Rotational Thromboelastometry (ROTEM)-Based Coagulation .

1y ago
1.42 MB
11 Pages
Last View : 26d ago
Last Download : 1m ago
Upload by : Annika Witter

REVIEW ARTICLESPaul G. Barash, MDGiovanni Landoni, MDSection EditorsRotational Thromboelastometry (ROTEM)-Based Coagulation Management inCardiac Surgery and Major TraumaKenichi A. Tanaka, MD, MSc,* Daniel Bolliger, MD,† Ratna Vadlamudi, MD,‡ and Alastair Nimmo, MB§FOR MAJOR BLEEDING related to severe trauma, majorsurgery, or chronic anticoagulation, a rapid assessment ofhemostatic function is crucial so that optimal fluid replacements and blood transfusion can be administered without delays.1-6 Although the safety of blood products with regard toviral transmission risks has improved in recent years,7,8 transfusions of allogeneic erythrocyte and plasma products havebeen implicated in serious adverse events, including nosocomial infections, acute lung injury, and organ dysfunction.9-12Obtaining conventional laboratory tests, such as the prothrombin time (PT), activated partial thromboplastin time (aPTT),and fibrinogen level, during acute bleeding is difficult becauseof a long turn-around time ( 30 min).13,14 Furthermore, laboratory PT/international normalized ratio and aPTT may not beparticularly useful in predicting bleeding after trauma or invasive procedures.15,16The prime example of bleeding management is preemptivetransfusions of fresh-frozen plasma (FFP) and platelet concentrates according to the erythrocyte requirement in major traumacases.17,18 This so-called “damage control resuscitation” (DCR;Table 1) originally was advocated for battlefield resuscitationin which laboratory testing and transfusion resources werelimited. However, plasma product transfusion according toDCR became increasingly popular in US civilian trauma centers and operating rooms.17,19 The prevention of trauma-induced coagulopathy and subsequent nonsurgical bleeding is amajor advantage of DCR,20 but the DCR approach lacks aspecific target for replacement and a consideration for interindividual variability in coagulation factor levels and vascular(endothelial) responses. Implementing transfusion algorithmsbased on point-of-care (POC) coagulation testing can be effective in decreasing transfusion requirements in elective or urgentcardiac surgical settings.2,5,21-23 In this review, the practical useof thromboelastometry is discussed relating to the diagnosis ofcoagulopathy and optimizing hemostatic interventions.POC TESTING AND TIMING OFHEMOSTATIC INTERVENTIONPT (or international normalized ratio), aPTT, fibrinogenlevel (Clauss method and its modifications), and platelet countare the tests performed most commonly in managing perioperative bleeding. Except for the platelet count, these laboratorytests require a separation of plasma from whole blood beforetesting, and, thus, a typical turn-around time is in the range of30-90 minutes.13,24 Abnormalities detected in these tests arefollowed by requests for specific blood components. The choiceof hemostatic therapies also affects the lag time before intervention. The time required for thawing FFP and cryoprecipitateis typically 30-60 minutes, but less time is needed for plateletconcentrates and thawed plasma. Factor concentrates, such asfibrinogen concentrate, and recombinant activated factor VII(rFVIIa) can be administered rapidly ( 10 min) because theyare reconstituted in small volumes and infused irrespective ofblood type.One of the key facts behind DCR is to prevent the delay oftransfusion therapy for patients in whom the risk of hemorrhagic death is considerably greater than transfusion-associatedcomplications.25 However, a substantial number of patientsmay receive allogeneic plasma products inappropriately or inexcess, which collectively increase the risk for transfusionrelated adverse events.26 By implementing rapid POC coagulation testing, hemostatic interventions can be more individualized and goal directed (targeted) instead of indiscriminateapplications of DCR. Currently available POC coagulation testsare classified into 3 categories. The first category includes POCwhole-blood PT and aPTT for a rapid evaluation (5-10 min) ofplasmatic coagulation. POC PT has been shown to have areasonable agreement with plasma-based PT.13,27,28 However,PT and aPTT are sensitive only to severe hypofibrinogenemia( 60-70 mg/dL) and are insensitive to FXIII deficiency orFrom the *Department of Anesthesiology, University of PittsburghMedical Center, Pittsburgh, PA; †Department of Anesthesia and Intensive Care Medicine, University of Basel Hospital, Basel, Switzerland;‡Department of Anesthesiology, Emory University School of Medicine,Atlanta, GA; and §Royal Infirmary of Edinburgh, Edinburgh, UK.Dr Bolliger was supported by a Myron B. Laver Grant, Departmentof Anaesthesia, University of Basel, Switzerland. Drs Tanaka, Bolliger,and Nimmo have received honoraria for consultation and/or lecturesfrom TEM International (Munich, Germany).Address reprint requests to Kenichi A. Tanaka, MD, MSc, VisitingProfessor of Anesthesiology, Department of Anesthesiology, UPMCPresbyterian C-215, 200 Lothrop Street, Pittsburgh, PA 15213.E-mail: 2012 Elsevier Inc. All rights reserved.1053-0770/2606-0022 5Key words: rotational thromboelastometry, coagulation monitoring,blood component transfusion, cardiac surgery, traumaJournal of Cardiothoracic and Vascular Anesthesia, Vol 26, No 6 (December), 2012: pp 1083-10931083

