Overview. B1 TX Field. RF Nonuniformities. NMR Signal 8/1/ :00. AAPM MRI Physics & Technology. G.D. Clarke, UTHSCSA 1
|
|
- Cecilia Gilbert
- 6 years ago
- Views:
Transcription
1 Overview Excitatin & Signal Cllectin Prcess The Principles f Quantitative MRI Geffrey D. Clarke Dept. f Radilgy University f Texas Health Science Center at San Antni Gradients fr Spatial Lcalizatin Measuring Tissue Vlumes Measuring NMR Prperties f Tissues Tissue Physilgy Measurements Tissue Bichemistry Measurements RF Nnunifrmities RF Nnunifrmities are the Single Biggest Cause f Errrs in qmri RF Nnunifrmities Increase as the B -Field Increases Dielectric Resnance Effects Becme Prnunced at High B B TX Field Directly related t current in TX cil Depends n Q f cil & cil lading Depends n TX Cil Gemtry TX pwer aut-adjusted (pre-scan) Values shuld be knw t % % =.86 db TX nnlinearities RF pulse drp 3 4 NMR Signal () t B M δv cs( ω t) δ v = ω x,y x, y s The B RF Magnetic Field z N S x y B 5 ξ = ( m B ) where m is the (nuclear) t magnetic diple mment and B = ( B iˆ B x + Principle f Reciprcity y ˆ) j 6 G.D. Clarke, UTHSCSA
2 RF Pulse Bandwidth (BW) BW is inversely prprtinal t RF pulse duratin: TX FT frequency FT Apprximatin A sinc functin ( sin x x ) envelpe n the r.f. pulse prduces a nearly square excitatin prfile f the phantm.. TX FT Slice select gradient is scaled based n BW & G ss : slice thickness π = γ BW G ss frequency 7 t p FT BW frequency 8 X Resnant Frequency Offset ΔΩ/γ B eff After 9, IS NOT n y axis M M B = B +ΔΩ/γ B eff = B x y +ΔΩ z /γ ΔΩ/γ X Y B eff X Y B X Y M x M y = real M x = imaginary M z des nt cntribute t signal M z M y Y 9 Sinc Pulse Prfile M y M x.5 M z Frequency (khz) Frequency (khz) ms, 5-lbe, chemical shift refcused 9 8 Sinc Pulse M y M x -.5 M z Frequency (khz) Frequency (khz) ms, 5-lbe, chemical shift refcused TX RX G sl Slice Selectin rf rf Spin Ech If cnstant gradient field is n during the rf pulse: Larmr frequency f spins varies with psitin The flip angle depends n the lcal Larmr frequency and the frequency cntent f the RF field pulse the RF pulse can be crafted t cntain frequencies in nly a specified range G.D. Clarke, UTHSCSA
3 Slice Prfile Variatins Flip Angle varies with lcatin Due t B, B nnunifrmities Nn-linearity f Excitatin (Blch Eqns) FT apprximatin invalid fr big flip angles Blch simulatr sftware T-weighting f excitatin prfile Blch Equatins A set f simultaneus differential equatins that describe the behavir f the magnetizatin under any cnditins. dmz Mz M =γ[ Mx By My Bx ] dt T dmx M =γ[ My( t) Bz MzBy ] dt x T dmy M =γ[ Mz( t) Bx MxBz ] dt y T alng the z-axis alng the x-axis alng the y-axis Brain Hargreaves 3 4 Pr RF Pulse Calibratin Miscalibratin f FSE 8 rf pulses (left image) is crrected (right image) B Field Mapping - Purpse a. Needed fr accurate measurement f many NMR parameters, i.e. relaxatin s b. Enables estimatin f systematic errrs in parameter measurement c. Enable crrectin f spatial sensitivity variatin using reciprcity 5 6 B Field Mapping - Methds a. One-pulse read M x,y Venkatsen et al. Magn Resn Med 998; 4:59 b. Spin Ech (bth pulses altered) Barker et al. BJR 998; 7: c. One-pulse read M z Vaughn et al. Mgn Resn Med ; 46: 4 B Field Mapping One-pulse M x,y methd Hard 8 pulse preceding D field ech sequence Bright center is maximum B Ring pattern ccurs at every 5% change in B -field 7 8 Deichmann R et al. Magn Resn Med ; 47: 398 G.D. Clarke, UTHSCSA 3
4 Dielectric Resnance Effect Fields inside a sample f diameter, d, can be resnant when d = nλ This can make the B field at the center f the sample larger than at the edges This effect is dampened as the cnductivity f the sample increases 9 Image Unifrmity at 3 Tesla.5T 3 T B field maps in a saline phantm (8 cm diameter) RL Greenman et al. JMRI 3, 7(6): Dielectric Resnance Spin-Ech Sequence TX RX rf rf Spin Ech G sl G r G pe Symblizes gradient increment frm excitatin t excitatin Hult DI, J Magn Resn Imag, ; :46-67 Gradient Subsystems One Dimensinal FT B (x) x Mag FT ν 3 4 G.D. Clarke, UTHSCSA 4
5 MRI Gemetric Distrtins ω = γ ( B + xg ) Machine dependent Patient-dependent Accessry device dependent x MRI Gradient Fields Surces f Errr: Gradient Amplitude Calibratin Best abut % errr Gradient Nn-linearities Eddy Currents 5 6 Eddy Currents Accelerating current in gradient cils (gradient pulse) causes induced currents in nearby metallic structures. These currents prduce magnetic fields which, in turn, ppse the magnetic fields f the gradient cils Eddy Currents The magnetic field prduced by Eddy Currents have tw -dependent cmpnents: An ffset f the B field An additinal gradient field B ec ( r, t) = Δg( r, t) + ΔB 7 8 Eddy Current Pre-emphasis Gradient Current Eddy Current Actual Gradient Field Gradient Wavefrms Gradient t Magnet Rati G/R=.8 G/R=.6 In free space In magnet In magnet In free space Gradient Current with Pre-Emphasis Actual Gradient Field 9 A. Whle bdy system. B. Whle bdy, G/R=.6 In magnet In free space In magnet In free space ms ms A. Micrscpy system. B. Micrscpy system 3 G.D. Clarke, UTHSCSA 5
