Fixed point property for a CAT(0) space which admits a proper cocompact group action

We prove that if a geodesically complete $\mathrm{CAT}(0)$ space $X$ admits a proper cocompact isometric action of a group, then the Izeki-Nayatani invariant of $X$ is less than $1$. Let $G$ be a finite connected graph, $\mu_1 (G)$ be the linear spectral gap of $G$, and $\lambda_1 (G,X)$ be the nonlinear spectral gap of $G$ with respect to such a $\mathrm{CAT}(0)$ space $X$. Then, the result implies that the ratio $\lambda_1 (G,X) / \mu_1 (G)$ is bounded from below by a positive constant which is independent of the graph $G$. It follows that any isometric action of a random group of the graph model on such $X$ has a global fixed point. In particular, any isometric action of a random group of the graph model on a Bruhat-Tits building associated to a semi-simple algebraic group has a global fixed point

Uniform estimates of nonlinear spectral gaps

By generalizing the path method, we show that nonlinear spectral gaps of a finite connected graph are uniformly bounded from below by a positive constant which is independent of the target metric space. We apply our result to an $r$-ball $T_{d,r}$ in the $d$-regular tree, and observe that the asymptotic behavior of nonlinear spectral gaps of $T_{d,r}$ as $r\to\infty$ does not depend on the target metric space, which is in contrast to the case of a sequence of expanders. We also apply our result to the $n$-dimensional Hamming cube $H_n$ and obtain an estimate of its nonlinear spectral gap with respect to an arbitrary metric space, which is asymptotically sharp as $n\to\infty$.Comment: to appear in Graphs and Combinatoric

An Intrinsic Characterization of Five Points in a CAT(0) Space

Gromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space

Mechanical Thrombectomy Beyond 2b Reperfusion: Should We Pursue a Higher Reperfusion Grade after Achievement of 2b?

Background Extended thrombolysis in cerebral infarction (eTICI) 2c/3 reperfusion after mechanical thrombectomy (MT) is associated with better stroke outcomes than eTICI 2b. Whether additional MT attempt after achieving eTICI 2b (beyond 2b attempt) leads to better outcomes is unknown. Methods Consecutive patients with acute anterior circulation stroke who achieved eTICI 2b during MT were divided into 2 groups: those who further tried MT (beyond‐2b group) and those without (nonbeyond‐2b group). The patients who directly achieved eTICI 2c/3 without experiencing 2b (direct‐2c/3 group) were also studied. The outcomes included the reperfusion status, favorable outcome (3‐month modified Rankin scale score of 0–2), neurological improvement (a ≥10‐point decrease of the National Institutes of Health Stroke Scale score from baseline or the score of 0) at 24 hours and symptomatic intracranial hemorrhage. Results Of 308 patients, 50 were in the beyond‐2b group, 87 in the nonbeyond‐2b group, and the remaining 171 in the direct‐2c/3 group. Perfusion of middle cerebral artery branches supplying the primary motor cortex was worse in the beyond‐2b than the nonbeyond‐2b group at the time of eTICI 2b (P=0.007). Favorable outcome was similarly common (48% for each, P=0.40). Neurological improvement was more frequent (52% versus 37%; P=0.04) and symptomatic intracranial hemorrhage tended to be more common (6% versus 1%, P=0.11) in the beyond‐2b than the nonbeyond‐2b group. Eighteen patients (36%) in the beyond‐2b group finally achieved eTICI 2c/3; 10 of these (56%) and 14 of the remaining 32 (44%) had favorable outcome (P=0.83). The former rate was similar to that in the direct‐2c/3 group (58%; P=0.99). Conclusions Patients undergoing additional MT attempt after achieving eTICI 2b had numerically but not significantly more symptomatic intracranial hemorrhage and showed a similar level of functional outcome at 3 months than those who did not. When eTICI 2c/3 was finally achieved by additional attempts, functional outcome was similar with that of patients who directly achieved eTICI 2c/3 without experiencing 2b. Clinical Trial Registration Information URL: https://www.clinicaltrials.gov. Unique identifier: NCT02251665

Anti-Apoptotic Effects of Recombinant Human Hepatocyte Growth Factor on Hepatocytes Were Associated with Intrahepatic Hemorrhage Suppression Indicated by the Preservation of Prothrombin Time

Hepatocyte growth factor (HGF) is an endogenously expressed bioactive substance that has a strong anti-apoptotic effect. In this study, we biochemically and histologically characterized the effects of rh-HGF on in vitro human hepatocyte injury and mouse acute liver failure (ALF) models, both of which were induced by antibody-mediated Fas signaling. rh-HGF inhibited intracellular caspase-3/7 activation and cytokeratin 18 (CK-18) fragment release in both models. Histologically, rh-HGF dramatically suppressed parenchymal damage and intrahepatic hemorrhage. Among the laboratory parameters, prothrombin time (PT) was strongly preserved by rh-HGF, and PT was well correlated with the degree of intrahepatic hemorrhage. These results showed that the anti-apoptotic effect of rh-HGF on hepatocytes coincided strikingly with the suppression of intrahepatic hemorrhage. PT was considered to be the best parameter that correlated with the intrahepatic hemorrhages associated with hepatocellular damage. The action of rh-HGF might derive not only from its anti-apoptosis effects on liver parenchymal cells but also from its stabilization of structural and vasculature integrity

