Comparison of TurboFLASH- and Spinecho-R1 measurements of FeMRI-Gel-Phantoms for Verification of 3D-dose Distributions

ORIGINALARBEIT

Comparison of TurboFLASH- and Spinecho-R1 measurements of FeMRI-Gel-Phantoms for Verification of 3D-dose Distributions A. W. Hartlep, M. Bock, F. Oberdorfer, L. R. Schad Deutsches Krebsforschungszentrum Heidelberg (DKFZ)

Ab tract

Recently, MR-imaging techniques have been developed to quantify radiation doses with use of Fricke-gels. Fricke-gel-dosimetry requires a precise measurement of longitudinal relaxation rates R I . In this study two MR-methods for Rrdetennination of irradiated Fricke-geLs were compared using a spinecho- and a TurboFLASH-technique. R I measurements were repeatedly performed in calibration viaLs and a Fricke-gel gLassphantom which wa irradiated by a bremsstrahl-spectrum of 15 MeVeLectrons of a Linear accelerator. Measured dose distributions in the phantom were compared with pre-caLculated lreatment pLanning dose distributions. The gel was irradiated with a maximumdose of 30 Gy. An average uncerlaint) of Less than 2.5 Gy (TurboFLASH) and 10.4 Gy (spinecho) wa measured at a spatiaL resolution of 2 x 2 x 6 mm3 (TurboFLASH) and 1 xl x6mm3 (spinecho). The reproducibility and the precision of these technique were determined. Keywords: FeMRI Fricke-gel, MR-do imetry, TurboFLASH treatment planning

Introduction [n order to minimize or avoid the side effects of irradiation in tereotactic radio surgery, like radiation damage of healthy ti sue or recidive as a con equence of surviving tumour cells, especially when single high do e irradiation is performed, preci e locali ation and verification of the target volume is an indi pen able prerequi ite. Fricke-gel-dosim try (FeMRI) offer an elegant way to measure radiation doses in complex 3D-distributions u ed in stereotactic radiation therapy. FeMRI is based on the radiation induced oxidation of Fe2+_ to Fe3 +-ions that depend linearly on the absorbed radiation dose [I). l[ an aqueou Fricke- olution is infused in a gelatine matrix, a three-dimen ional dose di tribution can be detected by mea uring the spatial concentration of feme ion. To measure the Fe3+-ion concentration Gore et aI. introduced a MR-technique which i based on the effect of different pin-lattice relaxation rate (R I) of proton in presence of ferroll or ferric ion [2). To evaluate the clinical u e of the FeMRI-Gel-dosimetry both the reproducibility and the precision of thi method have to be tudied. The characteristic of different Frickegels were investigated in numerous studie [3-9]. Due to the trong dependency of the delivered do e on the relaxation rate R 1 of the gel a crucial point of FeMRI do imetry is the R I measurement of an irradiated gel. In our tudy we present two different R I mea urement technique ,a pinecho (SE) and a TurboFLASH (TFL) method.

210

U ing the pinecho technique two SE-image with different repetition time TR were acquired and the value of R. wa calculated from the quotient of the ignal intensity at each pixel. For the TurboFLASH-method 25 TurboFLASHimages with different inversion times TI were u ed to determine the relaxation rate R 1•

Materials and Methods The Fricke-gel u ed in thi study wa gelatine based and related to a tandard Fricke-gel inve tigated in former studie [3]. It consisted of 7.5 % gelatine by weight and an ionic olution compo ed of aCI (1 mM), (NH 4hFe(S04h (1 mM) and H 2S04 (0.05 M) relative to the total volume. The pH-level wa found (Q be about one and the den ity of the FeMRl gel wa 1.005 g/cm. At ro m temperature the gel needed four hours to get tiff. Then it wa irradiated at a MEVATRO KD2™ (Siemens AG, Erlangen, Germany) linear accelerator. The energy distribution of the produced photon corre ponded to a brem trahlung pectrum of electrons accelerated up to 15 MeY. The average photon energy wa about 3 MeY. Immediately after irradiation the R 1 value were meaured at a MAGNETOM 63/64 SPTM (Siemen AG, Erlangen, Germany) whole-body MR-scanner at J.5 T u ing the standard head coil. Two different imaging pul e equence were u ed: a conventional pinecho (SE)- and a TurboFLASH (TFL)- equence.