6 Actively Screened Gradients Reduce gradient field strength utside f gradient cil frmer - Current in shield is ppsite plarity Reduces gradient field in imaging vlume als - Imprves magnet hmgeneity Each gradient cil is assciated with a screen cil - Twice as many amplifiers required 3 Measuring Eddy Currents 3 De Deene Y et a. Phys Med Bil ; 45:87-83 Eddy Currents Time curse f eddy current field ffset fllwing different numbers f gradient pulse units MRI Gradient Fields Gradient Nnlinearities are ften tlerated as part f trade-ffs with gradient field strength r cil size Manufacturers ften apply gradient distrtin crrectins in rder t make images appear t be distrtin free Influences image quality parameters (SNR, spatial reslutin, etc.) 33 De Deene Y et a. Phys Med Bil ; 45: Brain Vlume Measurement Brain Vlume Relatinships White Matter Basal Gray Cerebellum High agreement between qmri vlumetry and physical sectins qmri vlumetry is susceptible t high inter-bserver variability Prblems greatest in thse regins where tissue margins are prly defined 35 Jelsing J NeurImage 5; 6: Jelsing J NeurImage 5; 6: G.D. Clarke, UTHSCSA 6
7 Cartilage MRI Relaxatin Times T : lngitudinal relaxatin defines recvery f ptential fr next signal (T =/R ) T : transverse relaxatin defines rate f dephasing f MRI signal due t micrscpic prcesses (T =/R ) T *: transverse relaxatin with B inhmgeneity effects added; defines rate f dephasing f MRI signal due t macrscpic and micrscpic prcesses (T * =/R * ) Accuracy f 3T high and tends t be mre reprducible than.5 T 37 Eckstein F et al. Arth & Rheum 5; 5: Lngitudinal Relaxatin M = M (- exp(-tr/t) M Transverse T* Decay T T 3T 4T τ 39 4 Applicatins fr T Images Tissue characterizatin Cntrast agent uptake studies Measurement f Tissue Perfusin Measurement f Bld Vlume Factrs Influencing T Macrmlecular cncentratin in cytsl Water binding Water cntent Gd and Fermxide Cntrast Agents 4 4 G.D. Clarke, UTHSCSA 7
8 T Measurement Sequences Inversin Recvery ; the gld standard Inversin Recvery Spin Ech 8 Saturatin Recvery 9-8 Stimulated Ech Lk-Lcker Sequence (see belw) 43 TI TE TR Inversin Excitatin Refcusing +M M = M ( - exp[-ti/t ]) TI -M 44 Lk-Lcker Sequence 8 α α α α α Saturatin Recvery fr CMRI Encde Encde Encde Encde Encde τ τ τ Very sensitive t RF pulse errrs recvery rate, T * : T * τ = τ ln T τ ( csα ) τ Higgins DM, Med Phys 5; 3(6): (a) T Map f tubes f gel dped with Gd-DTPA T Parametric Maps (b) T-weighted image f heart in shrt axis (c) T parametric map image f heart in (b) T s calculated frm shrt-acquisitin perid T sequence (SAP-T) with varying delay s 47 Higgins DM, Med Phys 5; 3(6): Fr Accurate & Precise T Never Assume RF Flip Angle is Crrect Varies ver imaged slice due t slice prfile Flip angle must be calibrated acrss slice Be careful in assuming magnetizatin has reached steady state between acquisitins Optimize sequence acquisitin parameters t ensure maximal SNR Always check that fitted cnfrms t assumed mdel 48 G.D. Clarke, UTHSCSA 8
9 Signal Strength Multi-Ech with 8 Pulses SE 8 TE SE *TE M exp(-te/t ) M exp (-TE/T * ) 3*TE SE3 TE >> T * Signal Strength G slice G read G phase Multi-Ech Acquisitins M exp(-te/t ) M exp (-TE/T * ) SE 8 SE TE *TE 3*TE SE Time Scale f Relaxatin Calculatin f T Lngitudinal Transverse M exp (-TE/T * ) - exp (-TR / T ) s f ms s f ms M ln M ln( M T xy = M xy xy ' t / T e = / T / M ' ) = = / slpe t + ln M ' slpe = / T 5 5 Gel Dsimeters Used fr 3D Radiatin Dsimetry QC Relies n direct relatinship between relaxatin rate, R (R =/T ) f gel fllwing expsure and dse Eddy Current Effects n Slice a b c Ideal n eddy currents wrst case pre-gradient train RF pulse prfiles used fr T-relaxmetry a) Ideal prfile calculated frm Blch equatins b) prfile shwing the influence f eddy currents; c) pre-gradient pulse train establishes steady-state which regularizes the RF pulse prfile De Deene Y et a. Phys Med Bil ; 45:87-83 G.D. Clarke, UTHSCSA 9
10 B Changes with Slice Psitin Effective Flip Angles Average transverse magnetizatin within a slice as a fractin f M fr varius slice psitins fr flip angles ranging frm t De Deene Y et a. Phys Med Bil ; 45: De Deene Y et a. Phys Med Bil ; 45: R Calibratin T* Parametric Imaging M xy = M ' e t / T * Similar t T measurements but use gradient ech imaging with varying TE Cntrast Agent Maps Transfer Cntrast Multislice FSE: T-weighted image Parametric map f R * Transfer Cntrast Enhances T - Weighted Appearance G.D. Clarke, UTHSCSA
