B. water content (WC) = 0.4 WC CSF WC GM WC WM, or WC = = mol/l.

Transcription

1 9.. A. Rlvant quation: M (TR, TE) = M ( TR /T ) TE / T M (NAA) = 38. M (cratin) = 9.6 M (cholin) = 98.4 M (watr) = 7,4 B. watr contnt (WC) =.4 WC CSF +.5 WC GM +. WC WM, or WC = = 5.4 mol/l. C.. Corrct watr intgral for diffrnc in numbr of avrags M (watr) = 64 7,4 = Normaliz all intgrals for th numbr of protons M (NAA) =.7 M (cratin) = 69.9 M (cholin) =. M (watr) = [NAA] = [watr] (M (NAA)/M (watr)) = 6.7 mm [cratin] = [watr] (M (cratin)/m (watr)) = 4.3 mm [cholin] = [watr] (M (cholin)/m (watr)) =.3 mm D. Th volum contains 4% CSF which contains ngligibl lvls of th thr mtabolits. Thrfor, th brain concntration of th thr mtabolits is.667 tims highr than calculatd undr C. 9..

2 A. R =.7 and T = ms giv M =.5M at frquncy offsts of ± 35 Hz. Using th gnral xprssion of a Gaussian xcitation profil: M ( δ ) = M scal( δ δ ) watr givs scal =.5 and 6.85 ppm at 4.7 T and 9.4 T, rspctivly. Convrting th quation for M to an xprssion for M z (i.. M z = ( M ) / ) allows th calculation of M z aftr 6 CHESS lmnts (δ αηglucos = 5.6 ppm, s Tabl.), which is givn by.7m and.887m at 4.7 T and 9.4 T, rspctivly. Thrfor, CHESS watr supprssion supprsss 8.89% and.9% of th α-h-glucos rsonanc at 4.7 T and 9.4 T, rspctivly. B. From Tabl.5 it follows that J HC = 69.8 Hz, such that th satllits appar at {4.79 and 5.64} ppm and {5.4 and 5.48} ppm at 4.7 T and 9.4 T, rspctivly. At 4.7 T: M z (4.79 ppm) =.M M z (5.6 ppm) =.7M M z (5.64 ppm) =.8M At 9.4 T: M z (5.4 ppm) =.37M M z (5.6 ppm) =.887M M z (5.48 ppm) =.9953M For a 5% incrmnt, th thortical ratio is.5 : :.5. Howvr, in th prsnc of partial supprssion, th ratio bcoms : :.37 at 4.7 T and.73 : :.56 at 9.4 T, rspctivly.

3 C. At 4.7 T, FE =.8/(.8 +.7) % = 8.6 %. At 9.4 T, FE = ( )/( ) % = 59.5 % A. Th H NMR spctrum of aspartic acid consists of thr doublts of doublts (Fig..7) making up rsonanc lins. A compltly unconstraind fit would thus rquir 48 indpndnt paramtrs (amplitud, lin width, frquncy and phas for ach rsonanc). B. Whn full prior knowldg on aspartic acid is usd, th spctral fit can b prformd with four indpndnt paramtrs, namly th amplitud, lin width, frquncy and phas of th ntir spctrum. Whn th spctrum is proprly phasd prior to th spctral fit, th numbr of indpndnt paramtrs can b rducd to thr. Th undrlying assumptions includ:. Th amplitud of aspartat-h and H3/H3 ar idntical, i.. watr supprssion did not affct th aspartat-h rsonanc.. Ionic strngth, tmpratur, ph or any othr paramtr did not lad to diffrnt lin widths or frquncis for th aspartat-h or H3/H3 rsonancs. 3. Th gnral assumption bing that all prior knowldg usd is corrct. C. Instad of 4 indpndnt paramtrs, th 3 C POCE diffrnc spctrum of aspartat rquir 5 indpndnt paramtrs for a propr spctral fit. Bsids th lin width, frquncy and phas that ar idntical for all aspartat rsonancs, th amplituds for aspartat-h and aspartat-h3/h3 nd to b indpndnt. This is bcaus aspartat-c and asparat-c3 incorporat th 3 C-labl from [- 3 C]-glucos at diffrnt rats, such that thir amplituds do not hav to b idntical pr s A.

4 . Corrct lactat and watr intgrals for T and T rlaxation: M (lactat) = M (watr) = Corrct lactat intgral for diting fficincy: M (lactat) = Corrct for numbr of avrags and numbr of protons: M (lactat) = 46.3 M (watr) = From th txt th avrag muscl watr contnt = mol/l = mol/l, which lads to a lactat concntration givn by: [lactat] = [watr] (M (lactat)/m (watr)) = 8.4 mm B. Th signal intnsity during a gnral JDE squnc is givn by: TE /T TE / T M (TE) = M [ cos( πjte) ] Th maximum signal intnsity can b found by stting th drivativ with rspct to TE to zro, i.. dm /dte =. Th optimal cho-tim can thn b solvd as TE = 5. ms. S xrcis for th xact xprssion of th optimal cho-tim. This cho-tim givs.7% mor signal than th dfault cho-tim of /J = 44 ms A proton-dnsity-wightd MR imag is proportional to th amount of watr prsnt in ach pixl. This typ of imag is acquird with a long rptition tim and a short chotim. Potntial complications aris from th prsnc of imag inhomognity that is not rlatd to th brain structurs, such as inhomognity in th RF transmit and rciv filds. Howvr, providd that RF fild inhomognity is minimizd or masurd, proton-dnsity imaging is a simpl mthod to obtain rlativ watr lvls. Comparison of intnsitis to a known concntration, such as pur watr in CSF, allows th dtrmination of absolut watr lvls.

