' ' ' t. Moving Spins. Phase of a Moving Spin. Bioengineering 280A Principles of Biomedical Imaging. Fall Quarter 2007 MRI Lecture 6
|
|
- Franklin Holt
- 5 years ago
- Views:
Transcription
1 Moving Spins Bioengineering 28A Principles of Biomedical Imaging Fall Quarer 27 MRI Lecure 6 So far we have assumed ha he spins are no moving (aside from hermal moion giving rise o relaxaion), and conras has been based upon 1, 2, and proon densiy. We were able o achieve differen conrass by adjusing he appropriae pulse sequence parameers. Biological samples are filled wih moving spins, and we can also use MRI o image he movemen. Examples: blood flow, diffusion of waer in he whie maer racs. In addiion, we can also someimes induce moion ino he objec o image is mechanical properies, e.g. imaging of sress and srain wih MR elasography. Phase of Moving Spin ΔB z (x) x ΔB z (x) x ime "() = # ' ' Phase of a Moving Spin $%(&)d& = # ($B(&)d& = # ( G r (&) ) r (&)d& ' ' = #( G x (&)x(&) + G y (&)y(&) + G z (&)z(&) [ ]d& 1
2 Phase of Moving Spin Consider moion along he x-axis x() = x + v a 2 Phase of Moving Spin % "() = #$ x M + vm 1 + a 2 M ( 2 & ' ) * "() = #$ & G x (%)x(%)d% ' = #$ G x (%) x + v% a% * & 2 ( ) +, d% ' = #$ x & G x (%)d% + v & G x (%)%d% + a ( ) 2 ' = #$ x M + vm 1 + a 2 M * 2 ( ) +, & * G x (%)% 2 d% +, M = M 1 =,,, G x (+)d+ G x (+)+d+ M 2 = G x (+)+ 2 d+ Zeroh order momen Firs order momen Second order momen Flow Momen Example Phase Conras Angiography (PCA) G -G M = # G x (")d" = M 1 = # G x (")"d" 2 = $ # G "d" + # G "d" % = G ' $ " 2 &' " 2 2 ( * )* % = G $ $ 2 ( ' * = G 2 & 2 ) G -G G -G " 1 = #$v x M 1 = $v x G 2 " 2 = #$v x M 1 = #$v x G 2 "# = # 1 $# 2 = 2%v x G 2 v x = "# 2G 2 2
3 PCA example Aliasing in PCA -G Define VENC as he velociy a a which he phase is 18 degrees. # VENC " $G 2 Because of phase wrapping he velociy of spins flowing faser han VENC is ambiguous. +π a VENC -π a -VENC hp:// Aliasing Soluions velociy no aliased Use daa from regions wih slower flow velociy aliased Readou Gradien G -G Flow Arifacs During readou moving spins wihin he objec will accumulae phase ha is in addiion o he phase used for imaging. his leads o Use muliple VENC values so ha he phase differences are smaller han π radians. " 1 = # VENC 1 v x v x " 2 = # VENC 2 % 1 1 ( " 1 $" 2 = #v x ' $ * & VENC 1 VENC 2 ) 2 3 1) Ne phase a echo ime E = 2. 2) An apparen shif in posiion of he objec. 3) Blurring of he objec due o a quadraic phase erm. 3
4 Plug Flow Laminar Flow Flow Arifacs All moving spins in he voxel experience he same phase shif a echo ime. Spins have differen phase shifs a echo ime. he dephasing causes he cancelaion and signal dropou. Readou Gradien G -2G Flow Compensaion 2 3 Echo ime E A E boh he firs and second order momens are zero, so boh saionary and moving spins have zero ne phase. Inflow Effec ime of Fligh Angiography Prior o imaging ime Relaxed spins flowing in Sauraed spins 4
5 Cerebral Blood Flow (CBF) CBF = Perfusion = Rae of delivery of arerial blood o a capillary bed in issue. Unis: (ml of Blood) (1 grams of issue)(minue) High CBF Low CBF ypical value is 6 ml/(1g-min) or 6 ml/(1 ml-min) =.1 s -1, assuming average densiy of brain equals 1 gm/ml ime Arerial spin labeling (ASL) 1: ag by Magneic Inversion Acquire image 2: Bereczki e al 1992 Conrol Acquire image Conrol - ag = ΔM CBF 5
6 Mz(blood) conrol ag I ASL Signal Equaion ΔM - = ΔM PASL / VSASL R ag ASL Pulse Sequences Acquire Conrol Acquire A eff is he effecive area of he arerial bolus. I depends on boh physiology and pulse sequence parameers. M= CBF A eff I = Inversion ime CASL ag Acquire Conrol Labeling ime Pos Labeling Delay Acquire Mulislice CASL and PICORE ASL ime Series ag Conrol ag Conrol CASL Wai ag by Magneic Inversion ag by Magneic Inversion PICORE QUIPSS II Image 1 Image 2 Image 3 Image Perfusion Images Credi: E. Wong 6
