Heating Mechanisms of Magnetic Nanoparticles in Hyperthermia Treatment

Wright State University CORE Scholar

Special Session 5: Carbon and Oxide Based Nanostructured Materials (2013) Special Session 5

6-2013

Anna Lukawska

Gregory Kozlowski Wright State University - Main Campus, [email protected]

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Repository Citation Lukawska, A., & Kozlowski, G. (2013). Heating Mechanisms of Magnetic Nanoparticles in Hyperthermia Treatment. . https://corescholar.libraries.wright.edu/ss5_2013/1

This Presentation is brought to you for free and open access by the Special Session 5 at CORE Scholar. It has been accepted for inclusion in Special Session 5: Carbon and Oxide Based Nanostructured Materials (2013) by an authorized administrator of CORE Scholar. For more information, please contact [email protected]. Heating mechanisms of magnetic nanoparticles in hyperthermia treatment

Anna Lukawska and Gregory Kozlowski Wright State University, Physics Department 3640 Col. Glenn Hwy., Dayton, OH 45435, USA

Group Members

Bachelor Student: Seun

Master Students: Deema Xing Vartika Jessica Jason Anna

PhD Student: Starting this Fall

Postdoc: Erik New Lab Space

Labs: PLD system lab Nano lab with Hyperthermia system, AFM, Silver Nano Particles project and Testing films and fluids real and imaginary parts of permeability and permittivity project

Hyperthermia

• Magnetic hyperthermia is a new non-surgical treatment of cancerous tumors.

http://www.tutuz.com/world-conference-interventional-oncology-ferromagnetic-theory-cancer-oncogenesis/ Magnetism

http://www.nitt.edu/home/academics/departments/physics/faculty/lecturers/justin/students/magnetic/origin/ • Quantum Mechanical Phenomenon • Originates from orbital motion and spin-1/2 rotational motion of an electron • Governed by Maxwell’s equations • Magnetic Variables are: B, H and M Magnetization

Magnetization is the measure of the strength of magnetism in a material. It depends on density of magnetic dipole moments within material (N) and their magnitudes (mS).

 NM mss Classification of materials

• Magnetic materials are classified by their susceptibility, χ to magnetic fields: - Diamagnetic - negative χ, independent on temperature. - Paramagnetic - small and positive χ, highly dependent on temperature. - Ferromagnetic - large and positive χ, highly dependent on temperature. M   H M-H graph

In a large magnetic field the magnetic moments within the material align with the field, giving the

saturation magnetization, MS. As the magnitude of the field decreases the total magnetization decreases and reaches at zero field the

remanent magnetization, MR. The coercive field HC must be applied to get back zero magnetization.

• History of magnetization • Hysteresis loop for ferromagnetic materials • Magnetization is different with increasing fields as compared to decreasing fields Size dependence

• Magnetic domains exist to reduce the overall energy of the system. • Size restriction - material cannot gain favourable energy configuration by breaking into domains. • Nanoparticles with diameter less than DC have a single magnetic domain, a uniaxial anisotropy. • Coercivity is larger for single- domain • Difference between maximum and minimum magnetic energies (magnetization pointing along the anisotropy axis and perpendicular to it) is: where KV is an energy barrier, K is the anisotropy constant, and V is volume. Superparamagnetism

• KV value gets smaller as ferromagnetic nanoparticles (<100nm) gets smaller, and at some point it is comparable with the thermal -23 -1 energy kBT (kB – the Boltzmann constant, 1.38x10 JK ).

• Assuming that particles are immobilized, this leads to a spontaneous random orientation of the magnetic moment inside the particles (zero remanence magnetization and coercivity, so no hysteresis).

• The magnetization will be zero until it will be biased in one direction by applied an external magnetic field. In this state the particle is superparamagnetic (SNP).

• The lifetime of particles magnetization (the time which the systems need to achieve zero magnetization after an external magnetic field is switched off), is given by Néel process :

Heating process

i. Hysteretic losses (may be determined by integrating the area of hysteresis loops, a measure of energy dissipated per cycle of magnetization reversal) ii. Neel and Brown relaxation losses iii. Frictional losses in viscous suspensions

Multi-domain ferromagnetic particles

• Reversal of magnetization occurs by flipping of the magnetic moments in domains where the magnetic moment vector is antiparallel to the applied field. • If the applied field can fully saturate the magnetization, then the energy losses in multi- domain materials depend on the coercivity. • For fully saturated magnetic materials, the power loss decreases with increasing domain size. • Multi-domain particles should be avoided if the power loss is to be maximized. Single-domain NP

• In hyperthermia are immobilized - chemically attached through targeting moieties to tumor

• Magnetization rotating within particle Blocked and Superparamagnetic NP

• KV < kBT Blocked NP (each time the particle magnetization reverses an amount of energy equal to the anisotropy barrier is released to surroundings)

