RF Physics and Dosimetry

1Units and quantities

Every electromagnetic field comprises two component fields: an electric field (E field) and a magnetic field (H field). These are inseparable companions. Where one exists, so does the other, and together they constitute the total EM field.

One mW/cm² is equivalent to 10 W/m². Dosimetry work conventionally uses mW/cm².

2Frequency and wavelength

EM radiation of all types is periodic wave motion. The number of repetitions of the waveform per second is the frequency, measured in hertz.

Wavelength is the distance a wave travels during one complete oscillation cycle: the speed of travel, normally the speed of light, divided by the frequency.

All waves are composed of at least one sine wave or frequency element. Waveforms that appear non-sinusoidal are in fact combinations of two or more sine waves at different frequencies, termed harmonics. Fourier analysis is the branch of mathematics concerned with resolving a waveform into its sinusoidal component frequencies.

In the context of RFQMR, the frequencies of concern range from approximately 1 kHz to 300 MHz.

Table 1 — Wavelength to frequency relationship

3The electric–magnetic field relationship

The relationship of electric to magnetic fields is analogous to that between voltage and current in a simple circuit. The E field corresponds to electric voltage potential; the H field corresponds to electric current.

The complete mathematical relationship involves terms expressed in four dimensions and is beyond the scope of operational documentation. Under the simple condition of wave travel through free space, it reduces to:

The similarity to Ohm's law, E = I × R, is not coincidental. Both are special-case simplifications of the more complex statements defining electromagnetic theory, reduced to workable form by Maxwell, Gauss and Ohm.

The rate of energy transfer per unit area is the product of the field strengths:

These relationships hold at distances of about two or more wavelengths from the radiating source, in the far field, where the ratio between E and H becomes the fixed constant of 377 ohms. Under those conditions power density can be determined by measuring only one field component.

Because power is the rate of energy transfer, and the squares of E and H are proportional to power, E² and H² are proportional to the energy transfer rate and to the energy absorbed by the subject. Measuring instruments therefore read out in terms of E² or H².

4Exposure limits and absorption

Electromagnetic field exposure limits for human exposure are set out in ANSI C95.1-1982 as Radio Frequency Protecting Guides (RFPG). Values for field levels are listed in terms of E², H² and equivalent power density.

These values are based on the rate of energy absorbed into the human body. The term used in the standard to describe that absorption rate is the Specific Absorption Rate (SAR). A fuller discussion of SAR measurement appears in ANSI C95 (1990).

5Propagation and antennas

Electrical energy in a wire is a special case in which the energy is guided by the wire rather than passing through it. Some energy is internal to the conductor and some external to it. When an appliance is plugged in, the power delivered does not travel through the cord; electromagnetic energy is guided by the electron activity within it. The electron movement in the wire is proportional to the strength of the wave being guided.

For DC and low-frequency AC circuits, Ohm's law is sufficient and field theory is rarely required. Electromagnetic wave theory becomes necessary as frequency climbs into the megahertz range.

An antenna is the point at which RF waves leave the guiding influence of wires and move into free and unbounded travel, or the reverse. Antennas act as coupling points between guided and free-space propagation.

Antenna effectiveness

The effectiveness of an antenna in transmitting or receiving RF depends on three factors: the conductivity of the material used, the antenna's shape, and its physical dimensions relative to the wavelength of the RF field. Optimal transmission and reception occur when antenna dimensions properly match the wavelength — the reason television whip and dipole antennas require adjustment across channels, and why roof-mounted arrays carry elements of several lengths.

6Polarisation of RF fields

Polarisation is a characteristic of radiated RF waves describing the direction and amplitude relationship of the E field vector in relation to the direction of travel. A vector is a mathematical representation of a force or other quantity in terms of both direction and strength.

Polarisation explains why walkie-talkie antennas must be aligned for best reception. Operationally it is the reason patients must be positioned on the machine in a particular manner, and the reason the RF must be focused.

