397 4. Greenwald SE, Moore JEJ, Rachev A, Kane TP, Meister JJ. Experimental investigation of 398 the distribution of residual strains in the artery wall. J Biomech Eng. 1997 399 Nov;119(4):438–44. 400 5. Delfino A, Stergiopulos N, Moore JE, Meister JJ. Residual strain effects on the stress 401 field in a thick wall finite element model of the human carotid bifurcation. Journal of 402 Biomechanics. 1997;30(8):777–86. 403 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 18 6. Holzapfel GA, Sommer G, Auer M, Regitnig P, Ogden RW. Layer-specific 3D residual 404 deformations of human aortas with non-atherosclerotic intimal thickening. Ann Biomed 405 Eng. 2007 Apr;35(4):530–45. 406 7. Gasser TC, Ogden RW, Holzapfel GA. Hyperelastic modelling of arterial layers with 407 distributed collagen fibre orientations. Journal of the Royal Society Interface. 2006 Feb 408 22;3(6):15–35. 409 8. Humphrey JD. Cardiovascular solid mechanics: Cells, tissues, and organs. 1st ed. New 410 York: Springer; 2002. 758 p. Available from: https://doi.org/10.1007/978-0-387-21576-1 411 9. Polzer S, Gasser TC, Vlachovský R, Kubí č ek L, Lambert L, Man V, et al. Biomechanical 412 indices are more sensitive than diameter in predicting rupture of asymptomatic abdominal 413 aortic aneurysms. J Vasc Surg. 2020 Feb;71(2):617-626.e6. 414 10. Moll FL, Powell JT, Fraedrich G, Verzini F, Haulon S, Waltham M, et al. Management of 415 abdominal aortic aneurysms clinical practice guidelines of the European society for 416 vascular surgery. Eur J Vasc Endovasc Surg. 2011 Jan;41 Suppl 1:S1–58. 417 11. Cilla M, Peña E, Martínez MA. 3D computational parametric analysis of eccentric 418 atheroma plaque: Influence of axial and circumferential residual stresses. Biomechanics 419 and Modeling in Mechanobiology. 2012 Sep;11(7):1001–13. 420 12. Sadat U, Li ZY, Young VE, Graves MJ, Boyle JR, Warburton EA, et al. Finite element 421 analysis of vulnerable atherosclerotic plaques: A comparison of mechanical stresses 422 within carotid plaques of acute and recently symptomatic patients with carotid artery 423 disease. Journal of Neurology, Neurosurgery and Psychiatry. 2010;81(3):286–9. 424 13. Noble C, Carlson KD, Neumann E, Lewis B, Dragomir-Daescu D, Lerman A, et al. Finite 425 element analysis in clinical patients with atherosclerosis. J Mech Behav Biomed Mater. 426 2022 Jan;125:104927. 427 14. Li ZY, Howarth S, Trivedi RA, U-King-Im JM, Graves MJ, Brown A, et al. Stress 428 analysis of carotid plaque rupture based on in vivo high resolution MRI. J Biomech. 429 2006;39(14):2611–22. 430 15. Kock SA, Nygaard JV, Eldrup N, Fründ ET, Klaerke A, Paaske WP, et al. Mechanical 431 stresses in carotid plaques using MRI-based fluid-structure interaction models. J 432 Biomech. 2008;41(8):1651–8. 433 16. Kiousis DE, Rubinigg SF, Auer M, Holzapfel GA. A methodology to analyze changes in 434 lipid core and calcification onto fibrous cap vulnerability: the human atherosclerotic 435 carotid bifurcation as an illustratory example. J Biomech Eng. 2009 Dec;131(12):121002. 436 17. Auricchio F, Conti M, De Beule M, De Santis G, Verhegghe B. Carotid artery stenting 437 simulation: From patient-specific images to finite element analysis. Medical Engineering 438 and Physics. 2011;33(3):281–9. 439 18. Esmaeili Monir H, Yamada H, Sakata N. Finite element modelling of the common carotid 440 artery in the elderly with physiological intimal thickening using layer-specific stress-441 released geometries and nonlinear elastic properties. Computer Methods in Biomechanics 442 and Biomedical Engineering. 2016 Sep 9;19(12):1286–96. 443 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 19 19. Pierce DM, Fastl TE, Rodriguez-Vila B, Verbrugghe P, Fourneau I, Maleux G, et al. A 444

for incorporating three-dimensional residual stretches/stresses into patient-445 specific finite element simulations of arteries. Journal of the Mechanical Behavior of 446 Biomedical Materials. 2015 Jul 1;47:147–64. 447 20. Sigaeva T, Sommer G, Holzapfel GA, Di Martino ES. Anisotropic residual stresses in 448 arteries. Journal of the Royal Society Interface. 2019 Feb 1;16(151). 449 21. Ohayon J, Dubreuil O, Tracqui P, Le Floc’ S, Rioufol G, Chalabreysse L, et al. Influence 450 of residual stress/strain on the biomechanical stability of vulnerable coronary plaques: 451 potential impact for evaluating the risk of plaque rupture. Am J Physiol Heart Circ 452 Physiol. 2007;293:1987–96. 453 22. Patel SY, Kaazempur-Mofrad MR, Isasi AG, Kamm RD. DISEASED ARTERY WALL 454 MECHANICS: CORRELATION TO HISTOLOGY. In: Book of abstracts. Key 455 Biscayne, Florida; June 25-29. (CARDIOVASCULAR SOLID/FLUID 456 INTERACTIONS). 457 23. Holzapfel GA, Ogden RW. Modelling the layer-specific three-dimensional residual 458 stresses in arteries, with an application to the human aorta. J R Soc Interface. 2010 May 459 6;7(46):787–99. 