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1 Medical Imaging Image Processing with Biomedical Applications ELEG-475/675 Prof. Barner Image Processing Medical Imaging Prof. Barner, ECE Department, University of Delaware 2 Classes of Medical Imaging Modalities Anatomical or structural The ability to discriminate different constituents of the body Water, bone, soft tissue, etc. X-ray imaging, computed tomography (CT), ultrasound, and Magnetic Resonance Imaging (MRI) Functional or metabolic The ability to discriminate different levels of metabolism caused by specific biochemical activity Biochemical activity: Describes the functional behavior of tissue or organs May be caused by internal or external simulation Functional Magnetic Residents Imaging (fMRI), Single Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET) Image Processing Medical Imaging Prof. Barner, ECE Department, University of Delaware 3 Medical Imaging Examples Anatomical cases X-ray imaging for fracture identification, mammography tumor identification Ultrasound examinations of fetuses Functional cases fMRI methods for measuring blood flow or oxygenation level in brain tissue Changes in blood flow/oxygen level reflect numeral activity caused by stimulation Example: sound or light simulation PET imaging utilizing flurodeoxyglucose (FDG) administration shows blood flow and glucose metabolism in tissue Utilized to detect if tissue is affected by a tumor or epilepsy Image Processing Medical Imaging Prof. Barner, ECE Department, University of Delaware 4 X-Ray Imaging An incident electron, with energy higher than the binding energy of a particular shell level, is used to eject an electron Total energy preservation results in the release of a x-ray photon X-ray photons are focused in a monochromatic beam Scattering is a major problem in projection radiography Photons arrived at the same detector location through different paths Anti-scatter grids and collimators are used to reduce indirect arrivals at the sensor
Transcript

1

Medical Imaging

Image Processing with Biomedical Applications

ELEG-475/675Prof. Barner

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 2

Classes of Medical Imaging Modalities

Anatomical or structuralThe ability to discriminate different constituents of the body

Water, bone, soft tissue, etc.X-ray imaging, computed tomography (CT), ultrasound, and Magnetic Resonance Imaging (MRI)

Functional or metabolicThe ability to discriminate different levels of metabolism caused by specific biochemical activity

Biochemical activity: Describes the functional behavior of tissue or organsMay be caused by internal or external simulation

Functional Magnetic Residents Imaging (fMRI), Single Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET)

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 3

Medical Imaging Examples

Anatomical casesX-ray imaging for fracture identification, mammography tumor identificationUltrasound examinations of fetuses

Functional casesfMRI methods for measuring blood flow or oxygenation level in brain tissue

Changes in blood flow/oxygen level reflect numeral activity caused by stimulation

Example: sound or light simulation

PET imaging utilizing flurodeoxyglucose (FDG) administration shows blood flow and glucose metabolism in tissue

Utilized to detect if tissue is affected by a tumor or epilepsy

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 4

X-Ray Imaging

An incident electron, with energy higher than the binding energy of a particular shell level, is used to eject an electron

Total energy preservation results in the release of a x-ray photon

X-ray photons are focused in a monochromatic beamScattering is a major problem in projection radiography

Photons arrived at the same detector location through different pathsAnti-scatter grids and collimators are used to reduce indirect arrivals at the sensor

2

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 5

X-Ray Absorption

For a radiation beam passing through a medium with linear attenuation coefficient μ

N0=Nine-μt

Nin and N0 are the total number of photons entering and leaving the medium of thickness tIn more general cases, the attenuation coefficient and source are spatially varying

Yields integral expression along x-ray path

Example: attenuation coefficients for bone and fat

Photon energy dependent

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 6

X-Ray Example

Chest x-ray of a male

Normal result

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 7

X-Ray Computed Tomography (I)

Conventional x-ray radiography projects a 3-D object onto a 2-D detector plane

3-D information is diagnostically important

Bone fracture treatment may require 3-D imagingHeart and brain diagnoses require 3-D imaging

Consider a 3-D object as a stack of 2-D slicesAssume the x-ray radiation is parallel to the x-direction

The recorded radiation is given by

μ(x,y,z) is the attenuation coefficient and Iinand Iout are the source and detected radiation

( , ; )out in( ; , )

x t z dxI x y z I e

μ−∫=

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 8

X-Ray Computed Tomography (II)