7 Diffusion Diffusing Spins 2D random walk 1 seps ΔB z (x) x 4 seps ΔB z (x) ime N random seps of lengh d <Δx 2 >= Nd 2 = 2D D = diffusiviy In brain: D.1 mm 2 /s For =1 msec, Δx 15 µ Δx x Credi: Larry Frank G -G δ Diffusion Weighing Diffusion Weighed Images 2 weighed Diffusion Weighed Angiogram Signal S "e #$ 2 G 2 % 2 D = e #bd where b = $ 2 G 2 % 2 ( #% /3) Diffusiviy Afer a sroke, normal waer movemen is resriced in he region of damage. Diffusiviy decreases, so he signal inensiy increases. hp://lehighmri.com/cases/dwi/paien-b.hml 7
8 Resriced Diffusion Diffusion Imaging Example D depends on direcion z y x Diffusion ensor: 3 values of D 3 angles Credi: Larry Frank Q-ball imaging uch e al, Neuron 23 Fiber rac mapping of neural conneciviy Couresy of L. Frank 8
9 fmri MRI sudies brain anaomy. fmri Seup Funcional MRI (fmri) sudies brain funcion. hp://defian.ssc.uwo.ca/jody_web/fmri4dummies.hm fmri Acquisiion High spaial resoluion MP-RAGE Voxel volume: 1 mm3 Imaging ime: 6 min hp://defian.ssc.uwo.ca/jody_web/fmri4dummies.hm EPI Scans High emporal resoluion Phase Encode EPI Voxel volume: 45 mm3 Imaging ime: 6 msec Buxon 22 GE Medical Sysems 23 9
10 EPI Disorions and Signal Dropous Signal Dropous Field inhomogeneiies also cause he spins o dephase wih ime and hus for he signal o decrease more rapidly. o firs order his can be modeled as an addiional decay erm. Credi: R. Buxon Slower Faser Fig Credi: R. Buxon Precesses slower because of local field inhomogeneiy 1
11 Field Map Correcion Slower rajecory->more displacemen Nyquis Ghoss Visual Acivaion Flickering Checkerboard OFF (6 s) - ON (6 s) -OFF (6 s) - ON (6 s) - OFF (6 s) Brain Aciviy ime Source: Kwong e al., 1992 hp://defian.ssc.uwo.ca/jody_web/fmri4dummies.hm 11
12 Finger apping ask Hemoglobin Oxygen binds o he iron aoms o form oxyhemoglobin HbO 2 Release of O 2 o issue resuls in deoxyhemoglobin dhbo 2 hp:// Effec of dhbo 2 dhbo 2 is paramagneic due o he iron aoms. As i becomes oxygenaed, i becomes less paramagneic. dhbo 2 perurbs he local magneic fields. As blood becomes more deoxygenaed, he amoun of perurbaion increases and here is more dephasing of he spins. hus as dhbo 2 increases we find ha 2 * decreases and he ampliude exp(-e/ 2 *) image of a 2 * weighed image will decrease. Conversely as dhbo 2 decreases, 2 * increases and we expec he signal ampliude o go up. Buxon 22 12
13 BOLD Effec Blood Oxygen Level Dependen signal neural aciviy blood flow oxyhemoglobin 2* MR signal M xy Signal M o sin θ 2 * ask 2 * conrol Baseline Vascular Sae ASL Signal Cerebral Blood Volume S ask S conrol ΔS Neural Aciviy Cerebral Blood Flow E opimum ime Meabolism (CMRO 2 ) deoxyhb BOLD Signal Source: fmrib Brief Inroducion o fmri Source: Jorge Jovicich hp://defian.ssc.uwo.ca/jody_web/fmri4dummies.hm BOLD and Vascular Dynamics Effec of Caffeine on Funcional Conneciviy 13
14 J. Clarke, UC B J. Clarke, UC Berkeley J. Clarke, UC Berkeley Seeley e al, JMR 24 14
15 Seeley e al, JMR 24 15
' ' ' t. Moving Spins. Phase of a Moving Spin. Phase of Moving Spin. Bioengineering 280A Principles of Biomedical Imaging
Moving Spins Bioengineering 28A Principles of Biomedical Imaging Fall Quarer 28 MRI Lecure 7 So far we have assumed ha he spins are no moving (aside from hermal moion giving rise o relaxaion), and conras
More information' ' ' t. Moving Spins. Phase of Moving Spin. Phase of a Moving Spin. Bioengineering 280A Principles of Biomedical Imaging
Moving Spins Bioengineering 8A Principles of Biomedical Imaging Fall Quarer 1 MRI Lecure 6 So far we have assumed ha he spins are no moving (aside from hermal moion giving rise o relaaion) and conras has
More informationMoving Spins. Phase of a Moving Spin. Phase of Moving Spin. Bioengineering 280A Principles of Biomedical Imaging. Fall Quarter 2009 MRI Lecture 6
Moving Spins Bioengineering 28A Principles of Biomedical Imaging Fall Quarer 29 MRI Lecure 6 So far we have assumed ha he spins are no moving (aside from hermal moion giving rise o relaxaion), and conras
More informationRF Excitation. Rotating Frame of Reference. RF Excitation. Bioengineering 280A Principles of Biomedical Imaging. Fall Quarter 2012 MRI Lecture 6
RF Exciaion Bioengineering 8A Principles of Biomedical Imaging Fall Quarer 1 MRI Lecure 6 hp://www.drcmr.dk/main/conen/view/13/74/ RF Exciaion Roaing Frame of Reference Reference everyhing o he magneic