1084TANAKA ET ALTable 1. Damage Control ResuscitationEarly surgical control of bleeding sitesEarly transfusion of plasma, platelets, and erythrocytes; minimizedcrystalloid usagePermissive hypotension (mean arterial pressure 60 mmHg)Correction of hypothermia and acidosisTimely use of CaCl2, THAM, and rFVIIaAbbreviations: rFVIIa, recombinant factor VIIa; THAM, tris-hydroxymethyl aminomethane (alkalizer).fibrinolysis.29 Further, PT and aPTT have different sensitivitiesto hemodilution-induced decreases in procoagulant factor levels,15,16 and neither test reflects the total amount of thrombinthat can be generated in plasma.24 The second category includeswhole-blood platelet function tests, which are used increasinglyto monitor therapeutic responses to aspirin, clopidogrel, andother platelet adenosine-5 -diphosphate antagonists.30,31 Evaluating the extent of platelet inhibition by antiplatelet agents maybe useful in optimizing the perioperative risks of thrombosisand hemorrhage.32,33 Although a detailed discussion of plateletfunction monitoring is beyond the scope of this review,PlateletMapping will be discussed later as a modified techniqueof thrombelastography (TEG; Haemonetics-Haemoscope,Niles, IL).34 The third category includes TEG and rotationalthromboelastometry (ROTEM; TEM Systems, Raleigh, NC).These 2 systems are suitable for timely decision making ( 20min) in hemostatic interventions.2,4-6 Indeed, the decrease ofpostoperative blood loss without increasing the blood compo-DiodeLight detectorCOAGULATION TESTING ON ROTEMThe basic principles and technical aspects of TEG andROTEM have been reviewed elsewhere.14,38-40 In this article,the practical applications of ROTEM are described because thissystem currently offers comprehensive tests of coagulation. Forstandard ROTEM measurements, a citrated whole-blood sample (300 L) is placed in a plastic cup using an automatedpipette (Fig 1). The sample is recalcified with CaCl2, 0.2mmol/L (StarTEM; 20 L) and activated with 20 L of anEXTEM (tissue factor [TF]) or INTEM (ellagic acid) reagent.Subsequently, the plastic pin is immersed in the blood. Oncethrombin is generated in the blood, platelets are activated toexpress glycoprotein (GP) IIb/IIIa receptors, and fibrin isformed and polymerized. The interactions of GP IIb/IIIa receptors and polymerized fibrin increase the torque (viscoelasticity)between the cup and the rotating pin (at a 4.75 angle). Thebreakdown of fibrin strands by fibrinolysis decreases thetorque. The change in torque is detected optically and is processed by the microprocessor to trace the clot formation andbreakdown.The commonly used ROTEM variables include coagulationtime (CT; seconds), clot formation time (seconds), -angle(degrees), amplitude at 10 minutes after CT (A10; millimeters),100Clot firmness (mm)Dataprocessornent usage or mortality has been shown in a recent metaanalysis, including TEG and ROTEM.35 Rapid detection ofcoagulopathy by TEG or ROTEM allows a timely preparation(thawing) of blood products or a prompt intervention usingplasma-derived or recombinant factor 0MCFMLCFTCT10203040Clotting timeClot formation timeAlpha angleAmplitude 10 min after CTMaximum clot firmnessMaximum lysis5060Time (min)PinBloodFig 1. Basic principles of rotational thromboelastometry. For a rotational thromboelastometric measurement, a citrated blood sample isplaced with CaCl2 and a coagulation activator in the stationary cup. The rotating pin is lowered into the blood, and subsequent clot formationchanges the torque between the pin and the cup. The measured rotational thromboelastometric variables include the coagulation time (CT;seconds), clot formation time (CFT; seconds), -angle (degrees), amplitude at 10 minutes after CT (A10; millimeters), maximum clot firmness(MCF; millimeters), and maximum lysis (ML; percent decrease in amplitude 60 min after MCF). (Color version of figure is available online.)

