NMR/MRI Blood Flow Magnetization Equation in the Rotating Frame of Reference-Part I
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American Scientific Publishers
Abstract
Description
This paper describes thoroughly the need and the method of deriving the first of its kind the NMR/MRI blood
flow magnetization (y component) equation in the rotating frame when rf B1 field is applied along laboratory X
direction.
��
v ·� + �
�t
�
1
�B1�x� t�
�
v ·� + �
�t
+ 1
T2
�
+ 1
�B1�x� t�T1
�
v ·� + �
�t
+ 1
T2
+�2B2
1�x� t�T1
��
My
= Mo
T1
where
v ·� = vx
�
�x
+vy
�
�y
vx and vy are the components of blood flow velocity along the x and y directions of the rotating frame in
an NMR experiment. The equation is expected to serve as the mother equation for accurate non invasive
blood flow quantification through all NMR/MRI experiments. It is shown how Awojyogbe’s equation of blood
flow magnetization can be obtained from above equation under assumption of constant B1 field and vy
= 0.
The method of deriving the equation can be applied to modify Bloch Torey Diffusion MRI equation to include
relaxation times and flow and also to derive the NMR/MRI spin flow magnetization equation in the laboratory
frame of reference. The derivation of the corresponding equation for magnetization of flowing blood spins in the
laboratory frame of reference will be discussed in a separate paper.
Keywords
Q Science (General), QC Physics