Mazzocca, AD, Nissen, CW, Geary, M, Adams, DJ. 8(c) shows a scenario where the radiated energy ER is near-zero, and any further decrease in |$\overline{\tau ^{\rm fin}}_E$| would not be physical (as it would result in negative ER). Those results have been widely used in estimation of stress drops in seismology. The results of the present study provide new information regarding bone bruise locations within specific compartments of the tibia and femur. MR imaging of anterior cruciate ligament tears: is there a gender gap? Similarly, previous investigators have demonstrated that the volume of lateral compartment bone bruises was larger than that of the corresponding medial compartment bone bruises.14 Wittstein et al36 also reported that tibial bone bruises on the lateral side were more severe than those on the medial side in the majority of women and men. Elle se consacre sans relâche à ce défi qui l'entraîne au cœur des causes chargées d'émotion qui sont inhérentes à sa pratique. We find significant and systematic differences between these three average stress drop measures. Bone bruise distribution patterns of the femur and tibia. We calculated Coulomb stress changes from the earthquake sequence, suggesting that the previous strong earthquakes had significant stress-encouraging effects on the following events. Xie Y, Mintz GS, Yang J, Doi H, Iñiguez A, Dangas GD, Serruys PW, McPherson JA, Wennerblom B, Xu K, Weisz G, Stone GW, Maehara A. JACC Cardiovasc Imaging. The pattern of positive and negative stress drops has also been inferred from observations (e.g. Although a 6-week threshold has commonly been used in the literature, the 4-week threshold was selected to further minimize timing errors12 and preserve the signal characteristics of bone bruises. (b) Shear stress as a function of time at a point on the fault. an undershoot case where the stress on the fault plane during faulting becomes smaller than the final stress τfin, as discussed in Section 4.1), the dissipation on the fault can, in fact, be smaller than the dissipation with the final shear stress EF, and hence more energy than ΔW0 can be radiated. For some earthquakes, Venkataraman & Kanamori (2004) used a trimmed rupture area for estimating the stress drop. Yet they are equal to each other only for ruptures with spatially uniform stress drop within the ruptured domain, which results in an elliptical slip distribution for a circular rupture, as shown in Figs 1(a) and (b). The more severe bone bruises on the lateral side suggested that impact on the lateral side was more severe than that on the medial side. Bone bruises observed on magnetic resonance imaging (MRI) after an anterior cruciate ligament (ACL) injury could provide significant information about ACL injury mechanisms. The analytic solution for such a problem is not always known. Lavallée et al. (e)–(f) Streamlined versions of scenarios (c)–(d), in which the stress behaviour at the end of slip is simplified. However, we find substantial differences between |$\overline{\Delta \sigma }_M$| and |$\overline{\Delta \sigma }_E$|, by a factor of up to 8 for the cases considered. ACL, anterior cruciate ligament; MRI, magnetic resonance imaging; PCL, posterior cruciate ligament. If we define the ruptured domain by a threshold th with respect to the maximum slip, then the moment-based stress drop |$\overline{\Delta \sigma }_{Mth}$| increases with the value of th. spatially uniform) over the ruptured domain (Figs 1a and b). \end{eqnarray}, \begin{eqnarray} We find that 0.2 < thc < 0.4 for a broad range of the heterogeneity parameters, both in circular and rectangular cases. We assumed that the coseismic deformation fields were caused by the ruptures of two faults through EQ2 and EQ3. Given the discrepancy between the MRI scans in pixel size at acquisition as well as the fact that the signal intensity varied widely among patients, we compared the severity of lateral and medial bone bruises based on signal intensity only within the same imaging sequence in the same participant. Randomization and introduction of small scale heterogeneity increases |$\overline{\Delta \sigma }_E$|, but causes little additional changes in |$\overline{\Delta \sigma }_A$|. \frac{1}{2} \int _{\Sigma } \Delta {\sigma _{\rm p}} \cdot \Delta {u_{\rm u}}\, {\rm d}S = \frac{1}{2} \int _{\Sigma } \Delta {\sigma _{\rm u}} \cdot \Delta {u_{\rm p}}\, {\rm d}S = 0. (a) A conceptual simplified diagram for energy partitioning in an earthquake. The left-most column (χ = 0) corresponds to cases without randomization. \end{eqnarray}. The most common bone bruise pattern observed among the patients was LF + LT, followed by BF + BT and LF + BT (Table 2). First, let us define the mathematical quantities needed to describe slip in an earthquake, the resulting stress drop distribution and its averaging. Bone bruises on the lateral side were more severe than those on the medial side in patients with bone bruises on the lateral and medial sides of both the femur and tibia. AOSSM checks author disclosures against the Open Payments Database (OPD). Note. NLM We use cookies to help provide and enhance our service and tailor content and ads. The maximum gray values on the lateral side of both the tibia (158.73 ± 36.97) and the femur (161.71 ± 33.03) were significantly greater than those on the medial side of both the tibia (137.91 ± 33.42) and femur (139.51 ± 37.47) in