For x-ray radiation parallel to the x-direction

Sensor readings along the ydirection give information on the y-direction projection of the selected slice

Rotate the source and detector for alignment along the y-direction

Gives x-direction projection information

First generation CT scanners rotated parallel beam sources and detector

Obtain projections at multiple angles

Multiple angle scans are performed for each slice (z value)

Stack multiple slices to form volume

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Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 9

X-Ray Computed Tomography (III)First-generation CT scanner geometry

Source: parallel beamDetector: linear arrayScanning: translation and rotation of source/detector pair

Second-generation CT scanner geometrySource: fan beamDetector: linear arrayScanning: translation and rotation of source/detector pair

Third-generation CT scanner geometrySource: fan beam (covers entire object without translation)Detector: arc of detectorsScanning: Entire projection obtained from single source location

Additional views obtained by source/detector rotationRotate only – no translation required

Fourth-generation CT scanner geometrySource: fan beam (covers entire object without translation)Detector: ring of detectorsScanning: source rotation

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 10

CT Example

CT sliceCardiac cavity of a cadaver

Pathological image

Image corresponding to the actual CT slice

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 11

Magnetic Resonance Imaging (MRI)

Nuclear Magnetic Residents (NMR) independently explained by Felix Bloch and Edward Purcell in 1946

1952 Nobel PrizePaul Lauterbur and Peter Mansfield used the NMR principal in MRIimaging

Obtains physical and chemical properties based images of an object2003 Nobel Prize

Like CT, MRI is tomographic imaging that produces three-dimensional imagesUnlike CT, MRI is not based on the transmission of external radiation through the objectMRI uses nuclear magnetic resonance property of selected matter in the object

Images anatomical structures as well as biochemical propertiesBiochemical properties are based on physiological function, such as blood flow and oxygenation

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 12

MRI Example

MRI methods allow image capture based on multiple parameters that represent various physical and chemical properties

Parameters: T1 weighted, T2 weighted, and Spin-DensityHuman brain a cross-section example

T1 weighted, T2 weighted, and Spin-Density of hydrogen protonsFunctional MRI (fMRI) reports physiological behavior over time

MRI imaging can create any direction cross-sectional images and multi-dimensional imaging sequences without making any physical changes to the instrumentMRI has fast signal acquisition (fraction of the second)MRI has high spatial resolution (millimeter to hundreds of a millimeter)

Temporal and spatial resolution relaxed to increase signal-to-noise ratio

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Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 13

MRI Principles (I)

Objective: map the spatial location and associate properties of specific nuclei or protons in an objectNuclei with odd atomic number possess angular moment

Angular moment referred to as spinSpinning of the charge protons creates and magnetic fieldThe charged protons thus an possess angular moment and magnetic moment

Example shown of charge proton with angular moment (J) and magnetic moment (μ):

Magnet representationSymbolic representation

Note: μ=γJ where γ is a gyromagnetic ratio

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 14

MRI Principles (II)

A hydrogen atom has one proton in its nucleusOdd atomic number results in nuclear spinGyromagnetic ratio is 42.58MHz/T

External magnetic fields of 0.5-1.5T yield sufficient magnetic moment for imaging the human body

A significant percentage of the human body is waterWater molecules contained hydrogen protonsthe hydrogen proton is an excellent choice for NMR based imaging in the human body

Other protons that exhibit the NMR phenomenon are available in the body (C, F, and P)

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 15

MRI Principles (III)

No external magnetic field case:The direction of the magnetic moment is random

Zero net longitudinal and transverse vectors

External magnetic field case:Nuclear paramagnetic polarization with specific orientationsInteraction between the magnetic moment of the nuclei and external magnetic field cause the spinning nuclei to precess

Wobbles like a spinning top subject to a gravitational field

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 16

MRI Principles (IV)

External magnetic field case:Nuclei align along or against the magnetic field

Nuclei aligned along the field have lower energy levelNuclei aligned against the field have higher energy levelMore nuclei align along the field than aligned against it

Results in a net magnetization vector in the direction of the external magnetic fieldThe procession is still random – net zero vector in the transverse direction

5

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 17

MRI Principles (V)