Measurement

An isotropic probe is used as the receiving antenna when performing non-ionising radiation tests on the Cytotron. An isotropic probe receives electromagnetic signals regardless of polarisation or direction of travel, returning the same data whichever way it is pointed in the field.

Multipath interference

RF wave reflections caused by metal objects produce multipath interference. The reflected wave may carry a different polarisation from the original, and as the field is rotated from point to point this can have a significant interference impact on treatment results. It is therefore good practice to avoid metal objects both on the patient and in the near vicinity of the gantry.

7Field regions: near field, transition zone, far field

Certain behaviour characteristics of RF fields dominate at one distance from the radiating antenna while entirely different behaviour dominates at another. Three regions are defined as a function of distance from the source, with boundaries measured as a function of wavelength.

These regions categorise behaviours that vary even within each region, and the boundaries are approximate rules of thumb. More precise boundaries can be defined based primarily on antenna type and size, and even then authorities differ.

Far field

The region extending farther than two wavelengths from the source. Here the relationships given in section 3 apply, and combining them yields:

In the far field only the E field need be measured; power density and the value of H can be calculated from it. The far-field boundary is influenced principally by the maximum overall dimension D of the source antenna, and generally begins at a distance of 2D²/λ extending to infinity.

Transition zone

The region between near field and far field, approximately one to two wavelengths from the source. It combines characteristics of both. It may not always be necessary to measure both E and H to obtain a good approximation, but several measurements are needed to characterise the field.

Near field

The region less than one wavelength from the source. This is the region of particular importance to the Cytotron, which makes use of near-field delivery.

Here the relationship between E and H becomes very complex and measurement of both is required to determine power density. Unlike the far field, where EM waves are usually characterised by a single polarisation type, all four polarisation types may be present in the near field. Since both E and H components are absorbed by living tissue, and the relationship between them is complicated at this range, both must be measured when evaluating near-field deliveries.

The near field subdivides further. The outer boundary of the reactive near-field region is commonly taken as λ/2π, or 0.159λ, from the antenna surface. The radiative near field covers the remainder, from λ/2π out to one full wavelength.

8The reactive near field: dosimetry and hazard

In the reactive near field, very close to the antenna, the relationship between the strengths of E and H is too complex to predict. Either component may dominate at one point while the other dominates a short distance away. This makes determining true power density extremely difficult: both E and H must be measured, and a further term, the phase relationship between them, is required.

Dose computation

During dose computation the E field and H field components are measured separately, as E² and H² quantities, and each is compared individually against the Radio Frequency Protection Guides of the ANSI C95.1-1982 standard. If either component exceeds the RFPG limits, the level is considered high and the dose is altered automatically by changing parameters other than modulation, bringing the dose within safe limits.

The reactive component

In the reactive region the EM wave is not only radiated outward into space; a reactive component of the field exists in addition. Very close to the antenna, energy of an unknown amount is held back and stored near the antenna surface. In other regions power density is inversely proportional to the square of the distance from the antenna. In the immediate vicinity of the antenna, the energy level can rise dramatically with only a small additional movement towards it.

9Device parameters

Dosimetry is individualised and computed using proprietary automated algorithms combining inherent physical tumour characteristics with RF-related delivery parameters.

10Source

This reference is compiled from the Scalene Cybernetics Limited Cytotron® Training Manual, chapter "Fundamentals of Radio Frequency Signals", together with device specifications reported in Kumar R, Augustus M, Nair AR, Ebner R, Nayar GS, Kumar RV, "Quantum Magnetic Resonance Therapy: Targeting Biophysical Cancer Vulnerabilities to Effectively Treat and Palliate", Journal of Clinical & Experimental Oncology 2016; 5:2, article 1000156.

Equipment must be operated only in accordance with current manufacturer protocols. Where this reference and the manufacturer's current documentation differ, the manufacturer's documentation governs.