ROTEM IN COAGULATION MANAGEMENT1085Table 2. Indications and Reference Ranges of Rotational Thromboelastometric TestsTestsIndicated to EvaluateCT (s)CFT (s)A10 (mm)MCF (mm)ML (%)EXTEM, APTEMFIBTEMINTEM, HEPTEM2platelets, 2plasma factors, 1fibrinolysis2fibrinogen2platelets, 2plasma factors, 1heparin42-74 (55)—137-246 (184)46-148 (95)—40-100 (63)43-65 (53)9-24 (14)44-68 (55)49-71 (60)9-25 (16)52-72 (61)0-18 (4)—0-12 (3)NOTE. Normal ranges (medians) are shown for EXTEM, FIBTEM, and INTEM. The EXTEM reference range is used for APTEM and the INTEMreference range is used for HEPTEM. Data from Lang et al.41Abbreviations: A10, amplitude at 10 minutes after coagulation time; APTEM, modified EXTEM test with aprotinin; CT, coagulation time;EXTEM, tissue factor reagent; FIBTEM, modified EXTEM test with cytochalasin D; FFP, fresh-frozen plasma; HEPTEM, heparinase plus INTEMreagent; INTEM, ellagic acid reagent; MCF, maximum clot firmness; ML, maximum lysis (percent decrease in amplitude 60 min after MCF); PCC,prothrombin complex concentrate; TXA, tranexamic acid.maximum clot firmness (MCF; millimeters), and maximumlysis (ML; percent decrease in amplitude 60 min after MCF;Fig 1). CT represents the onset of coagulation, whereas the clotformation time and -angle represent the initial rate of fibrinpolymerization. MCF is a measurement of the maximal viscoelastic strength of the clot. An ML 15% is used for thediagnosis of a premature breakdown of clot (hyperfibrinolysis).Normal ranges are summarized in Table 2.41 The referenceranges of TEG differ from those of ROTEM because of different sample types (citrated v noncitrated) and coagulation activators (kaolin v INTEM or EXTEM).39In addition to EXTEM and INTEM, several other tests canbe used in conjunction to diagnose specific coagulation problems. FIBTEM is a modified EXTEM test (Fig 2A) withcytochalasin D, which inhibits platelet cytoskeletal reorganization and, thus, fibrin(ogen) binding to platelet GP IIb/IIIa.42 Bycombining EXTEM and FIBTEM, the differential diagnosis ofthrombocytopenia and/or hypofibrinogenemia is feasible within20 minutes (Fig 2B, C). APTEM is also a modified EXTEM, inwhich aprotinin inhibits plasmin in vitro if systemic fibrinolysiswas present (Fig 2D).37HEPTEM contains heparinase in addition to the INTEMreagent. It is used as a pair with INTEM for the diagnosis ofsystemic heparin activity (Fig 2E).43 Although INTEM andkaolin-activated TEG are intrinsic pathway tests, the sensitivityand specificity are considerably different. Therefore, the cutoffvalues for ROTEM cannot be applied simply to TEG.39HEMOSTATIC MECHANISMS IN VIVOIn the event of a vascular injury (Fig 3A), a localizedhemostatic response is triggered by subendothelial collagen andTF, which are exposed to the circulating blood. Circulatingplatelets play a particularly important role in arterial hemostasis. The initial tethering of platelets to collagen is mediated byplatelet GP Ib/IX and the von Willebrand factor. A transientbinding of platelets to the von Willebrand factor becomesstabilized by collagen-induced platelet activation (via 2 1and GP VI receptors).44 In parallel, a trace amount of thrombinis generated by TF-FVIIa/FXa (extrinsic pathway). Thus, adenosine-5 -diphosphate and thromboxane are released by collagen- and thrombin-activated platelets, forming the primaryhemostatic plug (Fig 3B). Subsequently, platelet aggregatesserve as catalytic surfaces and binding sites for coagulationresponses. Substrates (fibrinogen), proenzymatic factors (FII,FIX, FX, FXI, FXIII), and accelerators (FV, FVIII) are con-gregated (depicted as S-E-A in Fig 3C) on the activated plateletsurface to augment the local generation of thrombin and polymerized fibrin. After the initial activation of thrombin by theextrinsic pathway, the propagation of thrombin formationmainly involves the “intrinsic pathway.” Thrombin can activateFXI, which efficiently converts FIX to FIXa. On the activatedplatelet surface, FIXa in combination with thrombin-activatedFVIIIa becomes the major activator (intrinsic tenase) of FX.Subsequently, FXa and thrombin-activated FVa form a complex (prothrombinase), which exponentially increases the conversion of prothrombin (FII) to thrombin. Once activated byadenosine-5 -diphosphate-stimulated, each platelet expresses alarge number of GP IIb/IIIa receptors ( 12,000) for fibrinogenbinding.45 Platelet-bound fibrinogen is converted to a fibrinmonomer by thrombin. Fibrin monomers are polymerized byplasma and platelet-derived FXIIIa, a transglutaminase, whichrequires thrombin-mediated activation.46 Polymerization of fibrin on platelets stabilizes the primary hemostatic plug.47 OnROTEM and TEG, major hemostatic responses involvingthrombin-activated platelets (GP IIb/IIIa), fibrin, and FXIIIaare reflected, although the contributions of the von Willebrandfactor, platelet GP Ib/IX, and other platelet agonists are minimal.HEMOSTATIC INTERVENTIONSIt is well known that blood transfusion practice varies amongindividuals and institutions.48 In case of bleeding, FFP, plateletconcentrates, and cryoprecipitate often are transfused empirically without laboratory testing. In addition to these allogeneicproducts, plasma-derived or recombinant factor concentrates,such as fibrinogen concentrates, prothrombin complex concentrates, and rFVIIa, have been used for perioperative hemostasis.6,49 Recent clinical data have shown that ROTEM testing isa practical method to standardize the local transfusion practice.5,50,51 Normal ranges of ROTEM testing are based on amulticenter study in healthy adult volunteers (Table 2).41Hemostatic intervention(s) should be considered for nonsurgical bleeding in the presence of abnormal ROTEM results.Threshold ROTEM values for interventions may vary amongdifferent types of vascular injury. In this section, several hemostatic products are discussed in relation to ROTEM parameters, but the availability of products differs among institutionsand countries. Therefore, it is prudent to validate or modify theherein-described algorithm for suitability at each institution.