Using classical mechanics:The torque generated by the interaction of the magnetic moment of a proton and the external magnetic field is equal to the rate of change of angular momentum

Result given by the equation of motion for isolated spin:

where H0 is the strength of the external magnetic field and is the unit vector in the z-direction

Equation solution yields:

Larmor equation – precession frequency depends on gyromagnetic ratio and external magnetic field intensity

k

0 0

0

,

;

,

dJ H H kdt

J

dJ H kd

μ μ

μ γ

γμμ

= × = ×

=

= ×

0 0Hω γ=

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 18

MRI Principles (VI)

RF energy received by a nuclei at ω0 causes a change in stateResults in NMRThe excited nuclei returns to equilibrium through a relaxation process

Emits energy at the same precession frequency: ω0

During NMRNuclei can receive energy to move from a lower-energy state to a higher-energy state

Nuclei oriented along the external magnetic field can flip and oriented against the magnetic fieldResulting net longitudinal vector is no longer in the direction of the external magnetic field

90-degree pulseRF energy pulse at the Larmor frequency required to shift the net longitudinal vector by 90°All of the nuclei precess in phase

Longitudinal vector rotates in the x-y plane

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 19

MRI Principles (VII)

180-degree pulseRF energy pulse at the Larmor frequency required to shift the net longitudinal vector by 180°All of the nuclei precess in phase

Longitudinal vector rotates in the x-y planeRF Energy provided by a RF electromagnetic coil oscillating at the Lamor frequency

When RF pulses turned off, excited nuclei go through a relaxation phase

Net longitudinal magnetization vector returns to equilibrium state (in line with the field)Net transverse magnetization goes to zero as nuclei de-phase

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 20

MRI Principles (VIII)

Energy emitted during the relaxation process induces an electrical signal in the RF coil at the Larmor frequency

Basic MRI imaging signal: The free induction decay of the signal in the RF coil

Consider the external magnetic field and the RF pulls causing nuclear excitation

Change of the net magnet visitation vector:

T1 – longitudinal (spin-lattice) relaxation timeReturn to equilibrium net nine physicians vector in the z-direction

T2 – transverse (spend-spin) relaxation timeLoss of coherence (dephasing) leading to net zero vector in the x-yplane

( )02 1

z zx y M M kM i M jdM M Hdt T T

γ−+

= × − −

6

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 21

MRI Principles (IX)

Transverse relaxation processMagnetization relaxation after the RF pulse

TransverseLongitudinal

Free Induction Decay (FID)

Recorded in the coil at LarmorfrequencyRaw NMR imaging signal

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 22

MRI Principles (X)

The voltage induced in the RF coil is given by

Result is spatially dependentGoal: identify a magnetic resonance response of spinning nuclei are at a specific spatial location

Recall Larmor (precession) frequency is dependent on the net magnetic fieldSuperimpose gradient magnetic field on static external magnetic field

Yields spatially variant Lamor frequencySpatially encoded NMR signal by varying magnetic field

MRI images exploit three parameters of nucleiSpin density (density of nuclei)Longitudinal relaxation time, T1Transverse relaxation time, T2Parameter responses can be combined (weighted)

( )( ) ( ) ( , )robject

tV t H M t dt t

φ∂ ∂= − = − ⋅

∂ ∂ ∫ r r r

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 23

3-D Fourier Transform Description of MRI Imaging

Directional gradient magnetic fields: Gx, Gy, GzSelectively excites a spatial volume with spin nuclei density ρ(x,y,z)Overall gradient at spatial location r

FID NMR spin-echo signal from volume location r is

where and M0 is the magnetization vector at thermal equilibriumExpression can be rewritten as

ωx, ωy, ωz: Frequencies corresponding to Gx, Gy, GzTaking the inverse Fourier transform

Reconstruction of desired values

( ) ( ) ( ) ( )x y zt G t i G t j G t k= + +G

3( ) ( , )S t M t d r= ∫ r

0

( ') '

0( , ) ( )

r

i G t dt

M t M eγ

ρ− ∫

=r

r r

( )0( , , ) ( , , ) x y zi x y z

x y zS M x y z e dxdydzω ω ωω ω ω ρ − + += ∫∫∫

( )0( , , ) ( , , ) x y zi x y z

x y z x y zx y z M S e d d dω ω ωρ ω ω ω ω ω ω+ += ∫∫∫

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 24

MRI Parameters

Relaxation times and spin density for human tissues and fluidsNote considerable change in relaxation parameters of tissues/fluids of interest