patients with the BF + BT pattern (P < .001 and P < .001, respectively). &=& \Delta W_{\rm 0u} + \Delta W_{\rm 0p} + \frac{1}{2} \int _{\Sigma } \Delta {\sigma _u} \cdot \Delta {u_{\rm p}}\, {\rm d}S \nonumber \\ E_{\rm R} &=& \frac{1}{2} \int _\Sigma ({\tau }^{\rm ini} - {\tau }^{\rm fin}) \cdot \Delta {u}\, {\rm d}S + \int _0^{t^{\rm fin}} {\rm d}t \int _\Sigma \frac{{\rm d}{\tau }}{{\rm d}t} \cdot {\delta }\, {\rm d}S \nonumber \\ The most common bone bruise distribution pattern indicated that knee abduction and anterior tibial translation could both be important contributors to the injury mechanism. |$\overline{\Delta \sigma }_A$| represents the simplest (unweighted) average of the stress change over the ruptured domain (Section 2.2). We would like to emphasize that values ηR > 1 are theoretically allowed, but should be quite rare based on the observations. For α = 16, only the region near the end of the rupture is shown for convenience. The dependence of |$\overline{\Delta \sigma }_{Mth}$| and |$\overline{\Delta \sigma }_{Ath}$| on the threshold th in defining Σth for randomized cases with ν = 1 and χ = 0.3 based on the circular crack model with uniform stress drop. © 2020 The Authors. Fig. Noda & Lapusta (2012) proposed a rigourous way for averaging the stress-slip behaviour and constructing energy-partitioning diagrams for dynamic rupture that attempt to preserve the features of local stress-slip behaviour. 2with object Breach or disturb (a harmonious feeling or situation). Please read and accept the terms and conditions and check the box to generate a sharing link. For each selection of ϕ, ν and χ, we have analysed 100 random cases. Manighetti et al. The first one, which we denote by |$\overline{\Delta \sigma }_M$|, is the commonly estimated static stress drop based on the seismic moment and fault geometry/dimensions (Section 2.1). (23). In addition to bone bruise patterns, our study also found that patients without bone bruises had a greater percentage of meniscal injuries than patients with bone bruises. \end{equation}, \begin{eqnarray} Given that skeletally immature patients demonstrate unique bone bruise patterns,23 and bone mineral density decreases gradually in patients aged >40 years,13 which could affect the signal characteristics of a bone bruise, only those aged 18 to 40 years were selected. For more information view the SAGE Journals Article Sharing page. Association of compartmental bone bruise distribution with concomitant intra-articular and extra-articular injuries in acute anterior cruciate ligament tears after noncontact sports trauma, Multiplanar loading of the knee and its influence on anterior cruciate ligament and medial collateral ligament strain during simulated landings and noncontact tears, MRI of acute bone bruises: timing of the appearance of findings in a swine model, Cost analysis of converting from single-bundle to double-bundle anterior cruciate ligament reconstruction. \overline{\Delta \sigma }_E = \frac{\int _{\Sigma } \Delta \sigma _1 \Delta u_1\, {\rm d}S}{\int _{\Sigma } \Delta u_1\, {\rm d}S}. Meniscal and ligamentous injuries were confirmed by MRI, performed by an experienced radiologist, as well as arthroscopic surgery, performed by sports medicine orthopaedic surgeons. (6). The amplitude of variations in Δσ1 increases as χ increases and ν decreases. Three notions of the average static stress drop are interchangeably used in earthquake studies, yet would be different for heterogeneous stress drop distributions. When professional issues force her to start her own practice, Ariane discovers that … (especially of a pipe, a vessel, or a bodily part such as an organ or membrane) break or burst suddenly. (A) Determine the bone bruise location in the lateral-medial direction using the sagittal imaging sequence. (23) by randomizing the characteristic slip distribution ϕ. In this scenario, the prestress |$\overline{\tau ^{\rm ini}}_E$| moves further away from the peak stress |$\overline{\tau _{\rm p}}$|, resulting in fault operation under lower overall shear stress than |$\overline{\tau _{\rm p}}$| that may be comparable to the static strength. Surface Fault Ruptures and Slip Distributions of the M w 6.6 11 April 2011 Hamadoori, Fukushima Prefecture, Northeast Japan, Earthquake by Kazuo Mizoguchi, Shin-ichi Uehara, and Keiichi Ueta Mai & Beroza (2000) used the autocorrelation length. Kim, SY, Spritzer, CE, Utturkar, GM, Toth, AP, Garrett, WE, DeFrate, LE. 8(a) schematically reproduces one of the experimental curves (based on fig. (2006) reported that the probability distribution of slip in a single event is better explained by Lévy α-stable distribution than Gaussian or Cauchy distributions, both of which are special cases of Lévy α-stable distribution. Of these, 207 patients met the inclusion criteria and were entered into the study. (c)–(d) Scenarios with ηR smaller than unity obtained from the case of panel a by reducing only |$\overline{\tau ^{\rm fin}}_E$| (panel c) or both |$\overline{\tau ^{\rm ini}}_E$| and |$\overline{\tau ^{\rm fin}}_E$| (panel d). Published by Oxford University Press on behalf of The Royal Astronomical Society. Fig. †Beijing Key Laboratory of Sports Injuries, Institute of Sports Medicine, Peking University Third Hospital, Beijing, China. Femoral and tibial bone bruises are thought to represent a footprint of impact at the time of the injury, offering