One way to determine nanoparticles' temperature is by measuring their Brownian relaxation time, a metric that depends directly on the temperature. This can be achieved via magnetic spectroscopy of nanoparticle Brownian motion (MSB), a technique that uses an oscillating magnetic field to excite particles and simultaneously measures how they react. Their behaviour indicates the conditions of their environment and thus properties like temperature can be inferred. The exciting possibility is that the oscillating magnetic field can be used both to selectively heat tissue in therapies like hyperthermia and monitor temperature rises using MSB.

In a previously reported MSB method, measurements were calibrated by varying the amplitude of the applied magnetic field. Now, researchers from Dartmouth College (Hanover, NH) have come up with a new approach: varying the frequency of the applied field to measure the relaxation time. They demonstrate that this "frequency sweep" method is more accurate than the "amplitude sweep" approach at higher frequencies (Phys. Med. Biol. 59 1109).

"We had a method of measuring the temperature at low frequencies, but it is important to measure the temperature for applications that use higher frequencies, and we showed it could be done," said senior author John Weaver. "The frequency sweep method of measuring the relaxation time was developed previously – it only remained to apply this method to access the temperature."

Experimental accuracy

The MSB method exploits the fact that MNP magnetization is dependent upon the product of oscillation frequency and relaxation time. The relaxation time can therefore be determined experimentally by measuring the nanoparticle magnetization induced by an alternating magnetic field applied at various frequencies. The method could be implemented clinically using apparatus similar to, but less complex than, the scanners current employed for magnetic particle imaging.

For this study, research associate Irina Perreard and colleagues applied oscillating fields with frequencies of 290, 510, 755, 1050, 1270, 1890 and 2110 Hz to the MNPs and measured the changes in nanoparticle magnetization using a solenoid pickup coil. They recorded MNP spectra at temperatures from 21.5–50 °C, including normal body temperatures (37 °C, 39.89 °C) and common hyperthermia treatment temperatures (42, 45 °C).

The researchers generated a calibration curve using measurements (the ratio of the 5th to the 3rd harmonic) of reference MNPs at 37 °C. To determine an unknown temperature, measured data can be shifted back onto this calibration curve by a scaling factor, which represents the change in relaxation time. Comparisons of relaxation times calculated from measured ratios with those computed using Einstein's theoretical formulation for Brownian relaxation time showed a mean discrepancy of 2.53%.

The team then used the calculated relaxation times to estimate sample temperatures. Comparing MSB temperature estimates with thermometer readouts (taken 2–3 s prior to MSB data collection) revealed a mean error of 1.15%, corresponding to an accuracy of 0.42 °C.

Frequency sweep advantages

To assess the potential advantages of the frequency sweep approach, the researchers compared the above results with data recorded using the amplitude sweep method. They measured amplitude sweeps (over 5–15 mT) at frequencies of 290, 1050 and 2110 Hz and MNP temperatures of 21.5, 30, 35 and 45 °C, with 21.5 °C as the reference point for computing scaling factors. Mean error values increased with frequency, from 1.847% at 290 Hz to 3.501% at 2100 Hz.

In contrast, dividing the frequency sweep data into lower (290–1050 Hz) and higher (1050–2110 Hz) frequency ranges revealed that the mean error for the higher range (0.876%) was roughly half that of the lower range (1.721%).

Finally, the researchers performed simulations to validate the two methods further. For the amplitude-based method, they considered a low range of field values (1–2 mT) and frequency values of 20, 100, 200 and 1000 Hz. They observed a significant increase in mean error in temperature estimate with increasing frequency, from 0.128% at 20 Hz to 435% at 1000 Hz.

For the frequency sweep method, they examined four frequency intervals (290–2100, 2100–3000, 3000–4000 and 4000–5000 Hz) using an applied field amplitude of 50 mT. Results showed that the method gained accuracy with an increase in frequency range, with mean error decreasing from 0.093% in the lowest interval to 0.016% for the highest.

These findings are potentially important for monitoring of MNP-based thermal therapies, which use kilohertz frequencies. "The sensing method should still work at these frequencies, but this has not been experimentally verified," co-author Daniel Reeves told medicalphysicsweb. "We are now addressing whether it is possible to measure nanoparticle temperatures at higher frequencies, and have recently developed a new apparatus that may be able to do this concurrently with the hyperthermia apparatus (J. Phys. D: Appl. Phys. 47 045002)."

Related stories

• Particle-loaded blood cells enhance MPI
• Magnetic particle imaging: moving ahead
• Nano update: detect, image, treat
• Nanoparticles: image, target, treat