Z. Med. Phys. 8 (1998) 210-216

Comparison 01 TurboFLASH· and Spinecho-R, measurements 01 FeMRI·Gel·Phanloms lor Verification of 3D·dose Distributions

Spinecho-Melhod.· For the SE-method two pictures with different r petition time TR 1 and TR z were taken. The echo time (TE) for both images wa fixed to TE = 20 ms. For TE« TR the SE-signal SSE depend on the repetitiontime TR, the longitudinal relaxation rate R I and the transversal relaxation rate Rz [10]:

Ss£ = Mo(l - e-TR.RI) e-T£·R,-.

Here, Mo denotes the Boltzmann equilibrium magneti ation. All other constant factors, which are introduced by the amplifier chain are emitted. The RI-va]ue of each pixel was cakuJated from the quotient Q of the signal intensity of both image:

(2)

(1)

0.5,---------;::::=======;,

--

'.0 Tr=========:;--------:----:-:-:;--, 0.8

j

I l - - - - - - - - - - - '..........

0.6

.!2. Ii

0'

R'M ".7 S'::"

TR,=O.2s, TR,= 0.9 S .... TR, = 0.7 s : TR, = 2.9 s - - TR, = 1.3 s : TR, = 3.5 s

0.4

/'

./

./

./

..- .../

..... ..- ..-

..-

...-,-..-.-- I

0.4

...1- .' .. '

I I

j

.!2.

.....

-----

__

.......

TR , =0.2s, TR,=0.9s •... TR , = 0.7 s , TR, = 2.9 s - - TR, = 1,3 s , TR, = 3.5 s

.......

.......

0.3

,,

..

o'" 0.2

Ii

,.. '" ..

, .... '-

. . . . , ........ '1-. ..............

0.2

a

0.1

0.0 +-------.~------,-----.---+---__i 0.0

0.5

1.0

1.5

2.0

R, [l/s)

b

~--

L---------------ir--4

:

0.0 +-----"""T'"-~--____r----~.---+---__i 0.0 0.5

1.5

1.0

R, [lis)

2.0

Figure I (a) The ratio Q(R,) is plotted against the longitudinal relaxation rate R,. (b) To determine the strongest change of Q(R,) in the range of the expected Rrvalue of the measured tissue, R'M = 1.7 s-'. the slope oQf()R, is plotted against R, for three different combinations of TR, and TR z. The TR combination with the highest slope at the expected Rrvalue leads TR 1= 0.7 sand TR z = 2.9 s which wa used for the R, measurements. 500

3.0

'T"""------------------,

=0,034 ± 0002 Gy-'s"

r"TA.

= 0.98

= 0.033 ± 0.008 Gy-1S·'

r'SE

= 0.89

b TFL

..., " .!.

1:

b SE

400

2.5 300

10

i,l:

meal1 errors

'iii l:

G>

.~

'iii

200

T, = 949.9 ms ± 2.9 ms B = 157.4· ± 1.6·

l:

C>

'iii

100

0 0

1000

2000

2.0

measured values at 5 Gy

. . I'< •.

Spil1echo

3-parameler·fi1

_

TurboFLASH

3000

4000

TI [ms]

Figure 2 Example of calculating T, from 25 TurboFLASHimages acquired with different time delays Tl. This plot shows the measured values of a calibration vial irradiated with 5 Gy. The total value of the signal is plotted against the inversion delay Tl. The relaxation time T I is calculatedjrom the fit to T I = (949.9 ± 2.9)ms.

o

5

10

15 dose [Gy)

20

25

30

Figure 3 Comparison. of R, measurements using SE- and TFL-images. The error bars indicate the standard deviations of six measurements. The slope b of the regression line gives the sensitivity of the Fricke-gel.