1086A.TANAKA ET ALEFIBTEMEXTEMCTMCF 13 mmMCF 58 mm30103010minminB.EXTEMFIBTEMMCF 9 mmMCFMCF 3840 mmmm103010min30min30minC.EXTEMFIBTEMMCF 38 mmMCF 4 mm3010min10D.EXTEMAPTEMML 100%10ML 0%30min3010minE.INTEMHEPTEMCT 205 sCT 1500 s1030min1030minFig 2. Examples of rotational thromboelastometric tracings. (A) Normal(EXTEM, FIBTEM): EXTEM-MCF (normal,49-71 mm) and FIBTEM (normal, 9-25mm). (B) Thrombocytopenia (EXTEM,FIBTEM): platelet count 74 ⴛ 109/L andfibrinogen 170 mg/dL. (C) Thrombocytopenia and hypofibrinogenemia (EXTEM,FIBTEM): platelet count 57 ⴛ 109/L andfibrinogen 78 mg/dL. (D) Systemic fibrinolysis (EXTEM, APTEM): normal ML is 15%. (E) Heparin effect (INTEM,HEPTEM): prolonged CT (1,500 s) atINTEM (normal range, 137-246 s) is corrected at HEPTEM (ie, CTINTEM/CTHEPTEM ⴝ1.0 in the absence of heparin). APTEM,modified EXTEM test with aprotinin; CT,coagulation time; EXTEM, tissue factorreagent; FIBTEM, modified EXTEM testwith cytochalasin D; HEPTEM, heparinaseplus INTEM reagent; INTEM, ellagic acidreagent; MCF, maximum clot firmness;ML, maximum lysis (percent decrease inamplitude 60 min after MCF). (Color version of figure is available online.)