11 Transfer PROTON SPECTRUM Frequency (Hertz) Free Water Lipids Bund Water 7 Hz 5 Hz Frequency (Hertz) 6 Transfer Rati MTR = M M M Transfer Rati (MTR) the difference f the saturated versus nn-saturate images relative t the signal in the nrmal (nnsaturated images) s 6 MTR and Aging Gray matter and white matter MTR images reveal a quadratic change with age that is primarily attributed t nrmal demylenatin Physilgical Measurements Flw bulk mtin f bld and ther fluids within bdy Perfusin amunt f bld traveling thrugh capillaries in ml/s/gm f tissue Diffusin randm mtin f spins in a hmgeneus slutin Apparent Diffusin Cefficient measured diffusin rate f water thrugh tissue 63 Inglese & Ge, Tp Magn Resn Imag 4; 5: Attenuatin Due t Diffusin A( TE) = A() exp[ γ G Dappδ α ( Δ )] 4 δ Where: α=π/; G is amplitude f diffusin sensitive gradient pulse; δ is duratin f diffusin sensitive gradient; Δ is between diffusin sensitive gradient pulses; D app is the apparent diffusin cefficient 65 DWI Basic Pulse Sequence 9 8 G G δ δ Δ b = γ G δ ( Δ ) δ 66 Stejskal EO & Tanner JE, J Chem Phys : G.D. Clarke, UTHSCSA
12 The b-value Cntrls amunt f diffusin weighting in image The greater the b-value the greater the area under the diffusin-weighted gradient pulses lnger TE strnger and faster ramping the gradients 67 Anistrpic Diffusin H O H O Restricted diffusin alng neural fibers 68 Diffusin-Weighted MRI Hemispherical Hypperfusin Images acquired 55 minutes after nset f aphasia, hemiplegia, and hemiparesis. b = s/mm Tp. Cnventinal -sht EPI DWI B. SENSE EPI-DWI with R=3 shws reduced susceptibility artifacts in frntal brain 69 Bammer R, Schenberg SO. Tp Magn Resn Imag 4; 5: 9-58 T -weighted Diffusin Time-t-peak Weighted Perfusin 7 Sunshine JL et al. Radilgy 999; : Diffusin Fiber Tracking Diffusin-Weighted Breast MRI Diffusin tracks (red and blue) in the splenium f the crpus callsum selected with ellipsid filtering vlumes (black) Parametric maps calculated frm bimdal expnential decay mdel: I I = P ' ' ' ( bd ) + P ( bd ) ' exp exp 7 Cntur et al. PNAS 999; 96:44. 7 Paran Y et al. NMR Bimed 4; 7:7-8 G.D. Clarke, UTHSCSA
13 Diffusin Tensr Imaging Dephasing Due t Mtin In anistrpic tissues (neural fibers, muscle fibers) scalar ADC depends n directin f diffusin sensitizing gradient G slice +8 BLOOD: phase nt zer Diffusive transprt f water can be characterized by an effective diffusin tensr Directin f diffusin can be used t create a map shwing rientatin f mycardial fibers. PHASE -8 t = Phase Shift Due t Mtin in a Gradient Field TISSUE: phase equals zer 73 Tseng et al., Radilgy ; 6: PHASE PHASE -8 Phase Cntrast Imaging +8 Velcity Encded Image TISSUE: phase equals zer in BOTH images Velcity Cmpensated Image Phase Difference Mtin Cmpensatin Gradient (Biplar) Applied Velcity Encded Image BLOOD: phase is DIFFERENT in each image 75 Phase Cntrast Images Tw Signals: S = S s + S m ;S = S s + S m e(iϕ m ) where ϕ m = γδm υ (υ = velcity) Cmplex difference - ΔS =S -S =S m [e(iϕ m )-] =is m sin(ϕ m /) Phase difference - Δϕ = arg S -arg S, then υ = Δϕ / (γ ΔM ) 76 Phase Cntrast Velcity Velcity Encding (V enc ) Magnitude Phase Cntrast +V enc 8 N Flw Flw Velcity 9 cm/s Statinary In Out In Out MRI Velcity (cm/s) -V enc True Flw Velcity (cm/s) Phase Difference (degrees) G.D. Clarke, UTHSCSA 3
14 Anterir Anterseptal Inferseptal Inferir Inferlateral Anterlateral Anterir Anterseptal Inf ersept al Inf erir Inferlateral Anterlateral AAPM 6 - MRI Physics & Partial Vlume Effect Cardiac Output 5 S ttal φ S static S mving φ mving S ttal φ S static S mving φ mving Asc. Arta Flw (l/min) Cine Frame Number Cardiac Output = 4. L/min Strke Vlume = 68 ml 79 8 Crnary Artery Flw Gadlinium Uptake A B C D 8 8 Nnunifrmity Crrectin Real- TrueFISP cine study with GRAPPA was perfrmed between tw perfusin scans SI nrmalizatin = SI SI crrectin = SI SI perf /SI cine SI nrmalizatin -SI base Crrect fr verall effects Crrect fr baseline signal Max Upslpe Parametric Map SI (A.U.) SI (A.U.) Time (sec) Time (sec) 83 MRI perfusin image Maximum upslpe parametric map 84 G.D. Clarke, UTHSCSA 4
15 Data Analysis Results SUMMARY MPRI 3 anterir anterseptal inferseptal inferir inferlateral anterlateral Mycardial perfusin reserve index (MPRI) is nt significantly different between segments in asymptmatic individuals after crrectins Bullseye display depicts segmental MPRI frm mst apical slice (center ring) t mst basal slice (uter ring) Befre undertaking qmri: Check gradient calibratins Understand gradient nn-linearities Evaluate eddy currents Measure RF pulse changes in space Determine RF receive nnunifrmities Quantitative MRI Methds Learn Mre Details Measuring things with MRI: Diffusin Cefficients Frequency f a signal Relaxatin rates (T, T, MTC) Velcity f mtin Vlumes f tissues G.D. Clarke, UTHSCSA 5