211

Comparison of TurboFLASH· and Spinecho·R, measurements of FeMRI·Gel·Phanloms for Verification of 3D-dose Distributions

Figure 4 (a) Depth-do e of water and Fricke-gel. The relative dose is plotted again t the depth. Error bars indicate one tandard deviation. (b) Dose-image of the irradiated Fricke-gel. The dose increases in relation to The brightness (black = 0 Gy, whiTe = 30 Gy). The depth-dose was measured along The dotted line.

100

~ L

80

Q)

o

Vl

..e 't' Q)

60

>

IV

40

10

a

20

30 40 50 depth [mm]

60

70 b

Q i a monotonous function of R I _ Since Eq. (2) cannot be

olved anaJytically, a numerical technique wa implemented. A field of lew of 250 mm-, a matrix ize of 2562 pixel and a lice thickne of 6 mm lead to a spalial olution of I x l x6mm 3 . TurboFLASH-Method: The TurboFLASH- equence u cd in thi tudy consists of a 1800 -inver ion pulse to prepare the pin y tern, followed by a train of low flip angle excitation pul e. after a variable time delay TI [11]. Central kpace line are acquired fir t ( entric phase encoding) to provide a trong TI-contra t [12]. A uming the image contra t i clo e to that created by the preparation, the ignal inten ity for each pixel i. given by:

with

An = Mo sin ae- TE/Tj.

(3)

The factor N RF = (I-co 8)/2 < I de cribe the effect of an incomplete inver ion. The readout flip angle a wa set to a = 12° and an echo time of TE = 3 ms wa u ed. The repetition time TR was 7.6 m . A spatial olution of 2 x 2 x 6 mm wa achieved by u ing a field of view of 250 mm 2 a matrix ize of 1282 pixel and a slice thicknes of 6 mm. By acquiring image with different inver ion delay TI, a variation of the RI-contra t i introduced that aJJows the determination of the parameter R I, Average dose dependence: The gel wa filled in twelve calibration vial of 20 cm each and irradiated with discrete do e from 0 to 30Gy in tep of 5 Gy in an open field of 40 x 40 cm 2 . Do e value were verified with a calibrated conventional ion chamber (PTW Freiburg, Germany). The longitudinal relaxation rate R 1 wa m asured using both the spinecho- and TurboFLASH-sequence. For both techniques a calibration curve wa calculated. The do e value D of the calibration vial were plotted against the m a ured RI-va-

212

lues. The linear fit of the value. gives the caJibration equation of the Fricke-gel:

(4) where the lope b de 'cribe the sen itivity of the gel. This measurement was repeated with six gel to determine the reproducibility either of the gel production and the R 1 measurement. . Water equivalence: To verify the predicted water equivalence of the Fricke-gel [14] a do e-depth-curve of the gel wa mea ured and compared to the do e-deplh-curve of water. A glass vial of I J cm diameter and 14 cm height filled with Fricke-gel was in-adiated in a quadratic field of 3 x 3 cm 2 . The source to urface distance was 100 em. Glass phantom: To compare the TFL- and the SE-technique a round gla tube (0 = l60 mm) wa filled with Frickegel and irradiated coplanar from four directions with a ingJe dose of 8 Gy each. A Tungsten collimator (0 =30 mm) was used to collimate the beam. The dose measurement wa, calibrated u ing the same calibration vials as above. Do e images (Fig. 5) were calculated from TFL- and SE-R)image u ing the calibration equations (Tab. I). Four dose pr file were extracted perp ndicular to the four beams and acro the i ocenter. The e profile were fit to a Gau sian curve to compare the precision of the two method (Fig. 6). Do e gradients at the edge of the beams as well a the beam-width and the ize of the central region were measured. 3D-dose distribution: To demonstrate the ability of the Fricke-gel to represent a 3-dimen ional dO'e di tribution a reali tic 3D-treatment planning of a brain-tumour patient wa u ed. CT-image of the patient were u ed to calculate a uitable do e distribution that matches the tumour. The data of the calculated di tribution was tran, ferred to th linear accelerator and a Fricke-gel head phantom was irradiated. Thi phantom, a hollow headphone holder in the shape of a human skull (0= 16cm, volume: 3.51) wa filled with

Comparison of TurboFlASH- and Spinecho-R, measurements of FeMRI-Gel-Phantoms for Verification of 3D-dose Distributions