More informationRefocusing t. Small Tip Angle Example. Small Tip Angle Example. Bioengineering 280A Principles of Biomedical Imaging. Fall Quarter 2010 MRI Lecture 5
Bioengineering 280A Principles of Biomedical Imaging Fall Quarer 2010 MRI Lecure 5 RF N random seps of lengh d Refocusing ' M xy (,) = jm 0 "B 1 ()exp( jk(,))d %& 100 seps This has he 2D form random of
More informationSE Sequence: 90º, 180º RF Pulses, Readout Gradient e.g., 256 voxels in a row
Ouline for Today 1. 2. 3. Inroducion o MRI Quanum NMR and MRI in 0D Magneizaion, m(x,), in a Voxel Proon T1 Spin Relaxaion in a Voxel Proon Densiy MRI in 1D MRI Case Sudy, and Cavea Skech of he MRI Device
More informationHW6: MRI Imaging Pulse Sequences (7 Problems for 100 pts)
HW6: MRI Imaging Pulse Sequences (7 Problems for 100 ps) GOAL The overall goal of HW6 is o beer undersand pulse sequences for MRI image reconsrucion. OBJECTIVES 1) Design a spin echo pulse sequence o image
More informationRelaxation. T1 Values. Longitudinal Relaxation. dm z dt. = " M z T 1. (1" e "t /T 1 ) M z. (t) = M 0
Relaxaion Bioengineering 28A Principles of Biomedical Imaging Fall Quarer 21 MRI Lecure 2 An exciaion pulse roaes he magneiaion vecor away from is equilibrium sae (purely longiudinal). The resuling vecor
More informationPrinciples of MRI. Practical Issues in MRI T2 decay. Tissue is a combination of. Results are complex. Started talking about off-resonance
Projec Principles of MRI Lecure 18 EE225E / BIO265 Insrucor: Miki Lusig UC Berkeley, EECS No eams Oral presenaion (20min) Or, Repor as a wikepedia enry Level of presenaion -- assume exbook level of knowledge
More informationAdvanced Imaging Techniques
Advanced Imaging Techniques Perfusion Imaging Prof. Dr. Frank G. Zöllner Compuer Assised Clinical Medicine Medical Faculy Mannheim Heidelberg Universiy Theodor-Kuzer-Ufer 1-3 D-68167 Mannheim, Germany
More informationSampling in k-space. Aliasing. Aliasing. Bioengineering 280A Principles of Biomedical Imaging. Fall Quarter 2010 MRI Lecture 3. Slower B z (x)=g x x
Sampling in k-space Bioengineering 80A Principles of Biomedical Imaging Fall Quarer 00 MRI Lecure 3 Thomas Liu, BE80A, UCSD, Fall 008 Aliasing Aliasing Slower B z (G Faser Inuiive view of Aliasing FOV
More informationBioengineering 278" Magnetic Resonance Imaging" " Winter 2011" Lecture 9! Time of Flight MRA!
Bioengineering 278" Magnetic Resonance Imaging" " Winter 2011" Lecture 9 Motion Encoding using Longitudinal Magnetization: Magnetic Resonance Angiography Time of Flight Contrast Enhanced Arterial Spin
More informationBlood Water Dynamics
Bioengineering 208 Magnetic Resonance Imaging Winter 2007 Lecture 8 Arterial Spin Labeling ASL Basics ASL for fmri Velocity Selective ASL Vessel Encoded ASL Blood Water Dynamics Tissue Water Perfusion:
More informationIntroduction to MRI Acquisition
Introduction to MRI Acquisition James Meakin FMRIB Physics Group FSL Course, Bristol, September 2012 1 What are we trying to achieve? 2 What are we trying to achieve? Informed decision making: Protocols
More informationBasic MR image encoding
Basic MR image encoding HST.583: Funcional Magneic Resonance Imaging: Daa Acquisiion and Analysis Harvard-MIT Division of Healh Sciences and Technology Dr. Larry Wald Physical Foundaions of MRI Wha is
More informationTopics. 2D Image. a b. c d. 1. Representing Images 2. 2D Fourier Transform 3. MRI Basics 4. MRI Applications 5. fmri
Topics Neuroscience 200C Spring Quarter 2005 Imaging/MRI Lecture 1. Representing Images 2. 2D Fourier Transform 3. MRI Basics 4. MRI Applications 5. fmri Signals and Images Discrete-time/space signal/image:
More informationSpin echo. ½πI x -t -πi y -t
y Spin echo ½πI - -πi y - : as needed, no correlaed wih 1/J. Funcions: 1. refocusing; 2. decoupling. Chemical shif evoluion is refocused by he spin-echo. Heeronuclear J-couplings evoluion are refocused
More informationWEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x
WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile
More informationLecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.
Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in
More information[ ]e TE /T 2(x,y ) Saturation Recovery Sequence. T1-Weighted Scans. T1-Weighted Scans. I(x, y) ρ(x, y) 1 e TR /T 1
Sauraion Recovery Sequence 90 TE 90 TE 90 Bioengineering 280A Principles of Biomedical Imaging Fall Quarer 2015 MRI Lecure 5 TR Gradien Echo TR [ ]e TE /T 2 * (x,y ) I(x, y) = ρ(x, y) 1 e TR /T 1 (x,y)
More informationψ(t) = V x (0)V x (t)
.93 Home Work Se No. (Professor Sow-Hsin Chen Spring Term 5. Due March 7, 5. This problem concerns calculaions of analyical expressions for he self-inermediae scaering funcion (ISF of he es paricle in
More informationExam 8NC20-8NC29 - Introduction to NMR and MRI
Exam 8NC-8NC9 - Inroducion o NMR and MRI Friday April 5, 8.-. h For his exam you may use an ordinary calculaor (no a graphical one). In oal here are 6 assignmens and a oal of 64 poins can be earned. You
More informationPhysics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle
Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,
More informationOutline. Superconducting magnet. Magnetic properties of blood. Physiology BOLD-MRI signal. Magnetic properties of blood
Magnetic properties of blood Physiology BOLD-MRI signal Aart Nederveen Department of Radiology AMC a.j.nederveen@amc.nl Outline Magnetic properties of blood Moses Blood oxygenation BOLD fmri Superconducting
More informationUnit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3
A.P. Physics B Uni 1 Tes Reiew Physics Basics, Moemen, and Vecors Chapers 1-3 * In sudying for your es, make sure o sudy his reiew shee along wih your quizzes and homework assignmens. Muliple Choice Reiew:
More informationRF Excitation. RF Excitation. Bioengineering 280A Principles of Biomedical Imaging
Bioengineering 280A Principles of Biomedical Imaging Fall Quarer 2010 MRI Lecure 4 Simplified Drawing of Basic Insrumenaion. Body lies on able encompassed by coils for saic field B o, gradien fields (wo
More informationQ.1 Define work and its unit?
CHP # 6 ORK AND ENERGY Q.1 Define work and is uni? A. ORK I can be define as when we applied a force on a body and he body covers a disance in he direcion of force, hen we say ha work is done. I is a scalar
More informationSummary of shear rate kinematics (part 1)
InroToMaFuncions.pdf 4 CM465 To proceed o beer-designed consiuive equaions, we need o know more abou maerial behavior, i.e. we need more maerial funcions o predic, and we need measuremens of hese maerial
More informationClass Meeting # 10: Introduction to the Wave Equation
MATH 8.5 COURSE NOTES - CLASS MEETING # 0 8.5 Inroducion o PDEs, Fall 0 Professor: Jared Speck Class Meeing # 0: Inroducion o he Wave Equaion. Wha is he wave equaion? The sandard wave equaion for a funcion
More informationPhysics Equation List :Form 4 Introduction to Physics
Physics Equaion Lis :Form 4 Inroducion o Physics Relaive Deviaion Relaive Deviaion Mean Deviaion 00% Mean Value Prefixes Unis for Area and Volume Prefixes Value Sandard form Symbol Tera 000 000 000 000
More informationMechanical Fatigue and Load-Induced Aging of Loudspeaker Suspension. Wolfgang Klippel,
Mechanical Faigue and Load-Induced Aging of Loudspeaker Suspension Wolfgang Klippel, Insiue of Acousics and Speech Communicaion Dresden Universiy of Technology presened a he ALMA Symposium 2012, Las Vegas
More informationPhysics 127b: Statistical Mechanics. Fokker-Planck Equation. Time Evolution
Physics 7b: Saisical Mechanics Fokker-Planck Equaion The Langevin equaion approach o he evoluion of he velociy disribuion for he Brownian paricle migh leave you uncomforable. A more formal reamen of his
More informationSome Basic Information about M-S-D Systems
Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,
More informationKINEMATICS IN ONE DIMENSION
KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec
More informationZürich. ETH Master Course: L Autonomous Mobile Robots Localization II
Roland Siegwar Margaria Chli Paul Furgale Marco Huer Marin Rufli Davide Scaramuzza ETH Maser Course: 151-0854-00L Auonomous Mobile Robos Localizaion II ACT and SEE For all do, (predicion updae / ACT),
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan
Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure
More informationTraveling Waves. Chapter Introduction
Chaper 4 Traveling Waves 4.1 Inroducion To dae, we have considered oscillaions, i.e., periodic, ofen harmonic, variaions of a physical characerisic of a sysem. The sysem a one ime is indisinguishable from
More informationCHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK
175 CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK 10.1 INTRODUCTION Amongs he research work performed, he bes resuls of experimenal work are validaed wih Arificial Neural Nework. From he
More informationEE650R: Reliability Physics of Nanoelectronic Devices Lecture 9:
EE65R: Reliabiliy Physics of anoelecronic Devices Lecure 9: Feaures of Time-Dependen BTI Degradaion Dae: Sep. 9, 6 Classnoe Lufe Siddique Review Animesh Daa 9. Background/Review: BTI is observed when he
More informationSelf-Diffusion Imaging by Spin Echo in Earth s Magnetic Field
Journal of Magneic Resonance 136, 22 26 (1999) Aricle ID jmre.1998.1594, available online a hp://www.idealibrary.com on Self-Diffusion Imaging by Spin Echo in Earh s Magneic Field Aleš Mohorič, Janez Sepišnik,
More informationk B 2 Radiofrequency pulses and hardware
1 Exra MR Problems DC Medical Imaging course April, 214 he problems below are harder, more ime-consuming, and inended for hose wih a more mahemaical background. hey are enirely opional, bu hopefully will
More information( ) is the stretch factor, and x the
(Lecures 7-8) Liddle, Chaper 5 Simple cosmological models (i) Hubble s Law revisied Self-similar srech of he universe All universe models have his characerisic v r ; v = Hr since only his conserves homogeneiy
More informationEntanglement and complexity of many-body wavefunctions
Enanglemen and complexiy of many-body wavefuncions Frank Versraee, Universiy of Vienna Norber Schuch, Calech Ignacio Cirac, Max Planck Insiue for Quanum Opics Tobias Osborne, Univ. Hannover Overview Compuaional
More informationSupplementary Fig. 1: Schematic of the typical phase shift of the resonance. Supplementary Fig. 2: Rule out the scanning effect at the sample edges.
Supplemenary Fig. 1: Schemaic of he ypical phase shif of he resonance. The blue solid curve shows he phase signal as a funcion of frequency f a free resonance sae (when f = f 0, = 0). When he sysem is
More informationOpen loop vs Closed Loop. Example: Open Loop. Example: Feedforward Control. Advanced Control I
Open loop vs Closed Loop Advanced I Moor Command Movemen Overview Open Loop vs Closed Loop Some examples Useful Open Loop lers Dynamical sysems CPG (biologically inspired ), Force Fields Feedback conrol
More informationTopic 1: Linear motion and forces
TOPIC 1 Topic 1: Linear moion and forces 1.1 Moion under consan acceleraion Science undersanding 1. Linear moion wih consan elociy is described in erms of relaionships beween measureable scalar and ecor
More information3, so θ = arccos
Mahemaics 210 Professor Alan H Sein Monday, Ocober 1, 2007 SOLUTIONS This problem se is worh 50 poins 1 Find he angle beween he vecors (2, 7, 3) and (5, 2, 4) Soluion: Le θ be he angle (2, 7, 3) (5, 2,
More informationSecond Law. first draft 9/23/04, second Sept Oct 2005 minor changes 2006, used spell check, expanded example
Second Law firs draf 9/3/4, second Sep Oc 5 minor changes 6, used spell check, expanded example Kelvin-Planck: I is impossible o consruc a device ha will operae in a cycle and produce no effec oher han
More informationTwo Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
More informationOptimal Path Planning for Flexible Redundant Robot Manipulators
25 WSEAS In. Conf. on DYNAMICAL SYSEMS and CONROL, Venice, Ialy, November 2-4, 25 (pp363-368) Opimal Pah Planning for Flexible Redundan Robo Manipulaors H. HOMAEI, M. KESHMIRI Deparmen of Mechanical Engineering
More informationNumerical Dispersion
eview of Linear Numerical Sabiliy Numerical Dispersion n he previous lecure, we considered he linear numerical sabiliy of boh advecion and diffusion erms when approimaed wih several spaial and emporal
More informationIB Physics Kinematics Worksheet
IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?