ROTEM IN COAGULATION MANAGEMENT(a) Vascular injury(b) Primary hemostasisS-E-A1087(c) CoagulationS-E-AEventVascular injuryBleedingPrimary hemostasisLocalization of factorsThrombin generationFibrin polymerizationElementsCollagenTissue factorPlateletsADP, ThromboxanevWF, FibrinogenFVII, FX, FIIPlatelets(S) Fibrinogen(E) FII, FIX, FX, FXI, FXIII(A) FV, tatevWF concentrateDesmopressinFFP, PCCCryoprecipitateFibrinogenFXIII concentraterFVIIaDiego, CA) and whole-blood impedance aggregometry (Multiplate, DynaBite, Munich, Germany) are used increasingly tomonitor therapeutic responses to aspirin and P2Y12 antagonists.32,55 For TEG, PlateletMapping is available for the evaluation of platelet inhibition by aspirin or clopidogrel.34,56-58 Forthis assay, a heparin-anticoagulated blood sample is used specifically to inhibit thrombin, which masks the antiplatelet effects of aspirin and clopidogrel. For PlateletMapping, fibrinpolymerization is achieved by the mixture of reptilase andactivated FXIII. Platelets are activated separately by the specific platelet activator (arachidonic acid for aspirin and adenosine-5 -diphosphate for clopidogrel). Decreased maximum amplitudes on PlateletMapping compared with kaolin-activatedTEG have been observed in perioperative patients with grossplatelet inhibition by aspirin or clopidogrel.59Plasma and Prothrombin Complex ConcentrateFig 3. Hemostatic processes and phase-specific interventions. (A)Hemorrhage occurs after vascular injury. Extravascular (subendothelial) collagen and tissue factor are exposed to the flowing blood.Transfusion of erythrocytes is the initial intervention. The intactvascular wall (blue), platelets (white ovals), erythrocytes (red circles),and fibrin (green) are depicted. (B) Platelets adhere to the vascularinjury site by interacting with von Willebrand factor (vWF) by glycoprotein Ib/IX receptors. Mural platelets are activated by collagen andtrace thrombin (by the extrinsic pathway involving factors VII [FVII],X [FX], and II [FII]). They release adenosine-5 -diphosphate (ADP) andthromboxane, stabilizing platelet-platelet interactions with fibrinogen. Thus, the primary (hemostatic) plug is established. Platelettransfusion and measures to increase von Willebrand factor canaugment this process. (C) Activated platelet aggregates serve as acatalytic surface and binding sites for coagulation responses. Substrates (S; fibrinogen), proenzymatic factors (E; factors II, IX [FIX], X,XI [FXI], and XIII [FXIII]), and accelerators (A; factors V [FV] and VIII[FVIII]) are congregated. These factors can be replaced using freshfrozen plasma (FFP) or specific factor concentrates (see text fordetails). PCC, prothrombin complex concentrate; rFVIIa, recombinantfactor VIIa.PlateletsThe clot firmness of EXTEM shows the tensile strength ofthe whole-blood clot, which reflects the interaction betweenthrombin-activated platelets and polymerized fibrin via plateletGP IIb/IIIa receptors. For microvascular bleeding, EXTEMand FIBTEM-A10 values can be used differentially to diagnosethe need for platelet transfusion or fibrinogen replacement.Thrombocytopenia ( 50-100 109/L) is suspected when theEXTEM-MCF is 45 mm and the FIBTEM-MCF is 8-10mm (Table 3).5,52 When the FIBTEM-MCF is 10 mm, cryoprecipitate or fibrinogen is withheld unless bleeding is likelyto con

COAGULATION TESTING ON ROTEM The basic principles and technical aspects of TEG and ROTEM have been reviewed elsewhere.14,38-40 In this article, the practical applications of ROTEM are described because this system currently offers comprehensive tests of coagulation. For standard ROTEM measurements, a citrated whole-blood sam-

Related Documents:

study of 213 US centers that the mean cost for one unit of pRBCs was 210.74 37.9 and the mean charge to the pa-tient was 346.63 135. 10 Few studies have compared the cost of blood products and coagulation factors before and after the implem

the cobas t 411 coagulation analyzer is the first member in Roche’s new series of coagulation analyzers. Quality and reliability Proven premium Roche quality means the cobas t 411 coagulation analyzer is reliable and robust with minimum downtime. Combined with an established, experienced global support network Roche ensures maximum up-time.