Electric Current and Resistance
Electric Current and Resistance Electric Current Electric current is the rate f flw f charge thrugh sme regin f space The SI unit f current is the ampere (A) 1 A = 1 C / s The symbl fr electric current
More informationrcrit (r C + t m ) 2 ] crit + t o crit The critical radius is evaluated at a given axial location z from the equation + (1 , and D = 4D = 555.
hapter 1 c) When the average bld velcity in the capillary is reduced by a factr f 10, the delivery f the slute t the capillary is liited s that the slute cncentratin after crit 0.018 c is equal t er at
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More informationMaterials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals of Diffusion
Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals f Diffusin Diffusin: Transprt in a slid, liquid, r gas driven by a cncentratin gradient (r, in the case f mass transprt, a chemical ptential
More information( ) kt. Solution. From kinetic theory (visualized in Figure 1Q9-1), 1 2 rms = 2. = 1368 m/s
.9 Kinetic Mlecular Thery Calculate the effective (rms) speeds f the He and Ne atms in the He-Ne gas laser tube at rm temperature (300 K). Slutin T find the rt mean square velcity (v rms ) f He atms at
More informationFebruary 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA
February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal
More informationChapter 16. Capacitance. Capacitance, cont. Parallel-Plate Capacitor, Example 1/20/2011. Electric Energy and Capacitance
summary C = ε A / d = πε L / ln( b / a ) ab C = 4πε 4πε a b a b >> a Chapter 16 Electric Energy and Capacitance Capacitance Q=CV Parallel plates, caxial cables, Earth Series and parallel 1 1 1 = + +..
More informationSections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
More informationSynchronous Motor V-Curves
Synchrnus Mtr V-Curves 1 Synchrnus Mtr V-Curves Intrductin Synchrnus mtrs are used in applicatins such as textile mills where cnstant speed peratin is critical. Mst small synchrnus mtrs cntain squirrel
More informationand the Doppler frequency rate f R , can be related to the coefficients of this polynomial. The relationships are:
Algrithm fr Estimating R and R - (David Sandwell, SIO, August 4, 2006) Azimith cmpressin invlves the alignment f successive eches t be fcused n a pint target Let s be the slw time alng the satellite track
More informationShort notes for Heat transfer
Furier s Law f Heat Cnductin Shrt ntes fr Heat transfer Q = Heat transfer in given directin. A = Crss-sectinal area perpendicular t heat flw directin. dt = Temperature difference between tw ends f a blck
More informationSPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
More information(1.1) V which contains charges. If a charge density ρ, is defined as the limit of the ratio of the charge contained. 0, and if a force density f
1.0 Review f Electrmagnetic Field Thery Selected aspects f electrmagnetic thery are reviewed in this sectin, with emphasis n cncepts which are useful in understanding magnet design. Detailed, rigrus treatments
More informationOP AMP CHARACTERISTICS
O AM CHAACTESTCS Static p amp limitatins EFEENCE: Chapter 5 textbk (ESS) EOS CAUSED BY THE NUT BAS CUENT AND THE NUT OFFSET CUENT Op Amp t functin shuld have fr the input terminals a DC path thrugh which
More informationEngineering Approach to Modelling Metal THz Structures
Terahertz Science and Technlgy, ISSN 1941-7411 Vl.4, N.1, March 11 Invited Paper ngineering Apprach t Mdelling Metal THz Structures Stepan Lucyszyn * and Yun Zhu Department f, Imperial Cllege Lndn, xhibitin
More informationELECTRON CYCLOTRON HEATING OF AN ANISOTROPIC PLASMA. December 4, PLP No. 322
ELECTRON CYCLOTRON HEATING OF AN ANISOTROPIC PLASMA by J. C. SPROTT December 4, 1969 PLP N. 3 These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated. They are fr private
More informationLecture 5: Equilibrium and Oscillations
Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if
More informationFIELD QUALITY IN ACCELERATOR MAGNETS
FIELD QUALITY IN ACCELERATOR MAGNETS S. Russenschuck CERN, 1211 Geneva 23, Switzerland Abstract The field quality in the supercnducting magnets is expressed in terms f the cefficients f the Furier series
More informationChapter VII Electrodynamics
Chapter VII Electrdynamics Recmmended prblems: 7.1, 7., 7.4, 7.5, 7.7, 7.8, 7.10, 7.11, 7.1, 7.13, 7.15, 7.17, 7.18, 7.0, 7.1, 7., 7.5, 7.6, 7.7, 7.9, 7.31, 7.38, 7.40, 7.45, 7.50.. Ohm s Law T make a