More informationHow is it different from conventional MRI? What is MR Spectroscopy? How is it different from conventional MRI? MR Active Nuclei
What is MR Spectroscopy? MR-Spectroscopy (MRS) is a technique to measure the (relative) concentration of certain chemical or biochemical molecules in a target volume. MR-Spectroscopy is an in vivo (in
More informationRF Excitation. RF Excitation. Bioengineering 280A Principles of Biomedical Imaging. Fall Quarter 2013 MRI Lecture 4
Bioengineering 80A Principles of Biomedical Imaging Fall Quarer 013 MRI Lecure 4 TT. Liu, BE80A, UCSD Fall 01 Simplified Drawing of Basic Insrumenaion. Body lies on able encompassed by coils for saic field
More informationDynamic Analysis of Damped Driven Pendulum using Laplace Transform Method
, ISSN 0974-570X (Online), ISSN 0974-578 (Prin), Vol. 6; Issue No. 3; Year 05, Copyrigh 05 by CESER PUBLICATIONS Dynamic Analysis of Damped Driven Pendulum using Laplace Transform Mehod M.C. Agarana and
More informationContrast Mechanisms in MRI. Michael Jay Schillaci
Contrast Mechanisms in MRI Michael Jay Schillaci Overview Image Acquisition Basic Pulse Sequences Unwrapping K-Space Image Optimization Contrast Mechanisms Static and Motion Contrasts T1 & T2 Weighting,
More information1. VELOCITY AND ACCELERATION
1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under
More informationSpintronics of Nanomechanical Shuttle
* Spinronics of Nanomechanical Shule Rober Shekher In collaboraion wih: D.Fedores,. Gorelik, M. Jonson Göeborg Universiy / Chalmers Universiy of Technology Elecromechanics of Coulomb Blockade srucures
More informationBasics of Magnetic Resonance Imaging (MRI)
Basics of Magneic Resonance MRI Shaoing HUANG, PhD Singapore Universi of Technolog and Design OUTLINE Medical imaging modaliies Hisor of MRI Working principles of MRI Medical Modaliies Creae images of
More informationIntroduction to Physical Oceanography Homework 5 - Solutions
Laure Zanna //5 Inroducion o Phsical Oceanograph Homework 5 - Soluions. Inerial oscillaions wih boom fricion non-selecive scale: The governing equaions for his problem are This ssem can be wrien as where
More informationNavneet Saini, Mayank Goyal, Vishal Bansal (2013); Term Project AML310; Indian Institute of Technology Delhi
Creep in Viscoelasic Subsances Numerical mehods o calculae he coefficiens of he Prony equaion using creep es daa and Herediary Inegrals Mehod Navnee Saini, Mayank Goyal, Vishal Bansal (23); Term Projec
More informationSection 3.8, Mechanical and Electrical Vibrations
Secion 3.8, Mechanical and Elecrical Vibraions Mechanical Unis in he U.S. Cusomary and Meric Sysems Disance Mass Time Force g (Earh) Uni U.S. Cusomary MKS Sysem CGS Sysem fee f slugs seconds sec pounds
More informationPHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections
PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx
More informationModule 3: The Damped Oscillator-II Lecture 3: The Damped Oscillator-II
Module 3: The Damped Oscillaor-II Lecure 3: The Damped Oscillaor-II 3. Over-damped Oscillaions. This refers o he siuaion where β > ω (3.) The wo roos are and α = β + α 2 = β β 2 ω 2 = (3.2) β 2 ω 2 = 2
More informationPosition, Velocity, and Acceleration
rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME-9493 1 Car ME-9454 1 Fan Accessory ME-9491 1 Moion Sensor II CI-6742A 1 Track Barrier Purpose The purpose
More informationToday: Graphing. Note: I hope this joke will be funnier (or at least make you roll your eyes and say ugh ) after class. v (miles per hour ) Time
+v Today: Graphing v (miles per hour ) 9 8 7 6 5 4 - - Time Noe: I hope his joke will be funnier (or a leas make you roll your eyes and say ugh ) afer class. Do yourself a favor! Prof Sarah s fail-safe
More information( ) = b n ( t) n " (2.111) or a system with many states to be considered, solving these equations isn t. = k U I ( t,t 0 )! ( t 0 ) (2.