Example: blood and cerebrospinal fluid (CSF)Image contrast adjusted after reconstruction

Spin density images are T1 weighted by the parameter to improve contrast features the anatomical structures

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Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 25

MRI Instrumentation (I)

Three orthogonal coils provide gradient magnetic fields

Simple is case: linear spatially dependent magnetic fieldGeneral parameters:

Field strength, linearity, and switching time

RF coilTransmits time-varying are pulses

Causes nuclear excitationReceives signature Free Induction Decay (FID) signal

During nuclear relaxation phase

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 26

MRI Instrumentation (II)

RF pulses are encoded to selectively excite specific voxels

Frequency and phase encodingProper encoding provides slice views in various orientations

Axial, sagittal, coronal

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 27

MRI Encoding

Slice selection –frequency encoding

Linear gradient applied in the z direction

X direction encoding –phase encodingY direction encoding –frequency (read out) encodingBlock diagram shows overall spatial encoding

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 28

Transverse Relaxation and Rephasing

Transverse vector initially phased with 90° pulseDuring x-direction space in coding transverse vector begins dephasingRephasingachieved with 180° pulse

Received echo based on rephasedtransverse vector

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Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 29

Typical MRI Encoding Sequence – Spin Echo Case

Encoding scheme returns FID from a specified locationVarying the time between pulses (cycle repetition time) determines the influence of T1and T2 on the FIDVarious encoding schemes can be applied

Echo planar imagingGradient echo imagingFlow imaging

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 30

MRI Images of a Human Brain

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 31

Nuclear Medicine Imaging Modalities

Transmission based imaging (x-ray, CT) provides anatomical informationMRI provides some anatomical and some functional information

Detected chemical composition is related to metabolic information

Radionuclide imaging directly involve organ and tissues in the imaging process

Emission imaging is based on radioactivity decayUnstable nucleus disintegrates into a stable nucleus by releasing nuclear energy and emitting photons

Gamma photons or particles such as positrons and alpha particles are generally released and detected

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 32

Radioactivity Decay

Radioactivity decay is described byN(t)=N(0)e-ηt

N(0) is the number of initial radionuclides and η is the radioactivity decay constantThe decay half-life is given by

Thalf=0.693/η

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Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 33

Single Photon Emission Computed Tomography (SPECT)

SPECT imaging utilizes gamma raysRadioisotopes are injected into the body through radiopharmaceutical drugs that metabolize with specific tissuesGamma rays emanating from the tissues are captured by detectors surrounding the body

Recorded radiation form the raw projection data

Gamma ray attenuation is similar to x-ray attenuation

Id=I0e-xνx is the distance traveled by the gamma ray and ν is a medium dependent linear attenuation coefficient

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 34

SPECT System& Example

Source intensity is based on the dose, metabolism, and half-life of the radionuclideScattering causes loss of source information

Difficult to determine the travel path of the received photon

Lead collimators reduce detection of scatters

SPECT image of the human brainPoor resolution and anatomical structure informationResult shows radioactivity distribution in tissue representing specific metabolism or blood flow

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 35

Positron Emission Tomography (PET)

PET is based on the simultaneous detection of two 511 keV photonsPhotons are traveling in opposite directionsFeature: the ability to trace radioactive material metabolized in tissue

Provides specific information on biochemical and physiological behaviorMethod: some radioisotopes decay by admitting positrons

Positron emission is accompanied by a significant amount of kinetic energyPositrons typically travel 1-3 mm, losing some kinetic energyAnnihilation (with a loosely bound electron) occursAnnihilation causes the formation of two Gamma photons with 511 keV

Gamma photons travel in opposite directionsCoincidence detection is used to determine the annihilation location

Annihilation location is close to the positron emission location

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 36

PET Scanner System

Detector pair is moved in an arc around objectCoincidence detection localizes annihilation location

Arrivals are within nanosecondsScattered photons do not arrive within preset window of time

Reduces scattering problem

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Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 37

Series of Human Brain PET ImagesRadiopharmaceutical used: Fluorodeoxyglucose(FDG)FDG images show glucose metabolism and blood flow