1 Coagulation and Rapid Mixing Coagulation is the process by which particles become destabilized and begin to clump together. Coagulation

coagulation when analysed at 33 C compared with 37 C. Th e Multiplate Analyzer results were dependent on the temperature used in the analyses and the body temperature. In whole blood coagulation tests, the temperature used in the analyses should be kept at 37 C irre

Rotational Symmetry A figure has rotational symmetry if it can be turned around its center to match itself in less than a 360o turn. The number of times in one complete turn that a figure matches itself is referred to as: Order of Rotational Symmetry OR Degree of Rotational Symmetry Use

Rotational transitions Typical values of B for small molecules are in the range of 0.1-10 cm-1, so rotational transitions lie in the microwave region of the spectrum. The transitions are detected by monitoring the net absorption of microwave radiation. Rotational selection rules For a molecule to give a

Rotational Energy. When there is no vibrational motion we expect the molecule to have the internuclear separation (bond length) R R. e, and the rotational energy in cm-1. or wavenumbers becomes F(J) B. e. J(J 1) with where B. e. is the . Rotational Constant. and c is the speed of ligh

Rotational transitions B of small molecules 0.1 10 cm-1 (microwave region) (a) Rotational selection rules Gross selection rule: μ 0 (permanent electric dipole moment) for pure rotational spectrum, it must be polar Homonuclear diatomic molecules, symmetrical linea

The cobas t 711 coagulation analyser can also be connected with the cobas 8100 and the cobas connection modules. Both analysers can be used in rand om-access or batch modes, and offer true STAT capabilities, with dedica ted slots for urgen t samples. cobas t 511 coagulation analyzer

cobas t 411 coagulation analyzer 5.478 3.261 1 cobas t 511 coagulation analyzer 8.757 4.413 1 cobas t 711 coagulation analyzer 11.855 5.973 1 MultiplateT analyzer 1.310 – – – Urindiagnostik cobas u 601 urine analyzer 4.989 – – – cobas

and adding ozone and irradiating with ultraviolet light. 1.2.2 Coagulation. In wastewater treatment operations, the processes of coagulation and flocculation are employed to separate suspended solids from water. Although the terms coagulation and floccu

score, and CT characteristics have been routinely used to predict outcome in patients with TBI [15]. Although coagulation abnormalities may be a better predictor of mortality than the absence of the bilateral pupillary light reflex in some patients [16], prognosis is rarely predicted by coagulation status alone in the clinical setting.

Shaffrey, md,2 and edward c. Nemergut, md1,2 Departments of 1 Anesthesiology, 2 Neurosurgery, and 3 Pathology, University of Virginia, Charlottesville, Virginia OBJect Major spinal surgery in adult patients is oft

rotational motion and astrophysics can have impacts on our lives, as well on the environment/society. This application and development of skills can be achieved using a variety of approaches, including investigation and problem solving. The Unit will cover the key areas of kinematic relationships, angular motion, rotational dynamics, gravitation, general relativity, and stellar physics .

Considering rotational equilibrium about the back wheels. F 1 x 1.8 mg (1.8 – 1.05) 0.75 x 1800 x 9.8 or F 1 0.75 x 1800 x 9.8/1.8 7350 N Force on each front wheel is 7350/2 N or 3675 N. System of Particles and Rotational Motion NCERT Solutions for Class 11 Physics 7 Question 7. 10. (a) Find the moment of inertia of a sphere about a .

J J J N- m-s / rad B B B N- m-s/rad 2 T m L T m L Where: B T total viscous friction J T total rotational inertia B L load viscous friction B m motor viscous friction J m motor rotational inertia JL load rotational inertia With speed changer J1 N- m- s / rad N N J J B N m- s/rad N N 2 L 2 T m L 2 2 1 T m » ¼ º « ª » ¼ º .

only line symmetry only rotational symmetry both line symmetry and rotational symmetry neither line symmetry and nor rotational symmetry 30 . These printable Worksheets and Practice Papers are available for FREE download Helps stu

1/2 13: Symmetry 13.1 Line symmetry and rotational symmetry 4 To recognise shapes that have reflective symmetry To draw lines of symmetry on a shape To recognise shapes that have rotational symmetry To find the order of rotational symmetry for a shape 13.2 Reflections To

Reducing rotational speed will draw less electrical power compared to valve throttling. Increased service life by lowering rotational speed (seals, bearings and motor). Ability to integrate with system automation and monitoring. Rotational speed can be controlled to maintain

Advanced Engineering Mathematics Dr. Elisabeth Brown c 2019 1. Mathematics 2of37 Fundamentals of Engineering (FE) Other Disciplines Computer-Based Test (CBT) Exam Specifications. Mathematics 3of37 1. What is the value of x in the equation given by log 3 2x 4 log 3 x2 1? (a) 10 (b) 1(c)3(d)5 E. Brown . Mathematics 4of37 2. Consider the sets X and Y given by X {5, 7,9} and Y { ,} and the .