Andrei Tokmakoff, MIT Deparmen of Chemisry, 3/14/007-6.4 PERTURBATION THEORY Given a Hamilonian H = H 0 + V where we know he eigenkes for H 0 : H 0 n = E n n, we can calculae he evoluion of he wavefuncion
More informationPolymer Engineering (MM3POE)
Polymer Engineering (MM3POE) VISCOELASTICITY hp://www.noingham.ac.uk/~eazacl/mm3poe Viscoelasiciy 1 Conens Wha is viscoelasiciy? Fundamenals Creep & creep recovery Sress relaxaion Modelling viscoelasic
More informationLinear Response Theory: The connection between QFT and experiments
Phys540.nb 39 3 Linear Response Theory: The connecion beween QFT and experimens 3.1. Basic conceps and ideas Q: How do we measure he conduciviy of a meal? A: we firs inroduce a weak elecric field E, and
More informationLecture #8 Redfield theory of NMR relaxation
Lecure #8 Redfield heory of NMR relaxaion Topics The ineracion frame of reference Perurbaion heory The Maser Equaion Handous and Reading assignmens van de Ven, Chapers 6.2. Kowalewski, Chaper 4. Abragam
More informationCourse Notes for EE227C (Spring 2018): Convex Optimization and Approximation
Course Noes for EE7C Spring 018: Convex Opimizaion and Approximaion Insrucor: Moriz Hard Email: hard+ee7c@berkeley.edu Graduae Insrucor: Max Simchowiz Email: msimchow+ee7c@berkeley.edu Ocober 15, 018 3
More informationWeek 1 Lecture 2 Problems 2, 5. What if something oscillates with no obvious spring? What is ω? (problem set problem)
Week 1 Lecure Problems, 5 Wha if somehing oscillaes wih no obvious spring? Wha is ω? (problem se problem) Sar wih Try and ge o SHM form E. Full beer can in lake, oscillaing F = m & = ge rearrange: F =
More informationReliability of Technical Systems
eliabiliy of Technical Sysems Main Topics Inroducion, Key erms, framing he problem eliabiliy parameers: Failure ae, Failure Probabiliy, Availabiliy, ec. Some imporan reliabiliy disribuions Componen reliabiliy
More informationMeasuring cerebral blood flow and other haemodynamic parameters using Arterial Spin Labelling MRI. David Thomas
Measuring cerebral blood flow and other haemodynamic parameters using Arterial Spin Labelling MRI David Thomas Principal Research Associate in MR Physics Leonard Wolfson Experimental Neurology Centre UCL
More informationSPH3U: Projectiles. Recorder: Manager: Speaker:
SPH3U: Projeciles Now i s ime o use our new skills o analyze he moion of a golf ball ha was ossed hrough he air. Le s find ou wha is special abou he moion of a projecile. Recorder: Manager: Speaker: 0
More informationStructural Dynamics and Earthquake Engineering
Srucural Dynamics and Earhquae Engineering Course 1 Inroducion. Single degree of freedom sysems: Equaions of moion, problem saemen, soluion mehods. Course noes are available for download a hp://www.c.up.ro/users/aurelsraan/
More informationand v y . The changes occur, respectively, because of the acceleration components a x and a y
Week 3 Reciaion: Chaper3 : Problems: 1, 16, 9, 37, 41, 71. 1. A spacecraf is raveling wih a veloci of v0 = 5480 m/s along he + direcion. Two engines are urned on for a ime of 84 s. One engine gives he
More informationCHANGE IN THE RESISTANCE OF THE SEMICONDUCTOR IN THE VARIABLE DEFORMATION FIELD
CHANGE IN THE RESISTANCE OF THE SEMICONDUCTOR IN THE VARIABLE DEFORMATION FIELD M. AHMETOGLU (AFRAILOV) 1, G. GULYAMOV 2, S. H. SHAMIRZAEV 2, A. G. GULYAMOV 2, M. G. DADAMIRZAEV 2, N. APRAILOV 2, F. KOÇAK
More informationNMR Spectroscopy: Principles and Applications. Nagarajan Murali 1D - Methods Lecture 5
NMR pecroscop: Principles and Applicaions Nagarajan Murali D - Mehods Lecure 5 D-NMR To full appreciae he workings of D NMR eperimens we need o a leas consider wo coupled spins. omeimes we need o go up
More informationMOMENTUM CONSERVATION LAW
1 AAST/AEDT AP PHYSICS B: Impulse and Momenum Le us run an experimen: The ball is moving wih a velociy of V o and a force of F is applied on i for he ime inerval of. As he resul he ball s velociy changes
More information) were both constant and we brought them from under the integral.