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion
.54 Neutrn Interactins and Applicatins (Spring 004) Chapter (3//04) Neutrn Diffusin References -- J. R. Lamarsh, Intrductin t Nuclear Reactr Thery (Addisn-Wesley, Reading, 966) T study neutrn diffusin
More informationKinematic transformation of mechanical behavior Neville Hogan
inematic transfrmatin f mechanical behavir Neville Hgan Generalized crdinates are fundamental If we assume that a linkage may accurately be described as a cllectin f linked rigid bdies, their generalized
More informationKinetics of Particles. Chapter 3
Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between
More informationChapter 32. Maxwell s Equations and Electromagnetic Waves
Chapter 32 Maxwell s Equatins and Electrmagnetic Waves Maxwell s Equatins and EM Waves Maxwell s Displacement Current Maxwell s Equatins The EM Wave Equatin Electrmagnetic Radiatin MFMcGraw-PHY 2426 Chap32-Maxwell's
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationPhysics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018
Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and
More informationA Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture
Few asic Facts but Isthermal Mass Transfer in a inary Miture David Keffer Department f Chemical Engineering University f Tennessee first begun: pril 22, 2004 last updated: January 13, 2006 dkeffer@utk.edu
More informationChapter 6. Dielectrics and Capacitance
Chapter 6. Dielectrics and Capacitance Hayt; //009; 6- Dielectrics are insulating materials with n free charges. All charges are bund at mlecules by Culmb frce. An applied electric field displaces charges
More informationOTHER USES OF THE ICRH COUPL ING CO IL. November 1975
OTHER USES OF THE ICRH COUPL ING CO IL J. C. Sprtt Nvember 1975 -I,," PLP 663 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.
More informationDetermining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationAccelerated Chemistry POGIL: Half-life
Name: Date: Perid: Accelerated Chemistry POGIL: Half-life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng as
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationGeneral Chemistry II, Unit I: Study Guide (part I)
1 General Chemistry II, Unit I: Study Guide (part I) CDS Chapter 14: Physical Prperties f Gases Observatin 1: Pressure- Vlume Measurements n Gases The spring f air is measured as pressure, defined as the
More informationSolution to HW14 Fall-2002
Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges
More information13. PO TREATMENT OF DEPT (DISTORTIONLESS ENHANCEMENT POLARIZATION TRANSFER)
94 Prduct Operatr Treatment 3. PO TREATMENT OF DEPT (DISTORTIONLESS ENHANCEMENT POLARIZATION TRANSFER) DEPT is a ne-dimensinal sequence used as a tl fr unambiguus identificatin f the CH, CH, and CH 3 peaks
More informationAircraft Performance - Drag
Aircraft Perfrmance - Drag Classificatin f Drag Ntes: Drag Frce and Drag Cefficient Drag is the enemy f flight and its cst. One f the primary functins f aerdynamicists and aircraft designers is t reduce
More informationTOPPER SAMPLE PAPER 2 Class XII- Physics
TOPPER SAMPLE PAPER 2 Class XII- Physics Time: Three Hurs Maximum Marks: 70 General Instructins (a) All questins are cmpulsry. (b) There are 30 questins in ttal. Questins 1 t 8 carry ne mark each, questins
More informationRadiopharmaceuticals for nuclear medicine
Radipharmaceuticals fr nuclear medicine Medical University f Ldz Dr Janusz Kapuściński 1 Nuclear Medicine A branch f medicine and medicine imaging, that fr diagnstics and theraphy uses pen surces f radiatin
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical
More informationPHYS College Physics II Final Examination Review
PHYS 1402- Cllege Physics II Final Examinatin Review The final examinatin will be based n the fllwing Chapters/Sectins and will cnsist f tw parts. Part 1, cnsisting f Multiple Chice questins, will accunt
More information1 Course Notes in Introductory Physics Jeffrey Seguritan
Intrductin & Kinematics I Intrductin Quickie Cncepts Units SI is standard system f units used t measure physical quantities. Base units that we use: meter (m) is standard unit f length kilgram (kg) is
More informationEffect of Paramagnetic Ions in Aqueous Solution for Precision Measurement of Proton Gyromagnetic Ratio
240 Bulletin f Magnetic Resnance Effect f Paramagnetic Ins in Aqueus Slutin fr Precisin Measurement f Prtn Gyrmagnetic Rati Ae Ran Lim, Chang Suk Kim Krea Research Institute f Standards and Science, Taejn
More informationQ1. A) 48 m/s B) 17 m/s C) 22 m/s D) 66 m/s E) 53 m/s. Ans: = 84.0 Q2.
