¹²⁹Xe frequency calculator

Hyperpolarized ¹²⁹Xe lung MRI. Predicts the gas-phase ¹²⁹Xe frequency from the session's ¹H water frequency, then places the carrier on the gas, membrane (tissue/plasma) or RBC resonance. Shifts are in ppm relative to xenon gas (0 ppm).

Inputs

¹H water frequency from the protocol (MHz)

Ratio f(¹²⁹Xe gas) / f(¹H water)

Default from γ/2π = 11.777 MHz/T (Xe gas) and 42.576 MHz/T (water ¹H), good to about ±100 ppm. Calibrate it below from a measured gas frequency.

Target ¹²⁹Xe chemical shift for the carrier (ppm from gas)

Enter this ¹²⁹Xe frequency

—MHz

Where resonances will fall

Resonance	ppm	Offset from carrier (Hz)

Dissolved-phase shifts vary with field, oxygenation and subject (RBC roughly 216–222 ppm, membrane 196–199 ppm). Use the spectroscopy calibration from each session where you have it.

Calibrate from a measured gas frequency

¹H water frequency that session (MHz)

Measured ¹²⁹Xe gas frequency (MHz)

Ratio:—

Check an existing protocol

¹²⁹Xe frequency already in the protocol (MHz)

Carrier sits at

—ppm from gas

Formula and checks

f_gas(¹²⁹Xe) = f(¹H water) × R
f(¹²⁹Xe) = f_gas × (1 + δ_target·10⁻⁶)

R depends on how the gas reference is defined (low-pressure gas in the lungs sits a fraction of a ppm off the zero-density value) and on the water ¹H reference. 100 ppm of error in R moves the carrier by about 3.4 kHz at 2.89 T, so calibrate R from a measured gas frequency (a short gas-phase spectrum or the frequency adjustment) and keep that value for the study. Recompute every session: the ¹H frequency drifts and the ¹²⁹Xe frequency is a fixed number in the protocol.