5 9.6.. Incrasing th cho-tim during a non-spatially slctiv part of a puls squnc (glutamat + lactat). Providd that signal modulation du to scalar couplings is takn into account, this mthod will giv an accurat stimat of T. Th T rlation tims may bcom inaccurat whn th signal modulation is a dominant sourc of signal loss for th majority of cho-tims, as is likly th cas for glutamat.. Incrasing th cho-tim during a spatially slctiv part of a puls squnc (.g. PRESS, glutamat + lactat). This mthod is basd on similar argumnts as th prvious mthod, but has th additional complication that th signal intnsity is affctd by spatial displacmnt artifacts du to diffrnc in chmical shift. Whil this ffct can b taking into account on a homognous sampl, this mthod is not advisd for high-accuracy T masurmnts. 3. Incrasing th cho-tim of a Carr-Purcll-Miboom-Gill puls train (glutamat + lactat). Sinc glutamat is a strongly-coupld spin-systm, th CPMG mthod will lad to a high dgr of signal rfocusing, making this mthod idal for glutamat T masurmnts. As lactat is a wakly-coupld spin-systm, th bnfits of CPMG ovr a rgular spin-cho mthod ar somwhat rducd. Howvr, for both glutamat and lactat th CPMG is xpctd to provid a masurd T that is closr to th inhrnt T sinc ffcts of diffusion ar rfocusd to a highr dgr. 4. Incrasing th cho-tim in a spctrally slctiv puls squnc (lactat only). Sinc lactat has two wll-rsolvd rsonancs, a puls squnc can b dvisd which slctivly rfocuss on of th two rsonancs, thrby compltly inhibiting signal modulation du to scalar coupling volution A. Maximum signal would b obtaind whn th phas of all transints is idntical and qual to zro. Maximum signal loss occurs whn th signal continuously varis btwn +º

6 and º, such that th disprsiv componnt of th spctrum cancls (i.. sin(º) = sin( º)) and th intgral of th absorption spctrum is ( cos(º)) =.5% lowr than th maximum signal. B. Exprimntal duration =,4. s =,4 s. Th magntic fild drifts by.8 Hz ovr,4 s, such that th rsonanc broadns by.8 Hz. Givn that th lin width in th absnc of a magntic fild drift is 3.8 Hz, th final lin width bcoms 5.46 Hz. C. Instad of adding all transint togthr during th xprimnt, th transints ar first stord sparatly in mmory. Thn ach transint is individual phasd and frquncy corrctd bfor thy ar addd togthr. This approach works wll, providd that thr is nough signal-to-nois to phas and frquncy-corrct ach singl-transint spctrum A. Th xprssion for th stady-stat longitudinal magntization for this particular squnc is givn by: M ( ω,tr) = M z + cosωτ Not th + sign in th dnominator which aris from th fact that th 8º spin-cho puls invrts any rsidual M z following th xcitation puls. Th xprssion for M thn bcoms: M ( ω,tr,te) = M ( ) TE / T + cosωτ sin ωτ Not that th nutation angl has a frquncy dpndnc originating from th JR puls.

7 From Exrcis 9. it followd that th T and T corrctd mtabolit signals ar givn by: M (NAA) = 38. M (cratin) = 9.6 M (cholin) = 98.4 Th stady-stat mtabolit lvls obtaind with th JR spin-cho squnc (τ = /(4 5)) can thn b calculatd as: M (NAA) =.5 M (cratin) = 5. M (cholin) = 45.7 B. Bcaus of ddy-currnt-rlatd phas distortion, th JR squnc ffctivly bcoms: 9º º t 9º 8º Th xprssion for th stady-stat M thn bcoms: M ( ω,tr,te) = M ( ) TE / T + (cosωτ + π / 9) sin( ωτ + π / 9) In othr words, th additional º phas offsts shift th xcitation profil /(8τ) = Hz. Th stady-stat mtabolit lvls can thn b calculatd as: M (NAA) = 84.4 M (cratin) = 85. M (cholin) = 8.7

8 C. Th mtabolit and watr intnsitis corrctd for T, T and JR-rlatd signal loss ar givn by: M (NAA) = 5.4 M (cratin) = 3. M (cholin) = 85. M (watr) = 8, Corrct watr intgral for diffrnc in numbr of avrags M (watr) = Normaliz all intgrals for th numbr of protons M (NAA) = 5. M (cratin) = 4. M (cholin) = 9.4 M (watr) =.6 +5 Finally: [NAA] = [watr] (M (NAA)/M (watr)) = 7.7 mm [cratin] = [watr] (M (cratin)/m (watr)) = 6.3 mm [cholin] = [watr] (M (cholin)/m (watr)) =.46 mm