Phys10 Final-133 Zer Versin Crdinatr: A.A.Naqvi Wednesday, August 13, 014 Page: 1 Q1. A string, f length 0.75 m and fixed at bth ends, is vibrating in its fundamental mde. The maximum transverse speed
More informationChapter 4. Unsteady State Conduction
Chapter 4 Unsteady State Cnductin Chapter 5 Steady State Cnductin Chee 318 1 4-1 Intrductin ransient Cnductin Many heat transfer prblems are time dependent Changes in perating cnditins in a system cause
More informationLecture 7: Damped and Driven Oscillations
Lecture 7: Damped and Driven Oscillatins Last time, we fund fr underdamped scillatrs: βt x t = e A1 + A csω1t + i A1 A sinω1t A 1 and A are cmplex numbers, but ur answer must be real Implies that A 1 and
More informationBuilding to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.
Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define
More informationMODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b
. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but
More informationCHAPTER 8b Static Equilibrium Units
CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but
More informationPhysics 2010 Motion with Constant Acceleration Experiment 1
. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin
More informationNGSS High School Physics Domain Model
NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship
More informationBuoyancy Effect on the Fully Developed Air Flow in Concentric Inclined Annulus
Internatinal Jurnal f Mechanical & Mechatrnics Engineering IJMME-IJENS Vl:3 N:0 46 Buyancy Effect n the Fully Develped Air Flw in Cncentric Inclined Annulus Asmaa Ali Hussein Lecturer Fundatin Of Technical
More informationECE 546 Lecture 02 Review of Electromagnetics
C 546 Lecture 0 Review f lectrmagnetics Spring 018 Jse. Schutt-Aine lectrical & Cmputer ngineering University f Illinis jesa@illinis.edu C 546 Jse Schutt Aine 1 Printed Circuit Bard C 546 Jse Schutt Aine
More informationPhys102 Final-061 Zero Version Coordinator: Nasser Wednesday, January 24, 2007 Page: 1
Crdinatr: Nasser Wednesday, January 4, 007 Page: 1 Q1. Tw transmitters, S 1 and S shwn in the figure, emit identical sund waves f wavelength λ. The transmitters are separated by a distance λ /. Cnsider
More informationLEARNING : At the end of the lesson, students should be able to: OUTCOMES a) state trigonometric ratios of sin,cos, tan, cosec, sec and cot
Mathematics DM 05 Tpic : Trignmetric Functins LECTURE OF 5 TOPIC :.0 TRIGONOMETRIC FUNCTIONS SUBTOPIC :. Trignmetric Ratis and Identities LEARNING : At the end f the lessn, students shuld be able t: OUTCOMES
More informationChapter 9 Vector Differential Calculus, Grad, Div, Curl
Chapter 9 Vectr Differential Calculus, Grad, Div, Curl 9.1 Vectrs in 2-Space and 3-Space 9.2 Inner Prduct (Dt Prduct) 9.3 Vectr Prduct (Crss Prduct, Outer Prduct) 9.4 Vectr and Scalar Functins and Fields
More informationPhys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1
Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity
More informationStudy Group Report: Plate-fin Heat Exchangers: AEA Technology
Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery
More informationQ1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string?
Term: 111 Thursday, January 05, 2012 Page: 1 Q1. A string f length L is fixed at bth ends. Which ne f the fllwing is NOT a pssible wavelength fr standing waves n this string? Q2. λ n = 2L n = A) 4L B)
More informationDispersion Ref Feynman Vol-I, Ch-31
Dispersin Ref Feynman Vl-I, Ch-31 n () = 1 + q N q /m 2 2 2 0 i ( b/m) We have learned that the index f refractin is nt just a simple number, but a quantity that varies with the frequency f the light.
More informationNUMBERS, MATHEMATICS AND EQUATIONS
AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t
More informationCHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.
MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the
More informationPreparation work for A2 Mathematics [2017]
Preparatin wrk fr A2 Mathematics [2017] The wrk studied in Y12 after the return frm study leave is frm the Cre 3 mdule f the A2 Mathematics curse. This wrk will nly be reviewed during Year 13, it will
More informationhttps://goo.gl/eaqvfo SUMMER REV: Half-Life DUE DATE: JULY 2 nd
NAME: DUE DATE: JULY 2 nd AP Chemistry SUMMER REV: Half-Life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng
More informationThermodynamics Partial Outline of Topics
Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)
More informationSection I5: Feedback in Operational Amplifiers
Sectin I5: eedback in Operatinal mplifiers s discussed earlier, practical p-amps hae a high gain under dc (zer frequency) cnditins and the gain decreases as frequency increases. This frequency dependence
More informationInformation for Physics 1201 Midterm I Wednesday, February 20
My lecture slides are psted at http://www.physics.hi-state.edu/~humanic/ Infrmatin fr Physics 1201 Midterm I Wednesday, February 20 1) Frmat: 10 multiple chice questins (each wrth 5 pints) and tw shw-wrk
More informationEE247B/ME218: Introduction to MEMS Design Lecture 7m1: Lithography, Etching, & Doping CTN 2/6/18
EE247B/ME218 Intrductin t MEMS Design Lecture 7m1 Lithgraphy, Etching, & Dping Dping f Semicnductrs Semicnductr Dping Semicnductrs are nt intrinsically cnductive T make them cnductive, replace silicn atms
More informationChapter 23 Electromagnetic Waves Lecture 14
Chapter 23 Electrmagnetic Waves Lecture 14 23.1 The Discvery f Electrmagnetic Waves 23.2 Prperties f Electrmagnetic Waves 23.3 Electrmagnetic Waves Carry Energy and Mmentum 23.4 Types f Electrmagnetic
More informationPart III: Sequences and Contrast
Part III: Sequences and Contrast Contents T1 and T2/T2* Relaxation Contrast of Imaging Sequences T1 weighting T2/T2* weighting Contrast Agents Saturation Inversion Recovery JUST WATER? (i.e., proton density
More informationI. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is
Length L>>a,b,c Phys 232 Lab 4 Ch 17 Electric Ptential Difference Materials: whitebards & pens, cmputers with VPythn, pwer supply & cables, multimeter, crkbard, thumbtacks, individual prbes and jined prbes,
More informationECE 2100 Circuit Analysis
ECE 00 Circuit Analysis Lessn 6 Chapter 4 Sec 4., 4.5, 4.7 Series LC Circuit C Lw Pass Filter Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 00 Circuit Analysis Lessn 5 Chapter 9 &
More informationChE 471: LECTURE 4 Fall 2003
ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.
More information2. Introduction to plastic deformation of crystals
.1. Micrscpic mdels f plastic defrmatin f crystalline slids. Intrductin t plastic defrmatin f crystals As we knw frm fundamentals f plastic defrmatin f crystalline slids (e.g. [36]), Hke s law is valid
More informationCLASS XI SET A PHYSICS
PHYSIS. If the acceleratin f wedge in the shwn arrangement is a twards left then at this instant acceleratin f the blck wuld be, (assume all surfaces t be frictinless) a () ( cs )a () a () cs a If the
More informationMATHEMATICS SYLLABUS SECONDARY 5th YEAR
Eurpean Schls Office f the Secretary-General Pedaggical Develpment Unit Ref. : 011-01-D-8-en- Orig. : EN MATHEMATICS SYLLABUS SECONDARY 5th YEAR 6 perid/week curse APPROVED BY THE JOINT TEACHING COMMITTEE
More informationTissue Parametric Mapping:
Tissue Parametric Mapping: Contrast Mechanisms Using SSFP Sequences Jongho Lee Department of Radiology University of Pennsylvania Tissue Parametric Mapping: Contrast Mechanisms Using bssfp Sequences Jongho
More informationLecture 02 CSE 40547/60547 Computing at the Nanoscale
PN Junctin Ntes: Lecture 02 CSE 40547/60547 Cmputing at the Nanscale Letʼs start with a (very) shrt review f semi-cnducting materials: - N-type material: Obtained by adding impurity with 5 valence elements
More informationPhy 213: General Physics III 6/14/2007 Chapter 28 Worksheet 1
Ph 13: General Phsics III 6/14/007 Chapter 8 Wrksheet 1 Magnetic Fields & Frce 1. A pint charge, q= 510 C and m=110-3 m kg, travels with a velcit f: v = 30 ˆ s i then enters a magnetic field: = 110 T ˆj.