Mechanical Thrombectomy Up to 24 Hours in Large Vessel Occlusions and Infarct Velocity Assessment

Background We retrospectively compared early‐ (<6 hours) versus late‐ (6–24 hours) presenting patients using perfusion‐weighted imaging selection and evaluated clinical/radiographic outcomes. Methods and Results Large vessel occlusion patients treated with mechanical thrombectomy from August 2017 to July 2020 within 24 hours of onset were retrieved from a single‐center database. Perfusion‐weighted imaging was analyzed by automated software and final infarct volume was measured semi‐automatically within 14 days. The primary end point was good outcome (modified Rankin Scale 0–2 at 90 days). Secondary end points were excellent outcome (modified Rankin Scale 0–1 at 90 days), symptomatic intracranial hemorrhage, and death. Clinical characteristics/radiological values including hypoperfusion volume and infarct growth velocity (baseline volume/onset‐to‐image time) were compared between the groups. Of 1294 patients, 118 patients were included. The median age was 74 years, baseline National Institutes of Health Stroke Scale score was 14, and core volume was 13 mL. The late‐presenting group had more female patients (67% versus 31%, respectively; P=0.001). No statistically significant differences were seen in good outcome (42% versus 53%, respectively; P=0.30), excellent outcome (26% versus 32%, respectively; P=0.51), symptomatic intracranial hemorrhage (6.5% versus 4.6%, respectively; P=0.74), and death (3.2% versus 5.7%, respectively; P=0.58) between the groups. The late‐presenting group had more atherothrombotic cerebral infarction (19% versus 6%, respectively; P=0.03), smaller hypoperfusion volume (median: 77 versus 133 mL, respectively; P=0.04), and slower infarct growth velocity (median: 0.6 versus 5.1 mL/h, respectively; P=0.03). Conclusions Patients with early‐ and late‐time windows treated with mechanical thrombectomy by automated perfusion‐weighted imaging selection have similar outcomes, comparable with those in randomized trials, but different in infarct growth velocities. Registration URL: https://www.clinicaltrials.gov; Unique identifier: NCT02251665

Abstract 1122‐000009: Impact of RNF213 p.R4810K Variant on Endovascular Therapy Outcome for Acute Large Vessel Occlusion Stroke

Introduction: The ring finger protein 213 gene (RNF213) has been identified as a susceptibility gene for moyamoya disease, and the p.R4810K polymorphism as a founder variant commonly found in East Asian patients. 1  A recent large case‐control study including over 46,958 Japanese subjects reported that the RNF213 p.R4810K variant was a strong risk factor for Japanese cerebral infarction: the variant was found in 5.2% of patients with non‐cardioembolic stroke and in 2.1% of healthy controls. 2   Mechanical thrombectomy (MT) is a standard treatment for acute ischemic stroke due to occlusion of the internal carotid artery and M1 segment of the middle cerebral artery, but in East Asians, about 15–25% of LVOs for which MT was performed were reportedly caused by intracranial atherosclerotic disease (ICAD). 3  RNF213 p.R4810K variant may be involved to some extent in ICAD‐related LVO of Asian patients undergoing MT. In this study, we aimed to investigate the impact of RNF213 p.R4810K variant on EVT for anterior circulation LVO stroke. Methods: Of the consecutive ischemic stroke patients from 2011 to 2021 seen in our institute, patients who underwent EVT for acute occlusion of the intracranial ICA or M1 segment of MCA and signed a consent form for RNF213 genotyping were included. Outcomes were instant re‐occlusion, final modified Thrombolysis in Cerebral Infarction (mTICI) ≥2b reperfusion, early re‐occlusion, and modified Rankin Scale (mRS) score 0–2 at 90 days. Instant re‐occlusion was defined as occurrence of re‐occlusion during the procedure, whereas early re‐occlusion as re‐occlusion detected on magnetic resonance angiography within 2 weeks after confirmation of successful reperfusion at the end of the procedure. 4 Results: Of the 277 patients (128 women [46.2%]; median age, 76 years) analyzed, 10 (3.6%) patients had the RNF213 p.R4810K variant. The variant carriers were younger (67 years vs. 76 years, P<0.01), more frequently received angioplasty (40.0% vs. 12.0%, P<0.01), and more frequently had intracranial atherosclerotic disease‐related LVO as a cause of acute LVO (70.0% vs. 8.6%, P<0.01) than non‐carriers. The variant carriers showed higher rates of instant re‐occlusion (40.0% vs. 5.6%, P<0.01), but there were no statistically significant inter‐group differences for the final mTICI ≥2b reperfusion rate between carriers and non‐carriers (100.0% vs. 81.6%, P = 0.22). Early re‐occlusion was more frequent in the variant carriers than non‐ carriers (60.0% vs. 0.4%, P<0.01) with no intergroup difference in the rate of repeated EVT (67.7% vs. 100.0%, P = 0.71). There were no statistically significant inter‐group differences for achievement of mRS score 0–2 (60.0% vs. 51.7%, P = 0.75) Conclusions: Both instant and early re‐occlusion were more frequent in the RNF213 p.R4810K variant carriers who had received EVT for acute anterior circulation LVO than in the non‐carriers. Potential impact of RNF213 polymorphism status on EVT outcomes was clarified