YIELD-PER-RECRUIT (coninued The yield-per-recrui model applies o a cohor, bu we saw in he Age Disribuions lecure ha he properies of a cohor do no apply in general o a collecion of cohors, which is wha
More informationObject tracking: Using HMMs to estimate the geographical location of fish
Objec racking: Using HMMs o esimae he geographical locaion of fish 02433 - Hidden Markov Models Marin Wæver Pedersen, Henrik Madsen Course week 13 MWP, compiled June 8, 2011 Objecive: Locae fish from agging
More informationMath 4600: Homework 11 Solutions
Mah 46: Homework Soluions Gregory Handy [.] One of he well-known phenomenological (capuring he phenomena, bu no necessarily he mechanisms) models of cancer is represened by Gomperz equaion dn d = bn ln(n/k)
More informationComputation of the Effect of Space Harmonics on Starting Process of Induction Motors Using TSFEM
Journal of elecrical sysems Special Issue N 01 : November 2009 pp: 48-52 Compuaion of he Effec of Space Harmonics on Saring Process of Inducion Moors Using TSFEM Youcef Ouazir USTHB Laboraoire des sysèmes
More informationKinematics in two dimensions
Lecure 5 Phsics I 9.18.13 Kinemaics in wo dimensions Course websie: hp://facul.uml.edu/andri_danlo/teaching/phsicsi Lecure Capure: hp://echo36.uml.edu/danlo13/phsics1fall.hml 95.141, Fall 13, Lecure 5
More informationES240 Solid Mechanics Fall 2007
ES4 Solid Mechanics Fall 7 Viscoelasiciy References NG McCrum, CP Buckley, and CB Bucknall, Principles of Polymer Engineering, nd ediion, Oxford Universiy Press, 997 A good balance of heory and applicaion
More informationDisplacement ( x) x x x
Kinemaics Kinemaics is he branch of mechanics ha describes he moion of objecs wihou necessarily discussing wha causes he moion. 1-Dimensional Kinemaics (or 1- Dimensional moion) refers o moion in a sraigh
More informationLAPLACE TRANSFORM AND TRANSFER FUNCTION
CHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION Professor Dae Ryook Yang Spring 2018 Dep. of Chemical and Biological Engineering 5-1 Road Map of he Lecure V Laplace Transform and Transfer funcions
More informationLab #2: Kinematics in 1-Dimension
Reading Assignmen: Chaper 2, Secions 2-1 hrough 2-8 Lab #2: Kinemaics in 1-Dimension Inroducion: The sudy of moion is broken ino wo main areas of sudy kinemaics and dynamics. Kinemaics is he descripion
More informationChapters 6 & 7: Trigonometric Functions of Angles and Real Numbers. Divide both Sides by 180
Algebra Chapers & : Trigonomeric Funcions of Angles and Real Numbers Chapers & : Trigonomeric Funcions of Angles and Real Numbers - Angle Measures Radians: - a uni (rad o measure he size of an angle. rad
More informationPhysics 20 Lesson 5 Graphical Analysis Acceleration
Physics 2 Lesson 5 Graphical Analysis Acceleraion I. Insananeous Velociy From our previous work wih consan speed and consan velociy, we know ha he slope of a posiion-ime graph is equal o he velociy of
More informationBasic MRI physics and Functional MRI
Basic MRI physics and Functional MRI Gregory R. Lee, Ph.D Assistant Professor, Department of Radiology June 24, 2013 Pediatric Neuroimaging Research Consortium Objectives Neuroimaging Overview MR Physics
More informationPhysics for Scientists & Engineers 2
Direc Curren Physics for Scieniss & Engineers 2 Spring Semeser 2005 Lecure 16 This week we will sudy charges in moion Elecric charge moving from one region o anoher is called elecric curren Curren is all
More informationMath 333 Problem Set #2 Solution 14 February 2003
Mah 333 Problem Se #2 Soluion 14 February 2003 A1. Solve he iniial value problem dy dx = x2 + e 3x ; 2y 4 y(0) = 1. Soluion: This is separable; we wrie 2y 4 dy = x 2 + e x dx and inegrae o ge The iniial
More informationThe Paradox of Twins Described in a Three-dimensional Space-time Frame
The Paradox of Twins Described in a Three-dimensional Space-ime Frame Tower Chen E_mail: chen@uguam.uog.edu Division of Mahemaical Sciences Universiy of Guam, USA Zeon Chen E_mail: zeon_chen@yahoo.com
More informationMEI Mechanics 1 General motion. Section 1: Using calculus
Soluions o Exercise MEI Mechanics General moion Secion : Using calculus. s 4 v a 6 4 4 When =, v 4 a 6 4 6. (i) When = 0, s = -, so he iniial displacemen = - m. s v 4 When = 0, v = so he iniial velociy
More informationHST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis Fall 2008
MIT OpenCourseWare http://ocw.mit.edu HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More information- If one knows that a magnetic field has a symmetry, one may calculate the magnitude of B by use of Ampere s law: The integral of scalar product
11.1 APPCATON OF AMPEE S AW N SYMMETC MAGNETC FEDS - f one knows ha a magneic field has a symmery, one may calculae he magniude of by use of Ampere s law: The inegral of scalar produc Closed _ pah * d
More information= N 0!e. Topics... Nuclear Medicine: Gamma cameras, SPECT and PET. Radioactivity Discovery. Part 1: Radioactive Decay.
Topics... Nuclear Medicine: Gamma cameras, SPECT and PET 1: radioacive decay 2: deecion of radiaion A brief inroducion for DTU sudens Inroducion o medical imaging 31540, 2010 3: planar imaging 4: omographic
More information