Figure 5 Dose images of the irradiated glass phantom using the TurboFLASH (left) - and the spinecho-technique (right). The arrows indicate the beam directions. Above the phantom are twelve calibration vials that were irradiated with discrete doses. The grey vaLues indicate the dose (black =0 Gy, white =25 Gy). Figure 6 Dose profiles caLculated from the TFL (up) and SE (down) dose images oj Fig. 5. The profiles were taken along the dotted lines. The graph 011 the left show the profiles of the isocen/er, the graphs 0/'1 the right those of the beams. Ea h beam profiLe is the average offour profiles along the Jour beam. Error bars indicate the standard deviation ofthefour beam profiLes.

25

FWHM = .30.0±0.4 mm

~20 >-

<:>

~15

'"o

"

10

5 O'---'--~-'--~--'-~--'-~--'-->O=

.30

r--.-~-""-~-,-~--,-~-"'---'

25

FWHM

=

.34.6±0.8 mm

~20 ><:>

--: 15 '"o "t> 10

5 -40

-20

0 20 position [mm]

40

-.30

-20

-10 0 10 position [mm]

20

.30

Table J Measured vaLues of the fit-equation R, = a + b· D. The "caLibration "-Line contains the average values of six calibra/ion measurements, the "phantom"-line contains the values of the calibration measurement for the phantom. Method

Purpose

a [5-1]

b [5- 1Gy-1j

SE SE

calibration

1.4 ± 0.3

0.033 ± 0.008

phantom

1.7±0.1

0.035 ± 0.007

0.86

TFL

calibration

1.3

0.034 ± 0.002

0.98 ± 0.05

TFL

phantom

± 0.3

1.8±0.1

0.034

± 0.002

f 0.89

± 0.004 0.99

213

Comparison of TurboFLASH- and Spinecho-R, measurements of FeMRI-Gel-Phantoms for Verification of 3D-dose Distributions

35 - , - - - - - - - - - - - - - - - ,

30

-

.' - treatment-planning measured dose

25

>: 20 ~

~ 15 o 10

'"0

5 O-+-...!-.:...'--!--+-~-,---r----,-,-.!..I.~

o

~

~

W

00

1001~1~1W

distance [mm]

Figure 7 Comparison between CT-images of the treatment planning (left) and dose images calculated from a SE-measurement of an irradiated Fricke-gel head phantom (middle). The calculated dose di tribution is shown as isodose lines in the CT-images. These lines indicate the 20% (ourer line) and llO% (inner line) level of the maximum dose. A do e profile (right) is acquired along the dolled line oj the CT- and MR-image. The treatment planning (dolled line) is compared to the measured dose (straiglztline)

Fricke-gel to mimic th patient shead. lmmediately after irradiation pinecho image with repetition time of TR 1 = 584 m and TR 2 = 3000 ms were acquired. 2 x24 sagittal . lice with a thickne of 3 mm and a field of view of 250 mm 2 were made. From thi 3D data ser tran ver al and coronal lice were calculated and compared to the CTimage. of the treatment planning. Do e image were calculated u ing the reference data obtained from calibration vial in the images. A an exampl a coronal slice of a CTimage i compared with a MR-do e image of the same po'ition. A dose profile of this CT-image wa sampled and compared to a profile of the MR-dose image (Fig. 7). For calculation a work tation (Digital Alpha ration 200 4/166, Digital Equipment C IlJoration Maynard, Mas achuett , USA) and a VMS- (OPE -VMS 7.0, DEC Mass.. USA) based home-built oftware was u ed.

Results Spinecho-Melhod: To optimise the en itivity of the SEmethod a table of R.-values for three different pair ofTR I and TR 2 are calculated (Fig. la). The be t accuracy of thi meth d i achieved, if the change in Q(Rd are highest in the region of the expected R.-value . Therefore the lope aQ/aR I (Fig. I b) wa calculated for the e pair of TR I and TR 2 and compared for a ertain RIM= 1.7 -I that i known from former studie [3]. A suitable combination of repetition time was TR I = 700 ms and TR2 = 2900 m _ TurboFLASH-Method: 25 image with different inversion time TI between TI = 100 m and TI = 4000 ms were measured. The RI-value wa calculated for each point from a 3-paramerer fit of Eq. (3) using a non-linear least squares algorithm of Marquardt-Lev nberg [13) Fig. 2).

