Method to reduce non-specific tissue heating of small animals in solenoid coils

Figures & data

Figure 1. Calculated allowable power deposition for a simulated cylinder of muscle tissue based on limits proposed by Atkinson et al. [25], with (A) varying frequency (f) and field amplitude (H) for cylinder having a radius, r = 0.15 m, and (B) varying field amplitude (H) and radius (r) of simulated tissue at a fixed frequency of 160 kHz. Blue zones display combinations that do not exceed maximum allowable limits, whereas red zones represent fields and exposures that exceed tolerance limits.

Figure 2. (A) Circuit diagram of the AMF system. (B) The four turn solenoid coil modelled using MoM. The coil inner diameter is 45 mm and coil length is 32 mm.

Figure 3. Picture of the 4-turn solenoid coil, water jacket and mouse chamber with anaesthetised mouse inside.

Table I.  Physical parameters and data used for thermal simulations.

Parameter	Symbol	Value
Thermal conductivity	kt	0.5 W/(m.K)
Density of tissue	ρt	1080 kg/m^3
Specific heat of tissue	Ct_p	3680 J/(kg.K)
Blood perfusion constants		1065 W/(m^3°C)
Arterial temperature	Tb	37°C

Table II.  AMF coil electrical properties.

Analytical		Numerical		Experimental
Inductance	Resistance	Inductance	Resistance	Inductance	Resistance
740 nH	5.4 mΩ	738 nH	4.6 mΩ	753 nH	5.97 mΩ

Table III.  AMF coil voltage, V and magnetic field, kA/m.

Voltage (peak)	Magnetic field (kA/m)
	Analytical	Numerical	Experimental
137	16.3	17.3	15.2
275	32.8	35.2	33.7
410	49.0	52.2	51.9
535	63.8	68.3	69.0
690	82.4	87.4	86.7

Figure 4. Magnetic field across the (x–z plane) in the coil in the sample volume with no water (A) and with water (B) in the jacket; Magnetic field profile along the middle of solenoid in z direction without water (C) and with water (D) for 8 kW (peak) input power to AMF coil.

Table IV.  Comparison of experimentally measured magnetic field (kA/m) with and without water jacket.

No water jacket		Water jacket		% Change
Set voltage	Magnetic field	Set voltage	Magnetic field
81	16.03	80	15.99	0.24
270	39.76	270	38.46	3.27
457	62.12	455	57.35	7.67
631	80.74	628	76.48	5.27

Figure 5. Temperature profile at the end of 1200 s of AMF exposure. (A) No external cooling. (B) Dual chamber discontinuous cooling at 35°C. (C) Dual chamber discontinuous cooling at 27°C. (D) Single chamber continuous cooling at 35°C. (E) Comparison of maximum and minimum temperatures in the domain among cases B, C and D.

Table V.  Gel phantom temperature data.

Exposure	Corrected ΔT (°C)^†
	Core (0 mm)	Edge*
Condition 1: AMF	18.7	20.5
Condition 2: AMF	11.2	11.5
Condition 3: AMF	2.4	1.1

†Values reported are the difference at each time step (1-s intervals) with initial temperature (t = 0 s), i.e. ΔT = T(t) − T(t = 0). No sham data were taken.

*Reported value represents a mean taken from two temperature probes inserted into the gel at the wall of the vessel in contra-lateral positions.

Figure 6. Comparison of net initial rate of temperature change in the gels for conditions I, II, and III.

Figure 7. Observed temporal change in temperatures of (A) individual mice at each of the three conditions (I, II, and III) with no AMF, and (B) with 20 min exposures to AMF having amplitude of 84 kA/m. Displayed are corrected (T(t)–T(0)) data obtained from each of four temperature probes (two placed s.c. in left and right thorax, one affixed to skin surface of abdomen, and one inserted into rectum.

Figure 8. Corrected temperature change as measured in the thorax (A) and rectum (B) for mouse exposed to AMF with no water, i.e. condition I (solid line), mouse exposed to AMF with water but no active cooling, i.e. condition II (dashed line), and mouse exposed to AMF with actively cooled water, i.e. condition III (dash-dot-dot). Subcutaneous thoracic temperatures were averaged for both left and right side. In all cases the temperature change for each temperature probe was calculated from measured temperatures and the total change of temperature was estimated after subtracting temperature changes obtained from sham controls.

Table VI.  Mouse temperature data.

Mouse no.	Exposure*	Mass	Initial temperature (°C)				Final temperature (°C) (ΔT = Tfinal − Tinitial)†
		(kg)	LT**	RT**	Re**	B**	LT**	RT**	Re**	B**
1	Condition III: Sham	0.021	33.7	34.8	33.7	34.6	34.4 (0.7)	35.4 (0.6)	33.9 (0.2)	35.2 (0.6)
2	Condition III: AMF	0.026	35.5	36.6	36.2	36.2	36.9 (1.4)	38.6 (2.0)	37.0 (0.8)	38.7 (2.5)
3	Condition II-Sham	0.021	33.5	34.7	33.2	33.8	30.9 (−2.6)	32.3 (−2.4)	31.1 (−2.1)	32.5 (−1.3)
4	Condition II-AMF	0.021	35.6	36.6	35.4	36.4	38.2 (2.6)	38.9 (2.3)	35.7 (0.3)	38.0 (1.6)
5	Condition I-AMF	0.021	31.9	33.6	33.7	33.6	40.1 (8.2)	41.8 (8.2)	37.6 (3.9)	40.4 (6.8)
6	Condition I-Sham	0.021	33.8	35.1	34.6	34.9	29.6 (−4.2)	30.4 (−4.7)	29.4 (−5.2)	30.4 (−4.5)

†Values in parentheses are the difference of initial and final temperatures for corresponding probes.

*Condition I, no water; Condition II, water in jacket; Condition III, water with active cooling maintained at 35°C. AMF exposure was 20 min at amplitude 86 kA/m and frequency 160 kHz.

**Placement of the fibre-optic temperature probes: LT, subcutaneous left thorax; RT, subcutaneous right thorax; Re, rectum; B, skin of abdomen.

Horsman MR, Overgarrd J. Hyperthermia: A potent enhancer of radiotherapy. Clin Oncol 2007; 19: 418–426

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