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A rack, which is the algebraic distillation of two of the Reidemeister moves, is a set with a binary operation such that right multiplication is an automorphism. Any codimension two link has a fundamental rack which contains more information than the fundamental group. Racks provide an elegant and complete algebraic framework in which to study links and knots in 3–manifolds, and also for the 3–manifolds themselves. Racks have been studied by several previous authors and have been called a variety of names. In this first paper of a series we consolidate the algebra of racks and show that the fundamental rack is a complete invariant for irreducible framed links in a 3–manifold and for the 3–manifold itself. We give some examples of computable link invariants derived from the fundamental rack and explain the connection of the theory of racks with that of braids.

Summary. Background: Low fibrinogen levels are known to occur in trauma. However, the extent of fibrinogen depletion during trauma hemorrhage, the response to replacement therapy and association with patient outcomes remain unclear. Objectives: The study aims were to: characterize admission fibrinogen level and correlate it with factors associated with injury; describe the time course of fibrinogen depletion and response to replacement therapy; determine the correlation of fibrinogen level with rotational thromboelastography (ROTEM) parameters; evaluate the effect of fibrinogen supplementation ex vivo; and establish the association between fibrinogen level and clinical outcomes. Methods: This was a prospective cohort study of 517 patients. Blood samples were drawn on admission and after admistration of every 4 units of packed red blood cells. Fibrinogen levels were determined with the Clauss method, and global hemostatic competence was assessed with thromboelastometry. The effect of fibrinogen supplementation was assessed in a subgroup of coagulopathic patients. Results: Low admission fibrinogen level was independently associated with injury severity score (P < 0.01), shock (P < 0.001), and prehospital fluid volume (P < 0.001). Fibrinogen supplementation during transfusion maintained but did not augment fibrinogen levels. Administration of cryoprecipitate was associated with improved survival. ROTEM parameters correlated with fibrinogen level, and ex vivo fibrinogen administration reversed coagulopathic ROTEM parameters. Fibrinogen level was an independent predictor of mortality at 24 h and 28 days (P < 0.001). Conclusions: Fibrinogen level is decreased in injured patients on admission and is associated with poor outcomes. ROTEM is a rapid means of assessing hypofibrinogenemia. Earlier administration of specific fibrinogen replacement may improve outcomes, and prospective controlled trials are urgently needed.

Summary.  Background:  Trauma is a global disease, with over 2.5 million deaths annually from hemorrhage and coagulopathy. Overt hyperfibrinolysis is rare in trauma, and is associated with massive fatal injuries. Paradoxically, clinical trials suggest a much broader indication for antifibrinolytics. Objective:  To determine the incidence and magnitude of fibrinolytic activation in trauma patients and its relationship to clot lysis as measured by thromboelastometry. Methods:  A prospective cohort study of 303 consecutive trauma patients admitted between January 2007 and June 2009 was performed. Blood was drawn on arrival for thromboelastometry (TEM) and coagulation assays. Follow‐up was until hospital discharge or death. TEM hyperfibrinolysis was defined as maximum clot lysis of > 15%. Fibrinolytic activation (FA) was deterined according to plasmin–antiplasmin (PAP) complex and D‐dimer levels. Data were collected on demographics, mechanism, severity of injury, and baseline vital signs. The primary outcome measure was 28‐day mortality. The secondary outcome measures were 28‐day ventilator‐free days and 24‐h transfusion requirement. Results:  Only 5% of patients had severe fibrinolysis on TEM, but 57% of patients had evidence of ‘moderate’ fibrinolysis, with PAP complex levels elevated to over twice normal (> 1500 μg L−1) without lysis on TEM. TEM detected clot lysis only when PAP complex levels were increased to 30 times normal (P < 0.001) and antiplasmin levels were < 75% of normal. Patients with FA had increased 28‐day mortality as compared with those with no FA (12% vs. 1%, P < 0.001), fewer ventilator‐free days, and longer hospital stay. Conclusions:  FA occurs in the majority of trauma patients, and the magnitude of FA correlates with poor clinical outcome. This was not detected by conventional TEM, which is an insensitive measure of endogenous fibrinolytic activity.

SummaryBreaching endothelial cells (ECs) is a decisive step in the migration of leukocytes from the vascular lumen to the extravascular tissue, but fundamental aspects of this response remain largely unknown. We have previously shown that neutrophils can exhibit abluminal-to-luminal migration through EC junctions within mouse cremasteric venules and that this response is elicited following reduced expression and/or functionality of the EC junctional adhesion molecule-C (JAM-C). Here we demonstrate that the lipid chemoattractant leukotriene B4 (LTB4) was efficacious at causing loss of venular JAM-C and promoting neutrophil reverse transendothelial cell migration (rTEM) in vivo. Local proteolytic cleavage of EC JAM-C by neutrophil elastase (NE) drove this cascade of events as supported by presentation of NE to JAM-C via the neutrophil adhesion molecule Mac-1. The results identify local LTB4-NE axis as a promoter of neutrophil rTEM and provide evidence that this pathway can propagate a local sterile inflammatory response to become systemic.

Purpose: Contemporary trauma resuscitation prioritizes control of bleeding and uses major haemorrhage protocols (MHPs) to prevent and treat coagulopathy. We aimed to determine whether augmenting MHPs with Viscoelastic Haemostatic Assays (VHA) would improve outcomes compared to Conventional Coagulation Tests (CCTs). Methods: This was a multi-centre, randomized controlled trial comparing outcomes in trauma patients who received empiric MHPs, augmented by either VHA or CCT-guided interventions. Primary outcome was the proportion of subjects who, at 24 h after injury, were alive and free of massive transfusion (10 or more red cell transfusions). Secondary outcomes included 28-day mortality. Pre-specified subgroups included patients with severe traumatic brain injury (TBI). Results: Of 396 patients in the intention to treat analysis, 201 were allocated to VHA and 195 to CCT-guided therapy. At 24 h, there was no difference in the proportion of patients who were alive and free of massive transfusion (VHA: 67%, CCT: 64%, OR 1.15, 95% CI 0.76-1.73). 28-day mortality was not different overall (VHA: 25%, CCT: 28%, OR 0.84, 95% CI 0.54-1.31), nor were there differences in other secondary outcomes or serious adverse events. In pre-specified subgroups, there were no differences in primary outcomes. In the pre-specified subgroup of 74 patients with TBI, 64% were alive and free of massive transfusion at 24 h compared to 46% in the CCT arm (OR 2.12, 95% CI 0.84-5.34). Conclusion: There was no difference in overall outcomes between VHA-and CCT-augmented-major haemorrhage protocols.

In this paper we first give a one-move version of Markov's braid theorem for knot isotopy in S 3 that sharpens the classical theorem. Then a relative version of Markov's theorem concerning a fixed braided portion in the knot. We also prove an analogue of Markov's theorem for knot isotopy in knot complements. Finally we extend this last result to prove a Markov theorem for links in an arbitrary orientable 3-manifold.

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