(Solved): 4) (25 pts) Assume an MRI spin-echo (SE) sequence with B0=0.5T (see Figure). The following con ...

4) (25 pts) Assume an MRI spin-echo (SE) sequence with $$B_0=0.5\mathrm{T}$$ (see Figure). The following conditions are given. - In all the images TR $$=2000\mathrm{ms}$$. From (a) to (d) $$\mathrm{TE}=25\mathrm{ms},\mathrm{TE}=50\mathrm{ms}$$, $$\mathrm{TE}=100\mathrm{ms}$$, and $$\mathrm{TE}=200\mathrm{ms}$$ respectively. - $$T_1$$ (white brain matter) $$?500\mathrm{ms}$$ and $$T_1$$ (gray brain matter) $$?650\mathrm{ms}$$. - $$T_2$$ (white brain matter) $$?90\mathrm{ms}$$ and $$T_2$$ (gray brain matter) $$?100\mathrm{ms}$$. - $$T_1(\mathrm{CSF})>3000\mathrm{ms}$$ and $$T_2$$ (CSF) $$>2000\mathrm{ms}$$. - The proton density of gray matter is $$14\%$$ higher than that of white matter. The relative signal intensity can be (approximately) expressed by $$s(t)=?{\mathrm{e}}^{?\mathrm{TE}{\mathrm{T}}_2}\left[1?{\mathrm{e}}^{?{\mathrm{TRT}}_1}\right]$$. (a) First, draw (schematically) the longitudinal magnetization $$\left(M_2\right)$$ as a function of time after a $$90^{?}$$ pulse for white and gray matter and for CSF. (b) Next, draw (schematically) the transverse magnetization $$\left(M_x\right)$$ as a function of time after a $$90^{?}$$ pulse for white and gray matter and for CSF (note that TR is $$2000\mathrm{ms}$$ ). (c) Explain now on this last diagram why the contrast between CSF (cerebrospinal fluid) and surrounding white brain and brain matter varies from (a) to (d).