• KV < kBT – Superparamagnetic NP (Co NP have higher anisotropy barrier than Fe NP of the same size)

Diameter separating blocked state of NP with SNP depends on material and the temperature of the surrounding. E.g. Fe (at blood temp.) – 7nm

Eddy Currents

• For NP eddy currents heating can be neglected, since

- d is a particle’s diameter - E is the eddy current coefficient Heating (blocked NP)

• Heating due to: - Driving magnetization - Shaking of particles Use high amplitude and low frequency to be safe for healthy tissue • E.g. 20nm Co: KV=(2x10- 18J)(348kHz)=0.696pW

• From hysteresis loop: • Estimating hysteresis loop: - amplitude: the volume saturation magnetization - width: twice the coercive field Heating Mechanism for SNP (1) • The energy barrier is insignificant • By low amplitude and high frequency • Disorder (high entropy) assembly of superparamagnetic nanoparticles (SNP) • Magnetized by magnetic field • SNP go to a highly ordered (low entropy) state • Heat is added to the adiabatic system Heating Mechanism for SNP (2)

• The first thermodynamic law gives:

where, U - the internal energy; W - the magnetic work done on the system, H [A/m] - the magnetic field intensity, B [T] - the induction; Q is the heat added to the system (δQ=0, adiabatic process).

• Heating is a thermodynamic mechanism that relies on the fact that in a high-frequency magnetic field the nanoparticles magnetization is always trying to catch up with the applied filed.

• Since H and B are collinear, only magnitudes are required: -7 B=μ0H+M, where μ0=4π∙10 [Tm/A] is the permeability of free space. Thus, the change in the internal energy is:

• When the magnetization lags the field, the integrand is negative, indicating that magnetic work is converted to internal energy.

Heating Mechanism for SNP (3)

For ferrofluids the magnetization can be defined as a complex susceptibility: Since, then

The magnetic field intensity is: With The magnetization is:

Therefore, the change in internal energy is:

The volumetric power P generated by the assembly of nanoparticles and that heats surrounding environment is: Brownian relaxation

• Brownian relaxation - when magnetic moment aligns with the filed the particle rotate as well

• Where - η is the viscosity coefficient of the matrix fluid, - T is the absolute temperature,

- VH is the hydrodynamic volume of the particle with radius R,

- δ is the thickness of a attached surfactant layer,

- VM is the magnetic volume,

Neel relaxation

• Neel relaxation – magnetic moment rotates within crystal

• Where: - - K is the anisotropy constant originating from magnetocrystalline or shape properties

Heating Mechanism for SNP (4)

• High heating rates if the Neel relaxation is not dominant • Brownian and Neel processes take place in parallel • Time constant τ is the effective relaxation time

• Assuming constant susceptibility, χ0, the power loss is: Specific Power Loss

• SAR (Specific Absorption Rate) = SPL (Specific Power Loss) [W/g]

• Normalized SPL for different samples with different mass SPL’=SPL/m [W/g^2] System

• A custom-made power supply • A 20-turn insulated copper coil in the shape of a spiral solenoid • Cooling is done with water • A fiber-optic temperature sensor with an accuracy of 0.0001 K • At frequency 174 kHz the magnetic field with magnitude of 20.6 μT is generated inside the coil Temperature Sensor

• The temperature measurements are based on variations of reflected light – when compared to the emitted light due to thermal expansion of the glass used within the sensor. The thermal inertia is reduced almost to zero allowing ultra fast temperature monitoring.

Knowing where the sensor has a sensitive area is important in understanding how temperature is measured. The magnetic field relative to the position inside the coil

• Our custom coil consists of insulated copper sheets wrapped around each other 20 times in the form of a spiral. • The diameter of the coil is 3 cm and the length is 4 cm.

• 9 different samples were measured • Single-domain size limit: 15nm • Superparamagnetic size limit: 6nm • Heat capacity [J/°C g] = 0.4198 al: Co 1 175kHz, 15A

60 g 50 ~ ~ ~ 40 ~ .s 11'co ..c.~ 30 Q

50 100 150 200 250 time(s) Co 175kHz, 1SA 9

0.6

0.5

0.4 ~ ~ ~ ~ E 0.3 $ .!: (b CJ) :ii ~ () 0.2

0.1

40 60 80 100 120 140 160 180 time(s) Diameter D SPL' for Co naoopardeles

LB I I I I I I I 4 -r 1. 6 -r.._ - ~ 1.4 -' - - ~,__ ..__ ..... ~~ -..... 11 ...... _._ ...... '"""n .._._ I ~ - I I I 1. 2 1-J I u 1 I -M ..... < Oil 1

