Daqing ( Daching ) Piao , PhD Associate Professor School of Electrical and Computer Engineering

1. On The Feasibility Of Magneto-Thermo-Acoustic Imaging Using Magnetic Nanoparticles And Alternating Magnetic Field Daqing (Daching) Piao, PhD Associate Professor School of Electrical and Computer Engineering Oklahoma State University, Stillwater, OK 74078-5032

2. 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.

3. 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 generation • Rationale of applying frequency-chirped AMF to MNP to induce thermo-acoustic signal generation

4. SLP

6. 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 generation • Rationale of applying frequency-chirped AMF to MNP to induce thermo-acoustic signal generation

8. MNP under AMF The magnetic susceptibility of MNPs is dented as Under a time-varying magnetic fieldof an instant angular frequency become and the imaginry part of the susceptibility the real part of the susceptibility 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

9. 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

10. 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

11. 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 generation • Rationale of applying frequency-chirped AMF to MNP to induce thermo-acoustic signal generation

13. 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, as When MNPs are exposed to a pulse-enveloped AMF, the time-variant heat dissipation will result in volumetric power dissipationas

14. Short-burst of AMF on MNP excited by The acoustic pressure wave 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 generation 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

15. 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 generation • Rationale of applying frequency-chirped AMF to MNP to induce thermo-acoustic signal generation

17. 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 dissipation the resulted magnetization is for m=[1, n]

18. Frequency-chirped AMF on MNP the volumetric power dissipation at a position can be approximated by where is the frequency sweep rate. , and the Fourier transform of the excited acoustic pressure wave is denoted as If the Fourier transform of , we have the following Fourier-domain wave equation as can be written as the acoustic wave intercepted by an idealized point ultrasound transducer at

19. Summary We 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.

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