More informationCBSE Board Class XII Physics Set 1 Board Paper 2008 (Solution)
CBSE Bard Class XII Physics Set 1 Bard Paper 2008 (Slutin) 1. The frce is given by F qv B This frce is at right angles t &. 2. Micrwaves. It is used in radar & cmmunicatin purpses. 3. Or As m e e m S,
More informationPhysics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1
Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs
More informationCHM112 Lab Graphing with Excel Grading Rubric
Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline
More informationExperiment #3. Graphing with Excel
Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-
More information37 Maxwell s Equations
37 Maxwell s quatins In this chapter, the plan is t summarize much f what we knw abut electricity and magnetism in a manner similar t the way in which James Clerk Maxwell summarized what was knwn abut
More informationDead-beat controller design
J. Hetthéssy, A. Barta, R. Bars: Dead beat cntrller design Nvember, 4 Dead-beat cntrller design In sampled data cntrl systems the cntrller is realised by an intelligent device, typically by a PLC (Prgrammable
More informationExam #1. A. Answer any 1 of the following 2 questions. CEE 371 October 8, Please grade the following questions: 1 or 2
CEE 371 Octber 8, 2009 Exam #1 Clsed Bk, ne sheet f ntes allwed Please answer ne questin frm the first tw, ne frm the secnd tw and ne frm the last three. The ttal ptential number f pints is 100. Shw all
More informationLecture 6: Phase Space and Damped Oscillations
Lecture 6: Phase Space and Damped Oscillatins Oscillatins in Multiple Dimensins The preius discussin was fine fr scillatin in a single dimensin In general, thugh, we want t deal with the situatin where:
More informationPart One: Heat Changes and Thermochemistry. This aspect of Thermodynamics was dealt with in Chapter 6. (Review)
CHAPTER 18: THERMODYNAMICS AND EQUILIBRIUM Part One: Heat Changes and Thermchemistry This aspect f Thermdynamics was dealt with in Chapter 6. (Review) A. Statement f First Law. (Sectin 18.1) 1. U ttal
More informationENSC Discrete Time Systems. Project Outline. Semester
ENSC 49 - iscrete Time Systems Prject Outline Semester 006-1. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding
More informationFinding the Earth s magnetic field
Labratry #6 Name: Phys 1402 - Dr. Cristian Bahrim Finding the Earth s magnetic field The thery accepted tday fr the rigin f the Earth s magnetic field is based n the mtin f the plasma (a miture f electrns
More informationExample 1. A robot has a mass of 60 kg. How much does that robot weigh sitting on the earth at sea level? Given: m. Find: Relationships: W
Eample 1 rbt has a mass f 60 kg. Hw much des that rbt weigh sitting n the earth at sea level? Given: m Rbt = 60 kg ind: Rbt Relatinships: Slutin: Rbt =589 N = mg, g = 9.81 m/s Rbt = mrbt g = 60 9. 81 =
More informationMeasurement of Radial Loss and Lifetime. of Microwave Plasma in the Octupo1e. J. C. Sprott PLP 165. Plasma Studies. University of Wisconsin DEC 1967
Measurement f Radial Lss and Lifetime f Micrwave Plasma in the Octup1e J. C. Sprtt PLP 165 Plasma Studies University f Wiscnsin DEC 1967 1 The number f particles in the tridal ctuple was measured as a
More information3. Mass Transfer with Chemical Reaction
8 3. Mass Transfer with Chemical Reactin 3. Mass Transfer with Chemical Reactin In the fllwing, the fundamentals f desrptin with chemical reactin, which are applied t the prblem f CO 2 desrptin in ME distillers,
More informationAdvanced Topics and Diffusion MRI
Advanced Topics and Diffusion MRI Slides originally by Karla Miller, FMRIB Centre Modified by Mark Chiew (mark.chiew@ndcn.ox.ac.uk) Slides available at: http://users.fmrib.ox.ac.uk/~mchiew/teaching/ MRI
More information11. DUAL NATURE OF RADIATION AND MATTER
11. DUAL NATURE OF RADIATION AND MATTER Very shrt answer and shrt answer questins 1. Define wrk functin f a metal? The minimum energy required fr an electrn t escape frm the metal surface is called the
More informationLab 11 LRC Circuits, Damped Forced Harmonic Motion
Physics 6 ab ab 11 ircuits, Damped Frced Harmnic Mtin What Yu Need T Knw: The Physics OK this is basically a recap f what yu ve dne s far with circuits and circuits. Nw we get t put everything tgether
More informationMANIPAL INSTITUTE OF TECHNOLOGY
MANIPAL INSTITUTE OF TECHNOLOGY MANIPAL UNIVERSITY, MANIPAL SECOND SEMESTER B.Tech. END-SEMESTER EXAMINATION - MAY 013 SUBJECT: ENGINEERING PHYSICS (PHY101/10) Time: 3 Hrs. Max. Marks: 50 Nte: Answer any
More informationECE 5318/6352 Antenna Engineering. Spring 2006 Dr. Stuart Long. Chapter 6. Part 7 Schelkunoff s Polynomial
ECE 538/635 Antenna Engineering Spring 006 Dr. Stuart Lng Chapter 6 Part 7 Schelkunff s Plynmial 7 Schelkunff s Plynmial Representatin (fr discrete arrays) AF( ψ ) N n 0 A n e jnψ N number f elements in
More informationEdexcel GCSE Physics
Edexcel GCSE Physics Tpic 10: Electricity and circuits Ntes (Cntent in bld is fr Higher Tier nly) www.pmt.educatin The Structure f the Atm Psitively charged nucleus surrunded by negatively charged electrns
More informationPressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects
Pressure And Entrpy Variatins Acrss The Weak Shck Wave Due T Viscsity Effects OSTAFA A. A. AHOUD Department f athematics Faculty f Science Benha University 13518 Benha EGYPT Abstract:-The nnlinear differential
More informationSupporting information
Electrnic Supplementary Material (ESI) fr Physical Chemistry Chemical Physics This jurnal is The wner Scieties 01 ydrgen perxide electrchemistry n platinum: twards understanding the xygen reductin reactin
More informationKinetic Model Completeness
5.68J/10.652J Spring 2003 Lecture Ntes Tuesday April 15, 2003 Kinetic Mdel Cmpleteness We say a chemical kinetic mdel is cmplete fr a particular reactin cnditin when it cntains all the species and reactins
More information