214

Error determination: Determining the accuracy of the measured do e two different uncertaintie may occur. The calibration error 6.Db i a re ult of the RI-determination of the calibration ial. For average calibration parameter typical 6.Db -value are between 6.D b ,IOC) = 0.5 Oy and 6.D1J.3ocy = 6_8 Oy which yields a mean deviation 6.Db of about 4%. The uncertainty 6.D R1 is a consequence of the R 1 measurement of the irradiated gel-phantom. Th relaxation rate i mea ured at a certain region-of-intere t (RO!) and the do e of thi ROI i calculated from the calibration equation. An average valu of 6.D R1 is in the range of SOy. Thu th total error 6.D= 6.D/ + 6.D R/)1I2 f the dose determination i trongly dose depend nl. Average dose dependence: In the 2 x 6 calibration vial the maximum rror in the dose application wa Ie s than I % due to the calibration of the ion chamber. The MRl-R I mea urements were made by u ing both a SE- and a TurboFLASH-. equence (Fig. 3). An average linear relation RI(O) for each method was calculated from ix single mea urement Tab. 1). The error. are calculated a the um of the standard deviations from the single fit error. The average do. e en itivity u ing the SE- (TFL)-method was bs£

= 0.033 Oy-I

-I

0_0080y-I-1

with a relative en-or 6.b of about 23 % (4.7 %). ·or an applied dose of 300y this lead to a maximum do e error of 6.Db ./I/<1.,=6,8Gy (1.60y)_ The maximum RI-error in this study wa 0.4% (0.1 %) relating to 0.265- 1 (0.13 -I). Th

Comparison of TurboFLASH- and Spinecho-R, measurements of FeMRI-Gel-Phantoms for Verification of 3D-dose Distributions

resulting maximum do e error was 6.D RJ ,mQx=7.9Gy (3.7 Gy). The maximum total do e error of the irradiated gel-phantom at 30Gy was 6.D300)'= LO.4Gy (2.5 Gy). The con tant a in Eq. (4) differs between 0.8,,-1 and 1.8 S-I with an average value of 1.3 S-I. The calcuJation time for a do e image is about 30 min for the TFL-technique and about 1 min for tbe SE-method. Water equivalence: The dose was measured with the TFL-method and relative dose were plotted against the depth in the gel (Fig. 4). The average dose difference of water and Fricke-gel was about 3 % where the main difference is found at small depths of 0 to 15 mm. For depth. larger tban 20 rum the difference is about 1 %. The main difference between water and Fricke-gel was found at small depths lower than 20 mm. Glass phantom: In the glas phantom the dose maximum at the isocenter and the four beams are vi ible as bright areas (Fig. 5). The average dose gradient measured along the dotted lines ( ig. 5), wa LO Gy/mm at the i ocenter and 1.3 Gy/mm in the bam. The full width f half maximum (FWHM) wa 30.0 ± 0.4 mOl (TFL) and 34.6 ± 0.8 mOl (SE) at the beam and 43.5 mm (TFL) and 54.0 mm (SE) in the isocenter. The theoretical values of the FWHM taken from the calibration curve of the collimator were 30 rum (beam) and 45 mm isocenter). This leads to an average deviation of the width of tbe dose distribution of 1 % (TFL) or 15 % (SE) at the beams and 3.3 ~ (TFL) or 20 ~ (SE) at the isocenter. 3D-dose distribution: The mea ured do e gradient of 0.9 Gy/mm i ocenter) and 2.0 Gy/mm (beam) and the height and width of the profiles were in accordance to the value of the treatment planning (0.8 Gy/mm, 1.9 Gy/mm). The average deviation in the FWHM was about 15 % and 5 % in the maximum height. The average do e deviation was about 4 Gy and decrea e with increasing dose and the average noi e was 5 Gy according to the deviations of the S -method. Wid1in the e uncertainty limit do e profiles of the MR-images match well with planned profile (Fig. 7).