...~ 0.8 ~ 'I ... - ~ rl.l 0.6 - ,_ -= I _,__ - - I I • I I -- 0.4 I I L,_ 0.2 .. .. r! -tl I - I 0 ---· I 6 7 g '9 10 11 12 1~~ 14 15 16 17 18 19 20 Diameter [run] Fe

• 9 different samples were measured • Single-domain size limit: ~15nm • Superparamagnetic size limit: ~10nm • Heat capacity [J/°C g] = 0.4504 SPL'' for Fe nanoparticles

4.5 - ~

-" -" -• ~ 4 !• r-

c=ll 3.5 - • 3 M -< 2.5 bll 1.-.. '·i t,....+i- ~ ~ 2 .,... - I._ ~ ~ LS ~ tl.l ...-

1 H H H __ f-i ~.f- ~ ·- ..... s ~ 0.5 • ,... - I - I 0 - - - ~ - 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 .20 21 22 Diameter [nm.] Heat transfer Model

• The Matlab code was written to solve heat equations in cancerous (1) and healthy (2) tissue:

Ref: C.-T. Lin, K.-C. Liu / International Communications in Heat and Mass Transfer 36 (2009) 241–244

Parameters

• The magnetic field amplitude and frequency are 50 mT and 300 kHz, • Nanoparticles used are 19-nm magnetite MNPs, • 19-nm magnetite MNPs can dissipate the energy P=1.95×105 W/m3 (during proving that it can be assumed constant), • Initial condition body temperature for tumor and healthy tissue is 37°C, • The volume fraction of particles is ψ = 2 × 10− 5,

• Thermal conductivities are k1 = k2 = 0.502 W/mK, 3 3 • Perfusion rates of blood are wb1=wb2=0.0064 m /s/m , 3 • Metabolic heat generation parameters are qm1=qm2=540 W/m , × • Density and specific heat capacity of healthy tissue ρ2 c2 =1060×3600 J/m3/K, × 3 • Density and specific heat capacity of blood ρbcb =4.18 106 J/m /K,

• Density and specific heat capacity of tumor ρ1 =ψρM +(1−ψ)ρ2 and c1 =ψcM +(1−ψ)c2 where for magnetite ρM = 5180 kg/m3, cM = 670 J/kgK, • The dimensions of tumor and normal tissue were regarded as R = 5 mm and a=15mm. ··· ·:··· ...... ·· ...... :··· ...... ·····: .. .·:·...... ·· ' ...... ·-:··· ... · ~...... ',•, 37.01 6 ...... , ...... ·· ...··· ; ...... ~ ...... '• ...... ·~ ...... ·.. ···· . ····· 37.014 ..,; .. ······· ...... ···:· ...... ~. ... . 37.01 2 -.: .. ········ ...... ·.... ·· ...... ·· ·: ·,.. ... ··.. : 2: 37.01 ~ ·········· ...... ~ : ... ~ ...... ··.:· ...... •., . a 37.008 ~ ...... · : ...... ~ ...... ·· ··..: f! . . ··· .. : ...... a : :...... ·· . ··· ... : ... ·...... E 37.006 ~ ...... ]' ...... ·· .. ... SI : ...... ·· .. ; ... . 37.004 __; ...... ·· ...... ··. . ··. ·...... ·· "'"• ...... '•, . .. "· : ... . '• , .... 37. 002 -.: ...... ,,, ... ····· ··· ...... , ·...... '• , ...... " :::. ... 37 ...... ··...... =· ·:. 0.015 ...... : :•:::" ... ·...... 1200 ......

200 0 0 radius [m] time [s] Water experiments

• Done with Fe_9, m= 0.0391 g • Adding 0.01ml (0.0514 g) • Losing at least 0.0034 g of water during experiment • Sonication was ineffective, and particles were quickly falling on the bottom. (m=0.1071g+-0.0005) Summary

• Those are preliminary results and they demand further investigation.

• Measurements in water indicated that heat produced by particles was enough to heat water.

• By finding how to treat power of nanoparticles simulations of heat propagation in a body could be significantly simplified.

• THANK YOU Thanks

David Miller, Xing Zhao Wright State University, Physics Department 3640 Col. Glenn Hwy., Dayton, OH 45435, USA

Zafer Turgut, Hiroyuki Kosai, Alexander Sheets, and Tyler Bixel Propulsion Directorate, AFRL, Wright-Patterson AFB, Ohio 45433, USA

Andrew Wheatley, Pavel Abdulkin, and Benjamin Knappett Cambridge University, Chemistry Department, Lensfield Road, Cambridge CB2 1EW, UK

Thomas Houlding, and Volkan Degirmenci Queen’s University Belfast, School of Chemistry & Chemical Engineering, Stranmillis Road, Belfast BT9 5AG, Northern Ireland, UK