Doppler echocardiography & Magnetic Resonance Imaging.

Doppler echocardiography

& Magnetic Resonance

Imaging

Doppler echocardiography

& Magnetic Resonance

Imaging

Doppler echocardiographyDoppler echocardiography

History:

- Langevin developed sonar.

- 1940s development of pulse-echo.

- 1950s development of mode A and B.

- 1957 development of continuous wave Doppler.

- End 1960s real-time ultrasonic imaging.


http://krampf.com/experiments/Science_Experiment38.html

Advantages:

- Transmitted ultrasound appears to be quite safe.

- Relatively inexpensive compared to CT scan and MRI.

- Portability

Drawbacks:

- Bad resolution in time and space.

Echocardiagraphy is one of the most widely used tools for cardiac diagnosis


Physics of ultrasounds:

Echocardiography is a relatively low-energy long wavelength technique.

It is based on propagation of energy in the body. This energy will interact with the tissues and blood components.

An ultrasound wave disturbs the particles in a certain body without a net movement in the medium (transverse wave)



For ultrasounds f is between 1 and 10 MHz.

The periodic disturbance is propagated at a speed of:

A longitudinal wave is analog to a piston moving back and forth.

fv



Piezoelectricity

It is a property of ferroelectric materials. These are ovoid structures which are highly polarized.

The transition is not abrupt, but usually more or less damped depending on the properties of the piezoelectric material and the manufacturing process.



Piezoelectricity

The piezoelectric material used in ultrasounds is synthetic ceramic, PZT (Zirconate Titanate) .



The velocity of sound is a property of the material (330 m/s for air; 1480 m/s for water; 1540 soft tissue).

The velocity is related to the restoring force attempting to return the particles to their equilibrium position.

In reality K and are a function of T.

Density

MaterialtheofModulusElacticKv



- f is fixed by the properties of the material.

- v is fixed by the T.

So must vary to keep v= f constant.


Interaction of ultrasound with tissue:

Attenuation:

Displacement of particles during compression and rarefaction processes due to a longitudinal wave is given by:

However, in a homogenous medium without friction or viscous forces: A=Cte x

xvtsinAA

2

0



Attenuation:

But, human body is not homogenous, then there is a loss in energy and attenuation of the wave amplitude, due to:

- Scatter by large targets, which lead to wave dispersion.

- Mode conversion, example: into shear waves in bones.

- Absorption (conversion of wave energy into heat energy).



Attenuation:

Attenuation of ultrasounds by soft tissues can be formulated as:

is the attenuation coefficient (cm-1).

A0 is incident intensity.

- Attenuation is frequency dependent: the higher the frequency the greater the attenuation per centimeter of tissue traversed.

zeAzA 0)(



Reflection and refraction:

At the boundary between two tissues, a portion of the wave is reflected and the other one is propagated.

The amount reflected/propagated depends on the difference in characteristic impedances:

vz




Interfaces where:

- The surface is almost planar (surface >> ),

- The surface is smooth (surface irregularities << ),

Are called specular reflectors (mirror-like)

2

12

12

ZZ

ZZII ir

Water 1.52

Blood 1.62

Heart 1.65-1.74

Lung 0.26




In a specular reflector:

Refraction:

In real applications due to curvature, only the waves that are reflected and transmitted by perpendicular surfaces larger than the wavelength contribute to the visualization.

ri

2

1

v

v

sin

sin

t

i



Scattering:

If the wave encountered a target with a size << , then it is scattered. If the target is assumed as a spherical particle, with a radius of (r), so:

I is the intensity of the scattered wave.

In the body, the scattering targets are: blood, muscles, …

64

2rI



Speckle image

The probe detects constructive and destructive interferences resulting from scattering targets.

This can allow the differentiation between structures.


Doppler Effect:

- For stationary targets the number of waves encountered by unity of time is equal the wave frequency.

- If the target is moving toward the transducer the frequency increases.

The number of additional wave fronts encountered is a function of the velocity of the moving target and the velocity of sound.

Then; the frequency of ultrasound (perceived) at the target (cell):

v

vvff c

c 0


Doppler Effect:

However, in echo-Doppler, we are interested in measuring the frequency of sound returning to the transducer (stationary):

In this case:

000

22f

v

vf

vv

vfffso

vv

vff

f

v

f

v

c

c

crd

ccr

c

c

cr

For non // movement:

)(2

0 cosfv

vf cd


Instrumentation:

Beam patterns and focusing:

Near zone: Fresnel zone

Far zone: Fraunhofer zone

- Focusing can be performed by using a concave transducer.

- Using an acoustic beam that will focus the acoustic wave.

The problem is that the divergence in the field beyond the focal point occurs more rapidly than with an unfocused transducer.

4

2Dlength


Instrumentation:

Transmission of ultrasounds by a transducer generates side lobes:

The angle of these side lobes is given by:

D

msin

)(


Instrumentation:


Instrumentation:

Phase array

MRIMRI

The basis is spatial encoding of Nuclear Magnetic Resonance (NMR) signal.

NMR is a low energy electromagnetic radiation due to energetic transitions of nuclei in response to radiofrequency is the presence of a magnetic field.

MRI reproduces the amplitude and the phase of the NMR signal.

NMR signal depends on the physiochemical state of the sample. In practice: Hydrogen nuclei are targeted (Proton MRI).

MRIMRI

Physical principle:

NMR is based on the interaction of atomic nuclei with externally applied RF fields.

In the presence of an externally imposed magnetic field, the magnetic moment of protons will align with the field (// or anti-//)

MRIMRI

Physical principle:

The protons can switch between states by absorbing or emitting the required electromagnetic energy in the form of photons. Example: @ 0.35 T, the frequency of the photons is 15 MHz (radio wave band).

The two energies are almost the same, with an excess of less than 1 proton/million in the lower energy state.

MRIMRI

Physical principle:

In NMR experiments, the action of all protons in the sample is determined and not the behavior of a single proton.

This is represented by the macroscopic magnetization which is the vector sum of the individual magnetic moments of the protons.

If the macroscopic magnetization vector is moved away from the z-axis, it will precess about this axis with a frequency called: Larmor frequency:

0BL B0 Magnetic field

Gyromagnetic ratio (constant for each nuclei)

MRIMRI

Physical principle:

This perturbation is performed by an electromagnetic energy @ Larmor frequency.

This electromagnetic energy is produced by radio-frequency energy.

The magnitude and the duration of the burst of RF energy determines the degree of precession.

If the magnetization vector is lipped 90° (x-y plan), this called a 90° pulse.

MRIMRI

Physical principle:

Then, RF energy will be emitted @ Larmor frequency with an intensity proportional to the magnetization component in x-y plane (transverse magnetization).

This component (MT) will decay toward zero exponentially with a time constant T2:

2)0()( T

t

TT eMtM

MT Spin-spin relative time

(20 to 400 ms)

MRIMRI

Physical principle:

For the longitudinal magnetization:

11)( 0T

t

L eMtMM0 Magnetization after complete equilibrium

T1 Spin-Lattice relative time (200 ms to 3s)

MRIMRI

Image Contrast and Pulse Sequences

MRIMRI

Doppler echocardiography & Magnetic Resonance Imaging.

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Transcript of Doppler echocardiography & Magnetic Resonance Imaging.