Discussion FeMRI-do imtery is able to confirm spatial dose distribution,. Different gel how trong cbanges in the constant a of Eq. (4). This constant is strongly dependent on the starting concentration of Fe3 +-ions in the gel [7]. Thu it i ensitive to the production of the gel - e pecially to the accuracy of weighing ( H 4 hFe(S04h and the temperature whi h control the intrinsic oxidation of Fe 2+ [9]. The oxidation is proportional to the amount of oxygen in the gel and decrea es with increasing temperature. Additionally the age of the gel influences thi intercept. Although these change do not affect the dose determination a new calibration is required for every gel and leads to a general limitation of the quantitative reproducibility of different FeMRrgels.

A sensitivity of the Fricke-Gel of about 0.003 -I Gy-I reported by other authors [3 6] could be reproduced here. The sensitivity of the Fricke-gel shows an acceptable reproducibility for MR-measurements made in the fir t five hour after irradiation. Even if a Fricke-gel consisting of 5 % by weight gelatine is more sensitive [6], for large phantoms like skull-shaped head-phantoms 7.5 % gelatine hould be used to get sufficient mechanical tability. Like other authors [8 14] it could be shown that the Fricke-gel can be assumed to be a tissue-equivalent dosimeter. The comparison of the depth-doses-curves of water and Fricke-gel shows a small ystematic deviation at low depths. Tbis deviation can be attributed to the higher average atomic weight of Fricke-gel in relation to water (about 1 % by weight of S Na, Fe and Cl) and thus to the more effective production of secondary electrons at lower deptbs. Taking an average standard deviation of 5 % into account the difference between water and Fricke-gel can be neglected. The comparison of the SE- and the TFL-method shows differences in the precision of dose determination as well as in the spatial resolution. Compared to SE-image T Limages show much more artefact becau e of the non-ideal point-spread-function (PSF). The PS describes the amount of inten ity cattered from a point-shaped object to the neighbouring pixel . An increase of matrix size in TFL-imaging aLways implies a decrease of the PSF. Consequently, the patial resolution of dose images supplied by the SEmethod prevail the TFL-method. The profiles of the SE-dose image how more 'cattering than those of the TFL-dose images. This is a consequence of calculating R 1 from only two point of the relaxation curve, whereas the TFL-method u es 25 point. Additionally the SE-ratio-method is very sensitive to small deviations of the 90°-excitation flip angle. Eqs. (1-2) are valid for 90°-pulses but the accuracy in applying a precise 90 0 RF-excitation is limited which j followed by a strong cattering of the measured RI-values. We could show that the precision of dose-calcuJation could be increased more than fOUf time by u ing the TFL-method compared to the SEtechnique. Due to strong scattering and thus to dose errors of the SE-method, for quantitative dose determinations the TFL-method hould b pref rred. The advantage of this technique is the exact scan of the relaxation curve compared to the scanning time (25 points in six minutes) which increases the precision of R I-determination. The limitation i the non-ideal PSF that reduce the patial resolution. It wa shown that TFL- and SE-techniques have different limitations (Tab. 2). The TFL-method is suitable for quantitative measurements with an high do e re olution. The SEmethod with an increased spatial re olution should be u ed for qualitative mea urements. A general problem of FeMRI is the presence of different absorption coefficients in a buman brain (e. g. air in the sinus frontalis) that are not considered in phantom experiments and lead to mall dose deviations.

215

Comparison of TurboFLASH- and Spinecho-R, measurements of FeMRI·Gel·Phantoms for Verification of 3D-
Table 2 Comparison of TurboFJ.ASH and spinecho dose measurement techniques. Spin·Echo

TurboFLASH

Spatial resolution

1 xl x6mm 3

2x2x6mm 3

Dose resolution*

<10AGy

<2.5Gy

Purpose

qualitative

quantitative

Measurement time

-5min

-lOmin

Dose image calculation time

-1 min

-30min

• maximum delivered dose: 30 Gy

However, FeMRI is an interesting tool to verify complex dose distributions in 3D-imaging. In future tudies the advantages of the TFL- and SE-method should be combined and an imaging pulse sequence should be developed that allows calculating dose images with an sufficient spatial resolution and accuracy. To decrease the measurement time a saturation recovery could be used. The PSF could optimised by using a segmentation technique as well as a k-space-filter. FeMRI combined with TurboFLASH-R1·determinalion gives an opportunity for high re olution 3D-dosimetry.