insight into the mechanisms of an ACL injury.29,32,33 Previous studies have reported that the most common patterns observed in an ACL injury were bone bruises in the lateral compartment,23,29 which indicated that the valgus load was the primary mechanism of an ACL injury.20 Other studies reported that anterior tibial translation with a small knee flexion angle may be the primary mechanism of an ACL injury based on the observed bone bruises on the posterior tibia and anterior femur.2,34,36,38, Although many studies have been conducted on the bone bruise locations of the femur and tibia in patients with ACL ruptures, these studies separately reported the frequency and location of tibial and femoral bone bruises in patients with ACL injuries,34,36 and little is known regarding the relative bone bruise locations of the tibia and femur. -, Circulation. \end{eqnarray}, In our study, the fault has a uniform unit normal vector, \begin{eqnarray} The most common bone bruise distribution pattern indicated that knee abduction and anterior tibial translation could both be important contributors to the injury mechanism. All patients underwent MRI of the injured knee using our standard protocol. 1(especially of a pipe, a vessel, or a bodily part such as an organ or membrane) break or burst suddenly. empirical ruptures seems to include similar degrees of variation without introducing complications about how it arises. (A) Femoral bone bruise locations of the LF + LT pattern. More significant heterogeneity in slip distributions would lead to larger |$\overline{\Delta \sigma }_E$| in comparison to |$\overline{\Delta \sigma }_M$|, hence to more significant underestimation of the partial strain energy change ΔW0, and thus to more significant overestimation of ηR. Note that those values are such that the strain energy would diverge if all the wavenumbers were accounted for, and the truncation at a high wavenumber is required to deal with the problem in the framework of continuum mechanics. All statistical analyses were performed using SPSS (Version 16; IBM). Let us consider a uniform stress drop model, with, \begin{equation} Login failed. Copyright © 2020 Elsevier B.V. or its licensors or contributors. Therefore, we chose the simplest slip model for these two events. & \approx & \frac{1}{2} \int _\Sigma ( \tau ^{\rm ini}_1 - \tau ^{\rm fin}_1 ) \Delta u_1\, {\rm d}S + \int _0^{t^{\rm fin}} {\rm d}t \int _\Sigma \frac{{\rm d}\tau _1}{{\rm d}t} \delta _1\, {\rm d}S , Sign in here to access free tools such as favourites and alerts, or to access personal subscriptions, If you have access to journal content via a university, library or employer, sign in here, Research off-campus without worrying about access issues. 2005; Lavallée et al. , If instead one modifies eq. The mismatch is negligibly small, and the comparison between different averaged stress drops is not affected by the existence of periodicity. To the best of our knowledge, this is the first study that explicitly introduces the energy-based average measure of stress drop, |$\overline{\Delta \sigma }_E$|, although its notion has been indirectly implied by the developments in Kostrov & Das (1988); Noda & Lapusta (2012). From eq. Piping ruptures are typically a direct result of an over-pressurization event. 2000 Jan 1;355(9197):19-24 D. sr. ruptures synonyms, ruptures pronunciation, ruptures translation, English dictionary definition of ruptures. k_1k_3\nu _{\rm p}/(1-\nu _{\rm p}) & \quad k_1^2 + k_3^2/(1-\nu _{\rm p}) \end{array} \right]\nonumber \\ The details are given in Appendix B2. The relative bone bruise patterns of the tibia and femur were further classified based on the documented location in the lateral-medial direction after the abovementioned determination of the bone bruise (Figure 2C). The length of ruptures and ground fissures showed on the map are exaggerated. More generally, stress depends on slip through other variables, such as slip rate, state variables and temperature (e.g. Members of _ can log in with their society credentials below. (2005) examined not only results of finite source inversions of seismological and geodetic observations, but also geologically measured surface rupture profiles, and concluded that the slip distribution is typically triangular with various skewness. Elle est également diffusée sur la plateforme France.tv depuis le 16 décembre 2019[4] ainsi que sur Auvio depuis juillet 2020[5]. At the same time, |$\overline{\Delta \sigma }_E$| is independent of the definition of the ruptured domain. Note that the spectral structure of the slip distribution is modified from that implied by eq. (2006) and detailed in Section 3.1, the representation of slip heterogeneity in the model is based on the assumption that the seismic process is length scale-independent for a wide but truncated range (also see Andrews 1980). 11 (ν = 1 and χ = 0.3), thc has the mean value of 0.35, with the variance of 0.03, based on 100 random cases. Schematic diagrams showing energy partitioning in different stress evolution scenarios. The position of CNs and PRs were assigned to any of common iliac artery, external iliac artery, common femoral artery, and superficial femoral artery. The time from injury to MRI was determined by reviewing the collected clinical notes, which included the date of injury as reported by the patient.
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