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Functional MRI (second edition) -- 4. Basic Principles of MR Image Formation

Bloch Equation
dM⃗ dt=γM⃗ ×B⃗ +1T1(M0Mz)1T2(Mx+My)————————–1
可以分解為三個標量方程:
dMxdt=MyγBMxT2————–2
dMydt=MxγBMyT2————–3
dMzdt=(MzM0)T1—————-4
求解4得到
Mz=M0(1et/T1)———————5
求解2、3的解為
Mx=(Mx0cosωt+My0sinωt)et/T2—————6
My=(Mx0sinωt+My0cosωt)et/T2——————7
寫成
Mxy=Mx+iMy=(Mx0+iMy0)et/T2(cosωtisin

ωt)=Mxy0et/T2eiωt——————8
磁場不是均勻穩定磁場而是
B(τ)=B0+Gx(τ)x+Gy(τ)y+Gz(τ)z————–9
由於ω=γB————-10
得到
Mxy(x,y,z,t)=Mxy0(x,

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