Reference [I] Fricke. H.: Morse, S.: The chemical action of roentgen rays on dilute ferrous sulphate solutions as a measure of dose. Am. J. Roemgenol. Radium Therapy uel. Med. 18 (1927) 430-432 [2] Gore, J. C.: Kang. Y. S.: SchulZ, R. J.: Measurement of radiation dose distribmions by nuclear magnetic resonance (NMR) imaging. Phys.Mcd.Biol. 29 (10) (1984) 1189-1197 [3] Chan, M. F.: Ayyangar. K. M.: Confirmation of target localization and dosimetry for 3D conformal radiotherapy treatment planning by MR imaging of a ferrous sulphate gel head phantom. Med.Phys. 22 (7) (1995) 1l7l-1175

216

(4) Hazle, J. D.; Hefner, L.; Nyerick, C. E.; Wilson, L.; Boyer, A.L.: Dose-response characteristic 1'0 a ferrous-sulphate-doped gelatine system for determining radiation absorbed do e di lribution by magnetic resonance imaging (FeMRI). Phys.Med.Biol. 36 (8) (1991) 1117-1125 [5] Ols on, L. E.; Petersson, S.; Ahlgren. L.; Mallsson, S.: Ferrous sulphate gel for determination of absorbed do e distribution using MRJ technique: basic studies. Phys.Med.Biol. 34 (I) (1989) 43-52 [6] Obson, L. E.: Radiation dosimetry using magnetic resonance imaging Department of Radiation Physics, Malmo, Lund University. Diss., (1991) [7) Podgorsak, M. B.; Schreiner, L. J.: uclear magnetic relaxation characterization of irradiated Fricke olution. Mcd.Pbys. 19 (I) 1992) 87-95 [8] Prasad, P. v.; Nalcioglu, 0.; Rabbani, B.: Measurement of three-dimensional radiation dose distributions u ing MRJ. Rad. Res. 128 (1991) 1-13 r9] Schulz, R.J.; Maryan ki, M.J.; lbbott, G. .; Bond. J. E.: Assessment of the accuracy of stereotactic rddiosurgery using Fricke-infu ed gel and MRI. Med.Phys. 20 (6) (1993) 1731-1734 (10) Schad, L. R.: Brix, G.; Zuna, I.. Harle, w.; Lorenz, W.J.: Semmler, w.: Mulliexponential Proton Spin-Spin Relaxation in MR Imaging of Human Brain Tumors. J. Comput. Assist. Tomogr. 13 (4) (1989) 577-587 [II] Haase, A.; Mallhaei, D.; Bartkowski, R.; Diihmke, E.; LeibfrilZ, D.: Inversion recovery snapshot FLASH MR imaging. J. Compul. Assist. Tomogr. 13 (6) 1990) 1036 [12] BIUmI. S.; Schad. L. R.; Stepanow, B.; Lorenz, W.J.: Spin-lattice relaxarion time measurement by means of a TurboFLASH technique. Magn.Reson.Med. 30 (1993) 289-295 [13] Marquardt, D. W.: An algorithm for least-squares estimation of non linear parameters. J.Soc.lndust.Appl.Math. 11 (1963) 432 [14] Chan, M.F.; Ayyangar, K.M.: Verification of water equivalence of FeMRI gels using MOnle Carlo simulation. Med.Pbys. 22 (4) (1995) 475-478 Eingegangen am 27.10.1997: zum Druck angenommen am 24.08.1998. Korrespondenzanschrifl: Andreas W. Hartlep Forschungsschwerpunkt Radiologisehe Diagnostik und Therapie Deutsches Krebsforschungszcntrum Heidelberg (DKFZ) 1m euenheimer Feld 280 D-69 120 Heidelberg