460 24. Sommer G, Regitnig P, Költringer L, Holzapfel GA. Biaxial mechanical properties of 461 intact and layer-dissected human carotid arteries at physiological and supraphysiological 462 loadings. American Journal of Physiology - Heart and Circulatory Physiology. 463 2010;298(3):898–912. 464 25. Schröder J, von Hoegen M. An engineering tool to estimate eigenstresses in three-465 dimensional patient-specific arteries. Computer Methods in Applied Mechanics and 466 Engineering. 2016 Jul 1;306:364–81. 467 26. Holzapfel GA, Mulvihill JJ, Cunnane EM, Walsh MT. Computational approaches for 468 analyzing the mechanics of atherosclerotic plaques: A review. Journal of Biomechanics. 469 2014;47(4):859–69. 470 27. Venkatasubramanian RT, Grassl ED, Barocas VH, Lafontaine D, Bischof JC. Effects of 471 freezing and cryopreservation on the mechanical properties of arteries. Annals of 472 Biomedical Engineering. 2006 May;34(5):823–32. 473 28. Chow MJ, Zhang Y. Changes in the mechanical and biochemical properties of aortic 474 tissue due to cold storage. Journal of Surgical Research. 2011 Dec;171(2):434–42. 475 29. Grassl ED, Barocas VH, Bischof JC. Effects of Freezing on the Mechanical Properties of 476 Blood Vessels. In: IMECE2004. Heat Transfer, Volume 1; 2004. p. 699–703. Available 477 from: https://doi.org/10.1115/IMECE2004-60244 478 30. Hemmasizadeh A, Darvish K, Autieri M. Characterization of changes to the mechanical 479 properties of arteries due to cold storage using nanoindentation tests. Annals of 480 Biomedical Engineering. 2012 Jul;40(7):1434–42. 481 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint 20 31. Virues Delgadillo JO, Delorme S, El-Ayoubi R, DiRaddo R, Hatzikiriakos SG. Effect of 482 freezing on the passive mechanical properties of arterial samples. Journal of Biomedical 483 Science and Engineering. 2010;03(07):645–52. 484 32. Stemper BD, Yoganandan N, Pintar FA. Methodology to study intimal failure mechanics 485 in human internal carotid arteries. Journal of Biomechanics. 2005;38(12):2491–6. 486 33. O’Leary SA, Doyle BJ, McGloughlin TM. The impact of long term freezing on the 487 mechanical properties of porcine aortic tissue. Journal of the Mechanical Behavior of 488 Biomedical Materials. 2014;37:165–73. 489 34. Ebenstein DM, Coughlin D, Chapman J, Li C, Pruitt LA. Nanomechanical properties of 490 calcification, fibrous tissue, and hematoma from atherosclerotic plaques. Journal of 491 Biomedical Materials Research - Part A. 2009;91(4):1028–37. 492 35. Stary HC. Natural history and histological classification of atherosclerotic lesions: an 493 update. Arterioscler Thromb Vasc Biol. 2000 May;20(5):1177–8. 494 36. Atienza JM, Guinea GV, Rojo FJ, Burgos RJ, García-Montero C, Goicolea FJ, et al. The 495 influence of pressure and temperature on the behavior of the human aorta and carotid 496 arteries. Revista Española de Cardiología (English Edition). 2007;60(3):259–67. 497 37. Guinea GV, Atienza JM, Elices M, Aragoncillo P, Hayashi K. Thermomechanical 498 behavior of human carotid arteries in the passive state. American Journal of Physiology - 499 Heart and Circulatory Physiology. 2005;288(6 57-6):2940–5. 500 38. Pocaterra M, Gao H, Das S, Pinelli M, Long Q. Circumferential residual stress 501 distribution and its influence in a diseased carotid artery. 2009. (Summer bioengineering 502 conference; vol. ASME 2009 Summer Bioengineering Conference, Parts A and B). 503 Available from: https://doi.org/10.1115/SBC2009-206692 504 39. Teng Z, Tang D, Zheng J, Woodard PK, Hoffman AH. An experimental study on the 505 ultimate strength of the adventitia and media of human atherosclerotic carotid arteries in 506 circumferential and axial directions. Journal of Biomechanics. 2009;42(15):2535–9. 507 40. Broisat A, Toczek J, Mesnier N, Tracqui P, Ghezzi C, Ohayon J, et al. Assessing low 508 levels of mechanical stress in aortic atherosclerotic lesions from apolipoprotein E-/- mice-509 brief report. Arteriosclerosis, Thrombosis, and Vascular Biology. 2011;31(5):1007–10. 510 41. Martiel JL, Finet G, Holzapfel GA, Stuber M, Matsumoto T, Pettigrew RI, et al. Chapter 511 19 - Importance of residual stress and basal tone in healthy and pathological human 512 coronary arteries. In: Ohayon J, Finet G, Pettigrew RI, editors. Biomechanics of coronary 513 atherosclerotic plaque. Academic Press; 2021. p. 433–61. (Biomechanics of living organs; 514 vol. 4). Available from: 515 https://www.sciencedirect.com/science/article/pii/B9780128171950000196 516 42. Kural MH, Cai M, Tang D, Gwyther T, Zheng J, Billiar KL. Planar biaxial 517 characterization of diseased human coronary and carotid arteries for computational 518 modeling. Journal of Biomechanics. 2012;45(5):790–8. 519 [dataset] A. Hrubanová, O. Sochor, Raw images of CCA specimens, Zenodo, (2024). 520 https://doi.org/10.5281/zenodo.10932993. 521 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted October 17, 2024. ; https://doi.org/10.1101/2024.10.15.618414doi: bioRxiv preprint