On The Feasibility Of Magneto-Thermo-Acoustic Imaging Using - PowerPoint Presentation

Slide1

On The Feasibility Of Magneto-Thermo-Acoustic Imaging Using Magnetic Nanoparticles And Alternating Magnetic Field

Daqing (Daching) Piao, PhD Associate ProfessorSchool of Electrical and Computer EngineeringOklahoma State University, Stillwater, OK 74078-5032Slide2

Abstract

We propose a method of magnetically-induced thermo-acoustic imaging by using magnetic nanoparticle (MNP) and alternating magnetic field (AMF). The heating effect of MNP when exposed to AMF by way of Neel and Brownian relaxations is well-known in the applications including hyperthermia. The AMF-mediated heating of MNP may be implemented for thermo-acoustic imaging in ways similar to the laser-mediated heating for photo-acoustic or opto-acoustic imaging and the microwave-mediated heating for microwave-induced thermo-acoustic imaging. We propose two possible ways of achieving such magneto-thermo-acoustic imaging; one is a time-domain method that applies a burst of alternating magnetic field to MNP,the other is a frequency-domain method that applies a frequency-chirped alternating magnetic field to MNP. Slide3

OutlineHeating effect of magnetic nanoparticle (MNP) under alternating magnetic field (AMF)

Rationale of applying short burst of AMF to MNP to induce thermo-acoustic signal generationRationale of applying frequency-chirped AMF to MNP to induce thermo-acoustic signal generationSlide4

Symbol

IdentificationUnit

Speed of sound in tissue

[m s

-1

]

Specific heat at cons. press

[J kg-1 K-1]Specific heat at cons. volum.[Hz]Frequency[A m-1]Magnetic field strength[J K-1]Boltzmann constant[A m-1]Saturation magnetization[A m-1]Acoustic pressure[Pa]Volumetric power dissipation[W m-3]Specific power loss[W kg-1]Thermodynamic temperature[K]Time---duration[s]Time---instant[s]Internal energy[J]Hydrodynamic volume[m3]Magnetic volume[m3]

SLPSlide5

Symbol

IdentificationUnit

Isobaric vol.

ther

. exp.

coeff

.

[K-1]Grueneisen parameter[dimensionless]A change in a variable[dimensionless]Viscosity coefficient[N s m-2]Anisotropy energy density[J m-3]Permeability[V s A-1m-1]Absorption coefficient[m-1]Reduced scattering coefficient[m-1]Envelope function[dimensionless]Angular frequency[rad s-1]Mass density[kg m-3]Relaxation time[s]Néel relaxation time [s]Brownian relaxation time[s]Magnetic susceptibility[dimensionless]Slide6

OutlineHeating effect of magnetic nanoparticle (MNP) under alternating magnetic field (AMF)

Rationale of applying short burst of AMF to MNP to induce thermo-acoustic signal generationRationale of applying frequency-chirped AMF to MNP to induce thermo-acoustic signal generationSlide7
Slide8

MNP under AMF

The magnetic susceptibility of MNPs is dented as

Under a time-varying magnetic

fieldof

an instant angular frequency

the real part of the susceptibility

and the

imaginry part of the susceptibility become

If the MNPs are in the single-size domain of super-

paramagnetism

and dispersed in a liquid matrix, the relaxation time

is to be dominated by

Néel

and Brownian relaxations as Slide9

Heating effect of MNP under AMF

Under an AMF of constant frequency, i.e.

the resulted magnetization is

Change of the internal energy is

At a phase change of

the heat dissipation per unit volume Slide10

Heating effect of MNP under AMF

For MNPs exposed to a continuous-wave AMF, the instantaneous thermal energy deposited per unit volume per unit time, i.e. the

volumetric power dissipation

(unit: W m

-3

), is

where the subscript “CW” denotes “continuous-wave”, and accordingly the specific-loss-power (SLP) (unit: W kg-1) is The initial slope of temperature-rise of the sample containing the MNPs is

which is used by many studies to predict and experimentally deduce the heating power of MNPs to evaluate the model-data agreement Slide11

Outline

Heating effect of magnetic nanoparticle (MNP) under alternating magnetic field (AMF)Rationale of applying short burst of AMF to MNP to induce thermo-acoustic signal generationRationale of applying frequency-chirped AMF to MNP to induce thermo-acoustic signal generationSlide12
Slide13

Short-burst of AMF on MNP

We now consider the heating characteristics of MNPs exposed to a homogenous AMF of fixed frequency

and time-varying amplitude. We call this AMF a “

tim

-domain AMF

”,

which is equivalent to a “carrier” AMF

modulated by an envelope function as The simplest form of time-domain AMF may be the one obtained by turning on a “carrier” AMF repetitively at a short duration (s time-scale) over a period of µs-scale or longer, asWhen MNPs are exposed to a pulse-enveloped AMF, the time-variant heat dissipation will result in volumetric power dissipation as Slide14

Short-burst of AMF on MNP

The acoustic pressure wave

excited by

satisfies the following wave equation

The general solution of the acoustic pressure reaching a transducer at

and originating fro the source of thermo-acoustic signal generation at

in an unbounded medium is known to be

Since

the local temperature rises rapidly when AMF pulse is on then falls rapidly when AMF pulse is off, this time-variant heating could produce abrupt expansion and transient contraction of the local tissue, which is the condition for thermo-acoustic signal generationSlide15

Outline

Heating effect of magnetic nanoparticle (MNP) under alternating magnetic field (AMF)Rationale of applying short burst of AMF to MNP to induce thermo-acoustic signal generationRationale of applying frequency-chirped AMF to MNP to induce thermo-acoustic signal generationSlide16
Slide17

Frequency-chirped AMF on MNP

We now consider the heating of MNPs exposed to a homogenous AMF whose amplitude is fixed at

but angular frequency is time-varying. We call this AMF a “

frequency-domain AMF

”. The simplest form of frequency-domain AMF may be obtained by linearly sweeping the frequency of AMF . The instantaneous field strength of this linearly frequency-modulated, or chirped, AMF is represented by

We approximate the signal using

Short-time heat dissipationthe resulted magnetization is

for m=[1, n]Slide18

Frequency-chirped AMF on MNP

the

volumetric power dissipation

at a position

can be approximated by

whereis the frequency sweep rate.

If the Fourier transform of

is denoted as

, and the Fourier transform of the excited acoustic pressure wave

as

, we have the following Fourier-domain wave equation

the acoustic wave intercepted by an idealized point ultrasound transducer at

can be written as

Slide19

SummaryWe

predict that thermo-acoustic signal generation from MNPs is possible, by rapid time-varying heat dissipation and cooling of the local tissue volume, using time-domain or frequency-domain AMF on MNPs. Slide20

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