Used to determine heterogeneity and invasiveness of tumors

Resolution of PET is better than SPECTMain advantage:

Ability to tag specific biochemical activity and trace it with time

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 38

Ultrasound Imaging

Sonar technology was successfully used by the military in World War IIUltrasound waves in medical imaging were first explored in the 1970s and 1980sCurrent ultrasound uses:

Diagnostic imaging of anatomical structures, blood flow measurements, and tissue characterizationUltrasound machines are safe, portable, and low-cost

Ultrasound WAV definition: sound waves with frequencies above 20kHzVelocity (c), wavelength (λ), and frequency (ν) relationship: C=λν

Frequency remains constantWhen a sound wave leaves one medium and enters another (e.g., soft tissue to fat)

Wavelength changes (medium specific velocities, fixed frequency)Directional change – governed by laws of diffractionSound waves follow the principles of reflection, refraction, and superposition

Image resolution is limited by wavelengthShorter wavelengths provide better resolution and penetrate deeper into tissueCommonly used frequency range: 2-5MHz

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 39

Reflection and Transmission

When changing mediums, the acoustic impedance changes

Causes reflection of the incident soundIntensity of the reflected way it is given by

Intensity of wave transmitted to the second medium

Zi and Zj are the acoustic impedances of the two media

Application to a multilayer structure yields

Rearranging using 1+Rij=Tij yields

j iij

i j

Z ZR

Z Z−

=−

2 jij

i j

ZT

Z Z=

+

0 0 12 23 34 54 43 32 21R I T T T T T T T=

( )( ) ( )2 2 20 0 12 23 34 4510 1 1R I R R R R= − −

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 40

Refraction and Attenuation

The angle of reflection is equal to the angle of incidentsThe angle of the transmitted wave is given by Snell’s law

Dependent on the propagation speeds of the two mediums: c1and c2

Attenuation occurs as a wave propagatesAttenuation coefficients are characterized in dB/cm and are frequent independent

2

1

sin sint icc

θ θ=

11

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 41

Reflection Imaging

System parametersSource and object

s(x,y) – acoustic signal intensityω(t) – acoustic signal pulseR(x,y,z) – biological tissue reflectivity (desired parameter)

ReceiverK – normalizing constantώ(t) – received pulseJcr(t) – recorded reflected intensity (adaptive time varying gain applied to compensate for attenuation)

Recorded intensity signal can be written as a convolution

Imaging extracts R(x,y,z), which characterizes the tissue( ) ( ) ( ), , ,

2crctJ t K R x y s x y tω⎛ ⎞= ⊗ − −⎜ ⎟

⎝ ⎠

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 42

Ultrasound System

An ultrasound pulse is typically 2-3 cycles in durationA crystal element generates pulses and records the reflections

Acoustic echoes are position dependentUltrasound images appear noisy with speckles

Objects lack a continuous boundaryUltrasound image interpretation is difficult

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 43

Ultrasound Imaging Modes (I)

A-Mode:Record amplitude of returning echoes from tissue boundaries with respect to time

Perpendicular incident angleEcho time represents acoustic impedance and depth of reflecting boundary

Provides 3-D informationM-Mode:

Provides information about signal amplitude variation due to object motion

Fixed position transducer produces a sweep cycle of A-mode recordingsResponse displayed as a line of intensities representing object the collection

Example: Display of mitral valve leaflet of a beating heart.

Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 44

Ultrasound Imaging Modes (II)

B-Mode:Provides 2-D images representing the change in acoustic impedance of the tissue

Brightness shows echo strength2-D information is obtained by pivoting the transducer or using a transducer array

V-shaped imageExample: fetal abdomen

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Image ProcessingMedical Imaging

Prof. Barner, ECE Department, University of Delaware 45

Ultrasound Imaging Modes (III)

Doppler imagingEffective for imaging blood flowA stationary observer sees a frequency change from a moving sourceChange in frequency:

Velocity of moving source: νSource frequency: fVelocity of sound in the medium: cIncident angle of the moving source with respect to the sound propagation: θ

Spatial spanning used to generate 2-D imageDoppler shift mapped to intensity/color

Example: Doppler image of kidney

2 cosdoppler

v ffcθ

=


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