Patent ID: 7349729

Claim:
A method of obtaining magnetic resonance signals with signal separation for at least two chemical species in a heterogeneous magnetic field using rapid gradient echo imaging, comprising the steps of: a) obtaining first magnetic resonance signals from pixels in an object having at least two chemical species using a first repetition time and a first echo time, b) obtaining at least second and third magnetic resonant signals from the pixels using second and third echo times, wherein the magnetic resonance signals at time, n=1 to N, for species, j =1 to M, having real, R, and imaginary, I, parts is given by: s ^ n = s ^ n R + i ⁢ ⁢ s ^ n I = ∑ M j = 1 ⁢ ( ρ j R ⁢ c jn - ρ j I ⁢ d jn ) + i ⁢ ∑ M j = 1 ⁢ ( ρ j R ⁢ d jn + ρ j I ⁢ c jn ) and a least squares fitting of all signals is given by: {circumflex over (ρ)}=( A T A ) −1 A T Ŝ where A is a known matrix for M species, c) determining a signal estimate for each species and for each pixel by combining all measured signals for the pixel using a linear least squares fitting directly on the signals from each pixel to decompose the chemical species, assuming a first value of field heterogeneity (ψ 0 ), d) calculating a first error to the field heterogeneity, e) repeating step c) using the first value of field heterogeneity and the error from step d), f) repeating step d) to calculate a second error to the field heterogeneity, and g) updating the value of field heterogeneity and repeating steps c) and d) until an acceptable error is calculated, wherein: A = [ c 11 - d 11 c 21 - d 21 ⋯ c M ⁢ ⁢ 1 - d M ⁢ ⁢ 1 c 12 - d 12 c 22 - d 22 ⋯ c M ⁢ ⁢ 2 - d M ⁢ ⁢ 2 ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ c 1 ⁢ ⁢ N - d 1 ⁢ ⁢ N c 2 ⁢ ⁢ N - d 2 ⁢ ⁢ N ⋯ c MN - d MN d 11 c 11 d 21 c 21 ⋯ d M ⁢ ⁢ 1 c M ⁢ ⁢ 1 d 12 c 12 d 22 c 22 ⋯ d M ⁢ ⁢ 2 c M ⁢ ⁢ 2 ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ ⋯ d 1 ⁢ ⁢ N c 1 ⁢ ⁢ N d 2 ⁢ ⁢ N c 2 ⁢ ⁢ N ⋯ d MN c MN ] where c n fw =cos(2πΔf fw t n ), d n fw =sin(2πΔf fw t n ), g n R =2πt n (−{circumflex over (ρ)} w I −{circumflex over (ρ)} f R d n −{circumflex over (ρ)} f I c n ) and g n I =2πt n ({circumflex over (ρ)} w R +{circumflex over (ρ)} f R c n −{circumflex over (ρ)} f I d n ) are the matrix elements.